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stringlengths 2
88
| description
stringlengths 31
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| public_tests
dict | private_tests
dict | solution_type
stringclasses 2
values | programming_language
stringclasses 5
values | solution
stringlengths 1
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p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<iostream>
using namespace std;
//Minimum Cost Flow O(FE log V)
#include<algorithm>
#include<utility>
#include<vector>
#include<queue>
#include<limits>
template<typename T>
struct MCF{
struct edge{
int to,rev,cap;
T cost;
};
vector<vector<edge> >G;
vector<T>h,d;
vector<int>pv,pe;
MCF(int n_=0):G(n_),h(n_,0),d(n_),pv(n_),pe(n_){}
void add_edge(int from,int to,int cap,T cost)
{
G[from].push_back({
to,(int)G[to].size(),cap,cost
});
G[to].push_back({
from,(int)G[from].size()-1,0,-cost
});
}
T min_cost_flow(int s,int t,int f)//ans or -1
{
T ret=0;
while(f>0)
{
priority_queue<pair<T,int>,vector<pair<T,int> >,greater<pair<T,int> > >P;
fill(d.begin(),d.end(),numeric_limits<T>::max());
d[s]=0;
P.push(make_pair(0,s));
while(!P.empty())
{
pair<T,int>p=P.top();P.pop();
if(d[p.second]<p.first)continue;
for(int i=0;i<G[p.second].size();i++)
{
edge&e=G[p.second][i];
if(e.cap>0&&d[e.to]>d[p.second]+e.cost+h[p.second]-h[e.to])
{
d[e.to]=d[p.second]+e.cost+h[p.second]-h[e.to];
pv[e.to]=p.second;
pe[e.to]=i;
P.push(make_pair(d[e.to],e.to));
}
}
}
if(d[t]==numeric_limits<T>::max())return -1;
for(int u=0;u<G.size();u++)h[u]+=d[u];
int d=f;
for(int u=t;u!=s;u=pv[u])d=min(d,G[pv[u]][pe[u]].cap);
f-=d;
ret+=d*h[t];
for(int u=t;u!=s;u=pv[u])
{
G[pv[u]][pe[u]].cap-=d;
G[u][G[pv[u]][pe[u]].rev].cap+=d;
}
}
return ret;
}
};
int main()
{
int N,E,F;
cin>>N>>E>>F;
MCF<int>mf(N);
for(int i=0;i<E;i++)
{
int u,v,c,d;cin>>u>>v>>c>>d;
mf.add_edge(u,v,c,d);
}
cout<<mf.min_cost_flow(0,N-1,F)<<endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | import heapq
class PrimalDual:
def __init__(self, n: int):
"""頂点数をnとする。"""
self.INF = 10 ** 9 + 7
self.n = n
self.graph = [[] for _ in range(n)]
def add_edge(self, _from: int, to: int, capacity: int, cost: int):
"""辺を追加
1. _fromからtoへ向かう容量capacity、単位コストcostの辺をグラフに追加する。
2. toから_fromへ向かう容量0、単位コスト-costの辺をグラフに追加する。
"""
forward = [to, capacity, cost, None]
forward[3] = backward = [_from, 0, -cost, forward]
self.graph[_from].append(forward)
self.graph[to].append(backward)
def min_cost_flow(self, s: int, t: int, f: int) -> int:
"""s-tパス上に流量fを流すときの最小費用流を求める。
計算量: O(|F||E|log|V|)
"""
res = 0
potential = [0] * self.n
prv_v = [0] * self.n
prv_e = [None] * self.n
while f > 0:
# ポテンシャルを用いたダイクストラ法
dist = [self.INF] * self.n
dist[s] = 0
q = [(0, s)] # q = [(sからのコスト, 現在地)]
while q:
cost, _from = heapq.heappop(q)
if dist[_from] < cost:
continue
for edge in self.graph[_from]:
to, capacity, cost, _ = edge
p_diff = potential[_from] - potential[to]
if capacity > 0 and dist[_from] + cost + p_diff < dist[to]:
dist[to] = dist[_from] + cost + p_diff
prv_v[to] = _from
prv_e[to] = edge
heapq.heappush(q, (dist[to], to))
if dist[t] == self.INF:
return -1
for i in range(self.n):
if dist[i] != self.INF:
potential[i] += dist[i]
d = f
v = t
while v != s:
d = min(d, prv_e[v][1])
v = prv_v[v]
f -= d
res += potential[t] * d
v = t
while v != s:
edge = prv_e[v]
edge[1] -= d
edge[3][1] += d
v = prv_v[v]
return res
n, m, f = map(int, input().split())
edges = [list(map(int, input().split())) for _ in range(m)]
pd = PrimalDual(n)
for edge in edges:
pd.add_edge(*edge)
ans = pd.min_cost_flow(0, n - 1, f)
print(ans)
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <numeric>
#include <queue>
#include <algorithm>
#include <utility>
#include <functional>
using namespace std;
template<typename Int = int>
struct PrimalDual {
struct Edge {
int dst;
Int cap;
Int flow;
Int cost;
int rev;
bool isRev;
Edge(int dst, Int cap, Int flow, Int cost, int rev, bool isRev)
:dst(dst), cap(cap), flow(flow), cost(cost), rev(rev), isRev(isRev) {
}
};
int n;
vector<vector<Edge>> g;
PrimalDual(int n_) : n(n_), g(vector<vector<Edge>>(n_)) {}
void addEdge(int src, int dst, Int cap, Int cost) {
g[src].emplace_back(dst, cap, 0, cost, g[dst].size(), false);
g[dst].emplace_back(src, cap, cap, -cost, g[src].size() - 1, true);
}
Int solve(int s, int t, Int f) {
constexpr Int INF = numeric_limits<Int>::max();
Int res = 0;
vector<Int> h(g.size()), dist(g.size());
vector<int> prevv(g.size()), preve(g.size());
while (f > 0) {
priority_queue<pair<Int, int>> q;
fill(dist.begin(), dist.end(), INF);
dist[s] = 0;
q.emplace(0, s);
while (q.size()) {
int d, v;
tie(d,v) = q.top();
q.pop();
d = -d;
if (dist[v] < d) continue;
for(int i = 0; i < (int)g[v].size(); ++i){
Edge &e = g[v][i];
if (e.cap - e.flow > 0 && dist[e.dst] > dist[v] + e.cost + h[v] - h[e.dst]) {
dist[e.dst] = dist[v] + e.cost + h[v] - h[e.dst];
prevv[e.dst] = v;
preve[e.dst] = i;
q.emplace(-dist[e.dst], e.dst);
}
}
}
if (dist[t] == INF) return -1;
for (int i = 0; i < n; ++i) h[i] += dist[i];
Int d = f;
for (int v = t; v != s; v = prevv[v]) {
Edge &e = g[prevv[v]][preve[v]];
d = min(d, e.cap - e.flow);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
Edge &e = g[prevv[v]][preve[v]];
e.flow += d;
g[v][e.rev].flow -= d;
}
}
return res;
}
};
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int n, m, f;
cin >> n >> m >> f;
PrimalDual<int> pd(n);
for (int i = 0; i < m; i++) {
int u, v, c, d;
cin >> u >> v >> c >> d;
pd.addEdge(u, v, c, d);
}
cout << pd.solve(0, n - 1, f) << endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
using namespace std;
#include <utility>
#include <vector>
#include <queue>
typedef pair<int, int> P;
class MinCostFlow {
#define MAX_V 10001
private:
const int INF = 1e9 + 10;
struct Edge {
int to, cap, cost, rev;
Edge(int to, int cap, int cost, int rev):
to(to), cap(cap), cost(cost), rev(rev) { }
};
int V;
vector<Edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
public:
MinCostFlow(int V): V(V) { }
void AddEdge(int from, int to, int cap, int cost) {
G[from].push_back(Edge(to, cap, cost, G[to].size()));
G[to].push_back(Edge(from, 0, -cost, G[from].size() - 1));
}
int Solve(int s, int t, int f) {
int res = 0;
fill(h, h + V, 0);
while (f > 0) {
priority_queue<P, vector<P>, greater<P>> que;
fill(dist, dist + V, INF);
dist[s] = 0;
que.push(P(0, s));
while (!que.empty()) {
P p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) {
continue;
}
for (int i = 0; i < G[v].size(); i++) {
Edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) {
return -1;
}
for (int v = 0; v < V; v++) {
h[v] += dist[v];
}
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
Edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
int main() {
int V, E, F;
cin >> V >> E >> F;
MinCostFlow mcf(V);
for (int i = 0; i < E; i++) {
int u, v, c, d;
cin >> u >> v >> c >> d;
mcf.AddEdge(u, v, c, d);
}
int s = 0, t = V - 1;
int ans = mcf.Solve(s, t, F);
cout << ans << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
const int inf=0xfffffff;
struct edge{
int to,cap,cost,rev;
};
int v;
vector<edge> G[105];
int dist[105],prevv[105],preve[105];
void add_edge(int from,int to,int cap,int cost){
G[from].push_back((edge){to,cap,cost,(int)G[to].size()});
G[to].push_back((edge){from,0,-1*cost,(int)G[from].size()-1});
}
int min_cost_flow(int s,int t,int f){
int res=0;
while(f>0){
for(int i=0;i<105;i++) dist[i]=inf;
dist[0]=0;
bool update=true;
while(update){
update=false;
for(int i=0;i<v;i++){
if(dist[i]>=inf) continue;
for(int j=0;j<G[i].size();j++){
edge &e=G[i][j];
if(e.cap>0&&dist[e.to]>dist[i]+e.cost){
dist[e.to]=dist[i]+e.cost;
prevv[e.to]=i;
preve[e.to]=j;
update=true;
}
}
}
}
if(dist[t]>=inf) return -1;
int d=f;
for(int i=t;i!=s;i=prevv[i]){
d=min(d,G[prevv[i]][preve[i]].cap);
//cout<<preve[i]<<" ";
}
//cout<<endl;
f-=d;
res+=dist[t]*d;
//cout<<"d:"<<d<<" route:";
for(int v=t;v!=s;v=prevv[v]){
edge &e=G[prevv[v]][preve[v]];
//cout<<prevv[v]<<" ";
e.cap-=d;
G[v][e.rev].cap+=d;
}
//cout<<endl;
}
return res;
}
int main(){
int e,f;
cin>>v>>e>>f;
for(int i=0;i<e;i++){
int a,b,c,d;
cin>>a>>b>>c>>d;
add_edge(a,b,c,d);
}
cout<<min_cost_flow(0,v-1,f)<<endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
using namespace std;
#define mkp(x,y) (make_pair(x,y))
typedef pair<int,int> P;
class Edge
{
public:
int to,cap,cost,rev;
Edge(int a,int b,int c,int d)
{
to=a;cap=b;cost=c;rev=d;
}
};
class MCMF
{
public:
vector<vector<Edge> > G;
vector<int> dist;
vector<int> prev,pree;
const int INF=2e9+10;
MCMF(int n)
{
G.resize(n);
dist.resize(n);
prev.resize(n);
pree.resize(n);
}
void add(int from,int to,int cap,int cost)
{
G[from].emplace_back(to,cap,cost,G[to].size());
G[to].emplace_back(from,0,-cost,G[from].size()-1);
}
int mcmf(int s,int t,int f)
{
int res=0;
while(f>0)
{
priority_queue<P,vector<P>,greater<P> > q;
fill(dist.begin(),dist.end(),INF);
dist[s]=0;
q.push(P(0,s));
while(!q.empty())
{
P p=q.top();q.pop();
int v=p.second;
if(dist[v]<p.first) continue;
for(int i=0;i<G[v].size();i++)
{
Edge &e=G[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost)
{
dist[e.to]=dist[v]+e.cost;
prev[e.to]=v;
pree[e.to]=i;
q.push(P(dist[e.to],e.to));
}
}
}
if(dist[t]==INF)
{
return -1;
}
int tot=0;
int d=f;
for(int v=t;v!=s;v=prev[v])
{
Edge &e=G[prev[v]][pree[v]];
d=min(d,e.cap);
tot+=e.cost;
}
f-=d;
for(int v=t;v!=s;v=prev[v])
{
Edge &e=G[prev[v]][pree[v]];
e.cap-=d;
G[v][e.rev].cap+=d;
}
res+=tot*d;
}
return res;
}
};
int main()
{
int V,E,F;
while(cin>>V>>E>>F)
{
MCMF mcmf(V);
for(int i=0;i<E;i++)
{
int a,b,c,d;
cin>>a>>b>>c>>d;
mcmf.add(a,b,c,d);
}
cout<<mcmf.mcmf(0,V-1,F)<<endl;
}
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
using namespace std;
using Int = long long;
//BEGIN CUT HERE
struct PrimalDual{
const int INF = 1<<28;
typedef pair<int,int> P;
struct edge{
int to,cap,cost,rev;
edge(){}
edge(int to,int cap,int cost,int rev):to(to),cap(cap),cost(cost),rev(rev){}
};
int n;
vector<vector<edge> > G;
vector<int> h,dist,prevv,preve;
PrimalDual(){}
PrimalDual(int sz):n(sz),G(sz),h(sz),dist(sz),prevv(sz),preve(sz){}
void add_edge(int from,int to,int cap,int cost){
G[from].push_back(edge(to,cap,cost,G[to].size()));
G[to].push_back(edge(from,0,-cost,G[from].size()-1));
}
int flow(int s,int t,int f){
int res=0;
fill(h.begin(),h.end(),0);
while(f>0){
priority_queue<P,vector<P>,greater<P> > que;
fill(dist.begin(),dist.end(),INF);
dist[s]=0;
que.push(P(0,s));
while(!que.empty()){
P p=que.top();que.pop();
int v=p.second;
if(dist[v]<p.first) continue;
for(int i=0;i<(int)G[v].size();i++){
edge &e=G[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to]=v;
preve[e.to]=i;
que.push(P(dist[e.to],e.to));
}
}
}
if(dist[t]==INF){
return -1;
}
for(int v=0;v<n;v++) h[v]+=dist[v];
int d=f;
for(int v=t;v!=s;v=prevv[v]){
d=min(d,G[prevv[v]][preve[v]].cap);
}
f-=d;
res+=d*h[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e=G[prevv[v]][preve[v]];
e.cap-=d;
G[v][e.rev].cap+=d;
}
}
return res;
}
};
//END CUT HERE
int main(){
int v,e,f;
cin>>v>>e>>f;
PrimalDual pd(v);
for(int i=0;i<e;i++){
int u,v,c,d;
cin>>u>>v>>c>>d;
pd.add_edge(u,v,c,d);
}
cout<<pd.flow(0,v-1,f)<<endl;
return 0;
}
/*
verified on 2017/10/29
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B&lang=jp
*/ |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
#define INF 1000000000
#define MAX_V 100
#define MAX_E 1000
using namespace std;
typedef pair<int, int> P;
struct edge {
int to, cap, cost, rev;
edge(int to_, int cap_, int cost_, int rev_)
: to(to_), cap(cap_), cost(cost_), rev(rev_) {}
};
int V, E;
vector<edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
void AddEdge(int from, int to, int cap, int cost) {
G[from].push_back(edge(to, cap, cost, G[to].size()));
G[to].push_back(edge(from, 0, -cost, G[from].size() - 1));
}
int MinimumCostFlow(int s, int t, int f) {
int res = 0;
fill(h, h + V, 0);
while (f > 0) {
priority_queue<P, vector<P>, greater<P>> que;
fill(dist, dist + V, INF);
dist[s] = 0;
que.push(P(0, s));
while (!que.empty()) {
P p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (int i = 0; i < G[v].size(); i++) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) return -1;
for (int v = 0; v < V; v++)
h[v] += dist[v];
int d = f;
for (int v = t; v != s;v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s;v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main()
{
int F;
cin >> V >> E >> F;
for (int i = 0, u, v, c, d; i < E; i++) {
cin >> u >> v >> c >> d;
AddEdge(u, v, c, d);
}
cout << MinimumCostFlow(0, V - 1, F) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
const int INF = 1<<30;
typedef struct{
int to, cap, cost, rev;
}Edge;
class MinCostFlow{
private:
int V;
vector<vector<Edge>> G;
public:
MinCostFlow(int V): V(V){
G.resize(V);
}
void add_edge(int u, int v, int c, int d){
G[u].push_back({v, c, d, (int)G[v].size()});
G[v].push_back({u, 0, -d, (int)G[u].size()-1});
}
int solve(int s, int t, int f){
int res = 0;
while(f > 0){
vector<int> d(V, INF);
vector<int> pars(V, -1);
vector<int> eids(V, -1);
d[s] = 0;
bool updated = true;
while(updated){
updated = false;
for(int v=0; v<V; v++) if(d[v]!=INF){
for(int i=0; i<G[v].size(); i++){
auto edge = G[v][i];
if(edge.cap == 0)
continue;
if(d[edge.to] > d[v] + edge.cost){
d[edge.to] = d[v] + edge.cost;
pars[edge.to] = v;
eids[edge.to] = i;
updated = true;
}
}
}
}
if(d[t] == INF)
return -1;
int mc = f;
for(int v=t; v!=s; v=pars[v]){
mc = min(mc, G[pars[v]][eids[v]].cap);
}
res += mc * d[t];
f -= mc;
for(int v=t; v!=s; v=pars[v]){
auto &edge = G[pars[v]][eids[v]];
edge.cap -= mc;
G[v][edge.rev].cap += mc;
}
}
return res;
}
};
int V, E, F;
int main(){
cin >> V >> E >> F;
MinCostFlow mcf(V);
for(int i=0; i<E; i++){
int u, v, c, d;
cin >> u >> v >> c >> d;
mcf.add_edge(u, v, c, d);
}
cout << mcf.solve(0, V-1, F) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define INF 1<<30
#define LINF 1LL<<60
#define MAX_V 10000
struct edge{
int to;
int cap;
int cost;
int rev;
edge(){}
edge(int to,int cap,int cost,int rev):to(to),cap(cap),cost(cost),rev(rev){}
};
int V;
vector<edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V],preve[MAX_V];
void init_edge(){
for(int i=0;i<V;i++)G[i].clear();
}
void add_edge(int from,int to,int cap,int cost){
G[from].push_back(edge(to,cap,cost,(int)G[to].size()));
G[to].push_back(edge(from,0,-cost,(int)G[from].size()-1));
}
int min_cost_flow(int s,int t,int f){
int res = 0;
fill(h,h+V,0);
while(f>0){
priority_queue< pii, vector<pii>, greater<pii> > que;
fill( dist, dist+V , INF );
dist[s]=0;
que.push(pii(0,s));
while(!que.empty()){
pii p = que.top(); que.pop();
int v = p.second;
if(dist[v]<p.first)continue;
for(int i=0;i<(int)G[v].size();i++){
edge &e = G[v][i];
if(e.cap>0&&dist[e.to] > dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to]=v;
preve[e.to]=i;
que.push(pii(dist[e.to],e.to));
}
}
}
if(dist[t]==INF){
return -1;
}
for(int v=0;v<V;v++)h[v]+=dist[v];
int d=f;
for(int v=t;v!=s;v=prevv[v]){
d=min(d,G[prevv[v]][preve[v]].cap);
}
f-=d;
res+=d*h[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main(){
int E,F,a,b,c,d;
cin>>V>>E>>F;
while(E--){
cin>>a>>b>>c>>d;
add_edge(a,b,c,d);
}
cout<<min_cost_flow(0,V-1,F)<<endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <cstring>
#include <string>
#include <algorithm>
#include <iomanip>
#include <queue>
#include <functional>
using namespace std;
const int MAX_V = 100010;
using Capacity = int;
using Cost = int;
const auto inf = numeric_limits<Capacity>::max() / 8;
struct Edge {
int dst;
Capacity cap, cap_orig;
Cost cost;
int revEdge; bool isRev;
Edge(int dst, Capacity cap, Cost cost, int revEdge, bool isRev)
:dst(dst), cap(cap), cap_orig(cap), cost(cost), revEdge(revEdge), isRev(isRev) {
}
};
struct PrimalDual {
int n;
vector<vector<Edge> > g;
PrimalDual(int n_) : n(n_), g(vector<vector<Edge> >(n_)) {}
void add_edge(int src, int dst, Capacity cap, Cost cost) { // ?????????
g[src].emplace_back(dst, cap, cost, g[dst].size(), false);
g[dst].emplace_back(src, 0, -cost, g[src].size() - 1, true);
}
Cost solve(int s, int t, int f) {
Cost res = 0;
static Cost h[MAX_V], dist[MAX_V];
static int prevv[MAX_V], preve[MAX_V];
for(int i = 0; i < n; i++) {
h[i] = 0;
}
while(f > 0) {
typedef pair<Cost, int> pcv;
priority_queue<pcv, vector<pcv>, greater<pcv> > q;
for(int i = 0; i < n; i++) {
dist[i] = inf;
}
dist[s] = 0;
q.emplace(pcv(0, s));
while(q.size()) {
pcv p = q.top(); q.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(int i = 0; i < g[v].size(); i++) {
Edge &e = g[v][i];
if(e.cap > 0 && dist[e.dst] > dist[v] + e.cost + h[v] - h[e.dst]) {
dist[e.dst] = dist[v] + e.cost + h[v] - h[e.dst];
prevv[e.dst] = v;
preve[e.dst] = i;
q.emplace(pcv(dist[e.dst], e.dst));
}
}
}
if(dist[t] == inf) {
return -1;
}
for(int v = 0; v < n; v++) {
h[v] += dist[v];
}
// s-t ????????????????????£??????????????????
int d = f;
for(int v = t; v != s; v = prevv[v]) {
d = min(d, g[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for(int v = t; v != s; v = prevv[v]) {
Edge &e = g[prevv[v]][preve[v]];
e.cap -= d;
g[v][e.revEdge].cap += d;
}
}
return res;
}
// ??????????????????=???????????????-?????¨??????????????¨???
void view() {
for(int i = 0; i < g.size(); i++) {
for(int j = 0; j < g[i].size(); j++) {
if(!g[i][j].isRev) {
Edge& e = g[i][j];
printf("%3d->%3d (flow:%d)\n", i, e.dst, e.cap_orig - e.cap);
}
}
}
}
};
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
int V, E, F;
cin >> V >> E >> F;
PrimalDual pd(V);
for(int i = 0; i < E; i++) {
int u, v, c, d;
cin >> u >> v >> c >> d;
pd.add_edge(u, v, c, d);
}
int res = pd.solve(0, V - 1, F);
if(res == inf) res = -1;
cout << res << endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <stdio.h>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
namespace MCF{
const int MAXN=120;
const int MAXM=2100;
int to[MAXM];
int next[MAXM];
int first[MAXN];
int c[MAXM];
long long w[MAXM];
long long pot[MAXN];
int rev[MAXM];
long long ijk[MAXN];
int v[MAXN];
long long toc;
int tof;
int n;
int m;
void init(int _n){
n=_n;for(int i=0;i<n;i++)first[i]=-1;
}
void ae(int a,int b,int cap,int wei){
next[m]=first[a];to[m]=b;first[a]=m;c[m]=cap;w[m]=wei;m++;
next[m]=first[b];to[m]=a;first[b]=m;c[m]=0;w[m]=-wei;m++;
}
int solve(int s,int t,int flo){
toc=tof=0;
for(int i=0;i<n;i++)pot[i]=0;
while(tof<flo){
for(int i=0;i<n;i++)ijk[i]=9999999999999LL;
for(int i=0;i<n;i++)v[i]=0;
priority_queue<pair<long long,int> > Q;
ijk[s]=0;
Q.push(make_pair(0,s));
while(Q.size()){
long long cost=-Q.top().first;
int at=Q.top().second;
Q.pop();
if(v[at])continue;
v[at]=1;
for(int i=first[at];~i;i=next[i]){
int x=to[i];
if(v[x]||ijk[x]<=ijk[at]+w[i]-pot[x]+pot[at])continue;
if(c[i]==0)continue;
ijk[x]=ijk[at]+w[i]-pot[x]+pot[at];
rev[x]=i;
Q.push(make_pair(-ijk[x],x));
}
}
int flow=flo-tof;
if(!v[t])return 0;
int at=t;
while(at!=s){
flow=min(flow,c[rev[at]]);
at=to[rev[at]^1];
}
at=t;
tof+=flow;
toc+=flow*(ijk[t]-pot[s]+pot[t]);
at=t;
while(at!=s){
c[rev[at]]-=flow;
c[rev[at]^1]+=flow;
at=to[rev[at]^1];
}
for(int i=0;i<n;i++)pot[i]+=ijk[i];
}
return 1;
}
}
int main(){
int a,b,c;scanf("%d%d%d",&a,&b,&c);
MCF::init(a);
for(int i=0;i<b;i++){
int p,q,r,s;scanf("%d%d%d%d",&p,&q,&r,&s);
MCF::ae(p,q,r,s);
}
int res=MCF::solve(0,a-1,c);
if(!res)printf("-1\n");
else printf("%lld\n",MCF::toc);
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | import heapq
class MinCostFlow:
class Edge:
def __init__(self, to, cap, rev, cost):
self.to, self.cap, self.rev, self.cost = to, cap, rev, cost
def __init__(self, V):
self.V = V
self.E = [[] for _ in range(V)]
def add_edge(self, fr, to, cap, cost):
self.E[fr].append(self.Edge(to, cap, len(self.E[to]), cost))
self.E[to].append(self.Edge(fr, 0, len(self.E[fr])-1, -cost))
def run(self, source, sink, f, INF=10**5):
res = 0
h, prevv, preve = [0] * self.V, [0] * self.V, [0] * self.V
while (f > 0):
pque = []
dist = [INF] * self.V
dist[source] = 0
heapq.heappush(pque, (0, source))
while pque:
cost, v = heapq.heappop(pque)
cost = -cost
if dist[v] < cost:
continue
for i, e in enumerate(self.E[v]):
if e.cap > 0 and dist[v] - h[e.to] < dist[e.to] - e.cost - h[v]:
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to]
prevv[e.to], preve[e.to] = v, i
heapq.heappush(pque, (-dist[e.to], e.to))
if dist[sink] == INF:
return -1
for v in range(self.V):
h[v] += dist[v]
d, v = f, sink
while v != source:
d = min(d, self.E[prevv[v]][preve[v]].cap)
v = prevv[v]
f -= d
res += d * h[sink]
v = sink
while v != source:
self.E[prevv[v]][preve[v]].cap -= d
self.E[v][self.E[prevv[v]][preve[v]].rev].cap += d
v = prevv[v]
return res
V, E, F = map(int, input().split())
mcf = MinCostFlow(V)
for _ in range(E):
u, v, c, d = map(int, input().split())
mcf.add_edge(u, v, c, d)
print(mcf.run(0, V - 1, F)) |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
using ll=long long;
using vin=vector<int>;
using vll=vector<long long>;
using vvin=vector<vector<int>>;
using vvll=vector<vector<long long>>;
using vstr=vector<string>;
using vvstr=vector<vector<string>>;
using vch=vector<char>;
using vvch=vector<vector<char>>;
using vbo=vector<bool>;
using vvbo=vector<vector<bool>>;
using vpii=vector<pair<int,int>>;
using pqsin=priority_queue<int,vector<int>,greater<int>>;
#define mp make_pair
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep2(i,s,n) for(int i=(s);i<(int)(n);i++)
#define all(v) v.begin(),v.end()
#define decp(n) cout<<fixed<<setprecision((int)n)
const int inf=1e9+7;
const ll INF=1e18;
int MAX_V=110;
struct edge{int to;ll cap;ll cost;int rev;};
int tmp1,tmp2;
int V;//頂点数
vector<vector<edge>> g(MAX_V);
vll h(MAX_V);//ポテンシャル
vll dist(MAX_V);
vin prevv(MAX_V),preve(MAX_V);//直前の頂点と辺
void add_edge(int from,int to,ll cap,ll cost){
tmp1=g[to].size();tmp2=g[from].size();
g[from].push_back((edge){to,cap,cost,tmp1});
g[to].push_back((edge){from,(ll)0,-cost,tmp2});
}
//sからtへの最小費用流を求める
//ながせない場合は-1
ll min_cost_flow(int s,int t,ll f){
ll res=(ll)0;
fill(all(h),(ll)0);
ll d;
while(f>0){
//dijkstraを用いてhを初期化
priority_queue<pair<ll,int>,vector<pair<ll,int>>,greater<pair<ll,int>>> pq;
fill(all(dist),(ll)inf);
dist[s]=(ll)0;
pq.push(mp((ll)0,s));
while(pq.size()){
auto p=pq.top();pq.pop();
int v=p.second;
if(dist[v]<p.first)continue;
for(int i=0;i<g[v].size();i++){
auto& e=g[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to]=v;
preve[e.to]=i;
pq.push(mp(dist[e.to],e.to));
}
}
}
if(dist[t]==inf)return -1;
rep(v,V)h[v]+=dist[v];
d=f;
for(int v=t;v!=s;v=prevv[v])d=min(d,g[prevv[v]][preve[v]].cap);
f-=d;
res+=d*h[t];
for(int v=t;v!=s;v=prevv[v]){
auto& e=g[prevv[v]][preve[v]];
e.cap-=d;
g[v][e.rev].cap+=d;
}
}
return res;
}
int main(){
int e,f;cin>>V>>e>>f;
int u,v;ll c,d;
rep(i,e){
cin>>u>>v>>c>>d;
add_edge(u,v,c,d);
}
cout<<min_cost_flow(0,V-1,f)<<endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
#define pb push_back
using namespace std;
const int INF=0x3f3f3f3f;
const int maxn=105;
const int maxq=1005;
struct edge{int to,cap,cost,rev;};
int n,m,k;
int d[maxn];
int a[maxn];
int p1[maxn];
int p2[maxn];
bool inq[maxn];
vector<edge>G[maxn];
void add_edge(int u,int v,int c,int w) {
G[u].pb(edge{v,c,w,int(G[v].size())});
G[v].pb(edge{u,0,-w,int(G[u].size()-1)});
}
int mcmf(int s,int t) {
int flow=0 , cost=0;
while (1) {
memset(d,0x3f,sizeof(d));
d[s]=0; a[s]=max(0,k-flow);
int qh=0,qt=0,q[maxq];
q[qt++]=s; inq[s]=1;
while (qh<qt) {
int u=q[qh++];
inq[u]=0;
for (int i=0;i<G[u].size();i++) {
edge e=G[u][i];
if (d[e.to]>d[u]+e.cost && e.cap) {
d[e.to]=d[u]+e.cost;
a[e.to]=min(a[u],e.cap);
p1[e.to]=u;
p2[e.to]=i;
if (!inq[e.to]) {
q[qt++]=e.to;
inq[e.to]=1;
}
}
}
}
if (d[t]==INF || !a[t]) break;
flow+=a[t];
cost+=a[t]*d[t];
for (int u=t;u!=s;u=p1[u]) {
edge& e=G[p1[u]][p2[u]];
e.cap-=a[t];
G[e.to][e.rev].cap+=a[t];
}
}
if (flow<k) return -1;
else return cost;
}
int main() {
cin>>n>>m>>k;
for (int i=0;i<m;i++) {
int u,v,c,w; cin>>u>>v>>c>>w;
add_edge(u,v,c,w);
}
cout<<mcmf(0,n-1)<<'\n';
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | from heapq import *
# G : [to/from, cap, cost, rev]
def minimumCostFlow(N: int, G: list, s: int, t: int, flow: int):
ret = 0
INF = 1 << 60
potential = [0] * N
pre_vtx = [None] * N
pre_edge = [None] * N
while flow > 0:
dist = [INF] * N
dist[s] = 0
visited = [False] * N
q = [(0, s)]
while q:
d, cur = heappop(q)
if visited[cur]:
continue
visited[cur] = True
for i in range(len(G[cur])):
e = G[cur][i]
nxt = e[0]
if e[1] > 0 and dist[nxt] > dist[cur] + e[2] + potential[cur] - potential[nxt]:
dist[nxt] = dist[cur] + e[2] + potential[cur] - potential[nxt]
pre_vtx[nxt] = cur
pre_edge[nxt] = i
heappush(q, (dist[nxt], nxt))
if dist[t] == INF:
return -1
for i in range(N):
potential[i] += dist[i]
df = flow
now = t
while now != s:
df = min(df, G[pre_vtx[now]][pre_edge[now]][1])
now = pre_vtx[now]
flow -= df
ret += df * potential[t]
now = t
while now != s:
G[pre_vtx[now]][pre_edge[now]][1] -= df
G[now][G[pre_vtx[now]][pre_edge[now]][3]][1] += df
now = pre_vtx[now]
return ret
import sys
input = sys.stdin.buffer.readline
def main():
N, M, F = map(int, input().split())
G = [[] for _ in range(N)] # [to/from, cap, cost, rev]
for _ in range(M):
u, v, c, d = map(int, input().split())
G[u].append([v, c, d, len(G[v])])
G[v].append([u, 0, -d, len(G[u]) - 1])
print(minimumCostFlow(N, G, 0, N - 1, F))
if __name__ == '__main__':
main()
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <queue>
using namespace std;
template<typename CAP, typename COST>
class MinCostFlow {
public:
explicit MinCostFlow(int N) : g(N) {}
void addEdge(int src, int dst, CAP cap, COST cost){
int r1 = g[src].size();
int r2 = g[dst].size();
g[src].emplace_back(src, dst, cap, cost, r2);
g[dst].emplace_back(dst, src, 0, -cost, r1);
}
pair<COST, CAP> solve(int s, int t, CAP maxFlow){
const int n = g.size();
pair<COST, CAP> res = make_pair(0, 0);
vector<COST> h(n, 0);
while(maxFlow > 0){
vector<COST> dist(n, INF); dist[s] = 0;
vector<pair<int, int>> prev(n, make_pair(-1, -1));
priority_queue<pair<COST, int>, vector<pair<COST, int>>, greater<pair<COST, int>>> qu;
qu.emplace(0, s);
while(!qu.empty()){
auto e = qu.top(); qu.pop();
if(dist[e.second] < e.first) continue;
for(int i=0;i<g[e.second].size();i++){
auto& p = g[e.second][i];
if(p.cap > 0 && dist[p.dst] > dist[p.src] + p.cost + h[p.src] - h[p.dst]){
dist[p.dst] = dist[p.src] + p.cost + h[p.src] - h[p.dst];
prev[p.dst] = make_pair(p.src, i);
qu.emplace(dist[p.dst], p.dst);
}
}
}
if(prev[t].first == -1) break;
CAP f = maxFlow;
for(int u=t;u!=s;u=prev[u].first) f = min(f, g[prev[u].first][prev[u].second].cap);
for(int u=t;u!=s;u=prev[u].first){
auto& p = g[prev[u].first][prev[u].second];
auto& q = g[p.dst][p.rev];
res.first += f * p.cost;
p.cap -= f;
q.cap += f;
}
res.second += f;
for(int i=0;i<n;i++) h[i] += dist[i];
maxFlow -= f;
}
return res;
}
private:
class Edge {
public:
explicit Edge(int src, int dst, CAP cap, COST cost, int rev) : src(src), dst(dst), cap(cap), cost(cost), rev(rev) {}
const int src;
const int dst;
CAP cap;
COST cost;
const int rev;
};
private:
const COST INF = 1LL << 30;
vector<vector<Edge>> g;
};
int main(){
int V, E, F; cin >> V >> E >> F;
MinCostFlow<int, int> mcf(V);
for(int i=0;i<E;i++){
int a, b, c, d; cin >> a >> b >> c >> d;
mcf.addEdge(a, b, c, d);
}
auto res = mcf.solve(0, V-1, F);
cout << (res.second == F ? res.first : -1) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
using i64 = int64_t;
const i64 MOD = 1e9 + 7;
template <typename T, typename U>
struct PrimalDual{
struct Edge{
int to, rev;
U cap;
T cost;
Edge(int to, U cap, T cost, int rev) :
to(to), rev(rev), cap(cap), cost(cost){}
};
vector<vector<Edge>> edges;
T _inf;
vector<T> potential, min_cost;
vector<int> prev_v, prev_e;
PrimalDual(int n) : edges(n), _inf(numeric_limits<T>::max()){}
void add(int from, int to, U cap, T cost){
edges[from].emplace_back(to, cap, cost, static_cast<int>(edges[to].size()));
edges[to].emplace_back(from, 0, -cost, static_cast<int>(edges[from].size()) - 1);
}
T solve(int s, int t, U flow){
int n = edges.size();
T ret = 0;
priority_queue<pair<T,int>, vector<pair<T,int>>, greater<pair<T,int>>> que;
potential.assign(n, 0);
prev_v.assign(n, -1);
prev_e.assign(n, -1);
while(flow > 0){
min_cost.assign(n, _inf);
que.emplace(0, s);
min_cost[s] = 0;
while(!que.empty()){
T fl;
int pos;
tie(fl, pos) = que.top();
que.pop();
if(min_cost[pos] != fl)
continue;
for(int i = 0; i < edges[pos].size(); ++i){
auto& ed = edges[pos][i];
T nex = fl + ed.cost + potential[pos] - potential[ed.to];
if(ed.cap > 0 && min_cost[ed.to] > nex){
min_cost[ed.to] = nex;
prev_v[ed.to] = pos;
prev_e[ed.to] = i;
que.emplace(min_cost[ed.to], ed.to);
}
}
}
if(min_cost[t] == _inf)
return -1;
for(int i = 0; i < n; ++i)
potential[i] += min_cost[i];
T add_flow = flow;
for(int x = t; x != s; x = prev_v[x])
add_flow = min(add_flow, edges[prev_v[x]][prev_e[x]].cap);
flow -= add_flow;
ret += add_flow * potential[t];
for(int x = t; x != s; x = prev_v[x]){
auto& ed = edges[prev_v[x]][prev_e[x]];
ed.cap -= add_flow;
edges[x][ed.rev].cap += add_flow;
}
}
return ret;
}
};
signed main(){
int n, m, f;
cin >> n >> m >> f;
PrimalDual<int,int> p(n);
for(int i = 0; i < m; ++i){
int u, v, c, d;
cin >> u >> v >> c >> d;
p.add(u, v, c, d);
}
cout << p.solve(0, n - 1, f) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include "bits/stdc++.h"
using namespace std;
#ifdef _DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif
//#define int long long
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(c) begin(c),end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9) + 7;
template<class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; }
struct MinimumCostFlow {
using Flow = int;
using Cost = int;
struct Edge {
int to, rev;
Flow cap;
Cost cost;
Edge() {}
Edge(int to, int rev, Flow cap, Cost cost) :to(to), rev(rev), cap(cap), cost(cost) {}
};
int n;
vector<vector<Edge>> g;
vector<int> dist;
vector<int> prevv, preve;
MinimumCostFlow(int n) :n(n), g(n), dist(n), prevv(n), preve(n) {}
void addEdge(int from, int to, Flow cap, Cost cost) {
g[from].emplace_back(to, (int)g[to].size(), cap, cost);
g[to].emplace_back(from, (int)g[from].size() - 1, 0, -cost);
}
// s??????t????????????f???????°??????¨???
// ??????????????´?????? -1
Cost minimumCostFlow(int s, int t, Flow f) {
Cost total = 0;
while (f > 0) {
// Bellman-Ford
fill(dist.begin(), dist.end(), INF);
dist[s] = 0;
bool update = true;
while (update) {
update = false;
for (int v = 0; v < n; v++) {
if (dist[v] == INF)continue;
for (int i = 0; i < g[v].size(); i++) {
Edge &e = g[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
// ????????\???????????????
if (dist[t] == INF)
return -1;
// ?????????????????£??????????????????
int d = f;
for (int v = t; v != s; v = prevv[v])
d = min(d, g[prevv[v]][preve[v]].cap);
f -= d;
total += d*dist[t];
for (int v = t; v != s; v = prevv[v]) {
Edge &e = g[prevv[v]][preve[v]];
e.cap -= d;
g[v][e.rev].cap += d;
}
}
return total;
}
};
signed main() {
cin.tie(0);
ios::sync_with_stdio(false);
int V, E, F; cin >> V >> E >> F;
MinimumCostFlow mcf(V);
rep(i, 0, E) {
int u, v, c, d; cin >> u >> v >> c >> d;
mcf.addEdge(u, v, c, d);
}
cout << mcf.minimumCostFlow(0, V - 1, F) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | #!/usr/bin/env python3
# N,M = map(int,sys.stdin.readline().split())
# a = tuple(map(int,sys.stdin.readline().split())) # single line with multi param
# a = tuple(int(sys.stdin.readline()) for _ in range(N)) # multi line with single param
# a = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(N)) # multi line with multi param
# s = sys.stdin.readline().rstrip()
# N = int(sys.stdin.readline())
# INF = float("inf")
import sys,collections
sys.setrecursionlimit(100000)
INF = float("inf")
V,E,F = map(int,sys.stdin.readline().split())
uvcd = tuple(tuple(map(int,sys.stdin.readline().rstrip().split())) for _ in range(E)) # multi line with multi param
#uvcd = [[0,1,1,1],[0,2,3,2],[1,2,1,2],[2,3,2,1]]
capacityG = {i:{} for i in range(V)} #capacity
costG = {i:{} for i in range(V)} #capacity
for u,v,c,d in uvcd:
capacityG[u][v] = c
costG[u][v] = d
if not u in capacityG[v]:
capacityG[v][u] = 0
costG[v][u] = -d
def shortest_path(V,costG,capacityG,start=0):
distances = [INF]*V
distances[start] = 0
parents = list(range(V))
for _ in range(V):
modified = False
for src in range(V):
if distances[src] == INF: continue
for dst,cost in costG[src].items():
if capacityG[src][dst] > 0 and distances[dst] > distances[src] + cost:
distances[dst] = distances[src] + cost
parents[dst] = src
modified = True
if modified == False:
return distances,parents
return None,None
rest = F
total_cost = 0
while rest != 0:
distances,p = shortest_path(V,costG,capacityG,0)
if not distances or distances[V-1] == INF:
print(-1)
exit()
cur = V-1
flow = rest
while cur != 0:
flow = min(flow,capacityG[p[cur]][cur])
cur = p[cur]
rest -= flow
total_cost += distances[V-1]*flow
cur = V-1
while cur != 0:
capacityG[p[cur]][cur] -= flow
capacityG[cur][p[cur]] += flow #rev
cur = p[cur]
print(total_cost)
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | java | import java.io.*;
import java.util.*;
import java.util.Map.Entry;
import java.util.stream.Collectors;
@SuppressWarnings("unused")
public class Main {
//final boolean isDebug = true;
final boolean isDebug = false;
String fileName = "input.txt";
FastScanner sc;
PrintWriter out;
final int MOD = (int)1e9+7;
final int INF = Integer.MAX_VALUE / 2;
void solve() throws Exception{
int V = sc.nextInt();
int E = sc.nextInt();
int F = sc.nextInt();
PrimalDual pd = new PrimalDual(V);
for(int i = 0; i < E; i++) pd.addEdge(sc.nextInt(), sc.nextInt(), sc.nextLong(), sc.nextLong());
System.out.println(pd.minFlow(0, V-1, F));
}
/* end solve */
/* main */
public static void main(String[] args) throws Exception {
new Main().m();
}
void m() throws Exception {
long S = System.currentTimeMillis();
sc = (isDebug) ? new FastScanner(new FileInputStream(fileName)) : new FastScanner(System.in);
out = new PrintWriter(System.out);
solve();
out.flush();
long G = System.currentTimeMillis();
if(isDebug){
System.out.println("---Debug---");
System.out.printf("%8d ms", (G-S));
}
}
/* end main */
}
/* end Main */
class PrimalDual{
class Edge{
int to;
long cap;
long cost;
int rev;
boolean isRev;
public Edge(int t, long cp, long cs, int r, boolean i){
to = t; cap = cp; cost = cs; rev = r; isRev = i;
}
}
class Dist implements Comparable<Dist>{
long dist;
int v;
Dist(long dist, int v){
this.dist = dist;
this.v = v;
}
//近い順に並べる
@Override
public int compareTo(Dist d) {
return Long.compare(d.dist, this.dist);
}
}
long INF = Long.MAX_VALUE / 2;
int V;
ArrayList<ArrayList<Edge>> graph;
long[] potential, minCost;
int[] prevv, preve;
public PrimalDual(int V){
this.V = V;
graph = new ArrayList<>();
for(int i = 0; i < V; i++) graph.add(new ArrayList<>());
potential = new long[V];
minCost = new long[V];
prevv = new int[V];
preve = new int[V];
}
void addEdge(int from, int to, long cap, long cost){
graph.get(from).add(new Edge(to, cap, cost, graph.get(to).size(), false));
graph.get(to).add(new Edge(from, 0, -cost, graph.get(from).size()-1, true));
}
long minFlow(int s, int t, long f){
long ret = 0;
PriorityQueue<Dist> pq = new PriorityQueue<>();
Arrays.fill(potential, 0);
Arrays.fill(preve, -1);
Arrays.fill(prevv, -1);
while(f > 0){
Arrays.fill(minCost, INF);
pq.add(new Dist(0, s));
minCost[s] = 0;
while(!pq.isEmpty()){
Dist p = pq.remove();
if(minCost[p.v] < p.dist) continue;
for(int i = 0; i < graph.get(p.v).size(); i++){
Edge e = graph.get(p.v).get(i);
long nextCost = minCost[p.v] + e.cost + potential[p.v] - potential[e.to];
if(e.cap > 0 && minCost[e.to] > nextCost){
minCost[e.to] = nextCost;
prevv[e.to] = p.v;
preve[e.to] = i;
pq.add(new Dist(minCost[e.to], e.to));
}
}
}
if(minCost[t] == INF) return -1;
for(int v = 0; v < V; v++) potential[v] += minCost[v];
long addFlow = f;
for(int v = t; v != s; v = prevv[v])
addFlow = Math.min(addFlow, graph.get(prevv[v]).get(preve[v]).cap);
f -= addFlow;
ret += addFlow * potential[t];
for(int v = t; v != s; v = prevv[v]){
Edge e = graph.get(prevv[v]).get(preve[v]);
e.cap -= addFlow;
graph.get(v).get(e.rev).cap += addFlow;
}
}
return ret;
}
void output(){
for(int i = 0; i < graph.size(); i++){
for(Edge e : graph.get(i)){
if(e.isRev) continue;
Edge revEdge = graph.get(e.to).get(e.rev);
System.out.println(i + " -> " + e.to + " (flow: " + revEdge.cap + " / " + (e.cap + revEdge.cap) + ")");
}
}
}
}
class FastScanner {
private InputStream in;
private final byte[] buffer = new byte[1024];
private int ptr = 0;
private int buflen = 0;
public FastScanner(InputStream in) {
this.in = in;
}
private boolean hasNextByte() {
if (ptr < buflen) {
return true;
}else{
ptr = 0;
try {
buflen = in.read(buffer);
} catch (IOException e) {
e.printStackTrace();
}
if (buflen <= 0) {
return false;
}
}
return true;
}
private int readByte() {
if (hasNextByte()) return buffer[ptr++];
else return -1;
}
private static boolean isPrintableChar(int c){
return 33 <= c && c <= 126;
}
public boolean hasNext() {
while(hasNextByte() && !isPrintableChar(buffer[ptr]))
ptr++; return hasNextByte();
}
public String next() {
if (!hasNext()) throw new NoSuchElementException();
StringBuilder sb = new StringBuilder();
int b = readByte();
while(isPrintableChar(b)) {
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
public String nextLine() {
if (!hasNext()) throw new NoSuchElementException();
StringBuilder sb = new StringBuilder();
int b = readByte();
while(b != 10) {
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
public long nextLong() {
if (!hasNext()) throw new NoSuchElementException();
long n = 0;
boolean minus = false;
int b = readByte();
if (b == '-') {
minus = true;
b = readByte();
}
if (b < '0' || '9' < b) {
throw new NumberFormatException();
}
while(true){
if ('0' <= b && b <= '9') {
n *= 10;
n += b - '0';
}else if(b == -1 || !isPrintableChar(b)){
return minus ? -n : n;
}else{
throw new NumberFormatException();
}
b = readByte();
}
}
public int nextInt() {
long nl = nextLong();
if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
return (int) nl;
}
public double nextDouble() {
return Double.parseDouble(next());
}
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <queue>
using namespace std;
const int INF = 1e9;
struct Edge {
int from, to, cap, flow, cost;
Edge(int from, int to, int cap, int flow, int cost):from(from), to(to), cap(cap),
flow(flow), cost(cost){}
};
struct MaxflowMinCost {
int n;
vector<Edge> edges;
vector<vector<int>> g;
vector<int> p; //The id of the edge that connects to a vertex on the shortest path
vector<int> a; //The possible flow change from the start to a vertex
int flow = 0;
int cost = 0;
int f; //flow limit
MaxflowMinCost(int n) : n(n) {
g.assign(n + 1, vector<int>());
}
void addEdge(int from, int to, int cap, int cost) {
edges.push_back(Edge(from , to, cap, 0, cost));
edges.push_back(Edge(to, from, 0, 0, -cost));
g[from].push_back(edges.size() - 2);
g[to].push_back(edges.size() - 1);
}
int solve(int s, int t, int f) {
this->f = f;
while (bellmanFord(s, t)) {
}
return flow;
}
bool bellmanFord(int s, int t) {
vector<int> d(n + 1, INF); //distance from s
vector<bool> inq(n + 1, false);
p.assign(n + 1, -1);
a.assign(n + 1, 0);
queue<int> q;
p[s] = -2;
a[s] = INF;
d[s] = 0;
inq[s] = true;
q.push(s);
while (!q.empty()) {
int u = q.front(); q.pop();
inq[u] = false;
for (int eid: g[u]) {
Edge e = edges[eid];
if (e.cap > e.flow && d[e.to] > d[u] + e.cost) {
d[e.to] = d[u] + e.cost;
p[e.to] = eid;
a[e.to] = min(a[u], e.cap - e.flow);
if (!inq[e.to]) {
q.push(e.to);
inq[e.to] = true;
}
}
}
}
if (d[t] == INF) {
return false;
}
int aug = min(f, a[t]);
f -= aug;
flow += aug;
cost += d[t] * aug;
for (int u = t; u != s; u = edges[p[u]].from) {
edges[p[u]].flow += a[t];
edges[p[u] ^ 1].flow -= a[t];
}
if (f == 0) {
return false;
}
return true;
}
};
int main() {
int v, e, s, t, f;
cin >> v >> e >> f;
s = 0;
t = v - 1;
MaxflowMinCost maxflow(v);
for (int i = 0; i < e; i++) {
int from, to, cap, cost;
cin >> from >> to >> cap >> cost;
maxflow.addEdge(from, to, cap, cost);
}
int ans = maxflow.solve(s, t, f);
if (ans < f) {
cout << -1 << endl;
}
else {
cout << maxflow.cost << endl;
}
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <stdio.h>
#include <cmath>
#include <algorithm>
#include <cfloat>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#include <iostream>
#include <set>
#include <map>
#include <time.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;
#define NUM 100
struct Edge{
Edge(int arg_to,int arg_capacity,int arg_cost,int arg_rev_index){
to = arg_to;
capacity = arg_capacity;
cost = arg_cost;
rev_index = arg_rev_index;
}
int to,capacity,cost,rev_index;
};
int V;
vector<Edge> G[NUM];
int dist[NUM];
int pre_node[NUM],pre_edge[NUM];
void add_edge(int from,int to,int capacity,int cost){
G[from].push_back(Edge(to,capacity,cost,G[to].size()));
G[to].push_back(Edge(from,0,-cost,G[from].size()-1));
}
int min_cost_flow(int source,int sink,int flow){
int ret = 0;
while(flow > 0){
for(int i = 0; i < V; i++)dist[i] = BIG_NUM;
dist[source] = 0;
bool update = true;
while(update){
update = false;
for(int node_id = 0; node_id < V; node_id++){
if(dist[node_id] == BIG_NUM)continue;
for(int i = 0; i < G[node_id].size(); i++){
Edge &e = G[node_id][i];
if(e.capacity > 0 && dist[e.to] > dist[node_id]+e.cost){
dist[e.to] = dist[node_id]+e.cost;
pre_node[e.to] = node_id;
pre_edge[e.to] = i;
update = true;
}
}
}
}
if(dist[sink] == BIG_NUM){
return -1;
}
int tmp_flow = flow;
for(int node_id = sink; node_id != source; node_id = pre_node[node_id]){
tmp_flow = min(tmp_flow,G[pre_node[node_id]][pre_edge[node_id]].capacity);
}
flow -= tmp_flow;
ret += tmp_flow*dist[sink];
for(int node_id = sink; node_id != source; node_id = pre_node[node_id]){
Edge &e = G[pre_node[node_id]][pre_edge[node_id]];
e.capacity -= tmp_flow;
G[node_id][e.rev_index].capacity += tmp_flow;
}
}
return ret;
}
int main(){
int E,F;
scanf("%d %d %d",&V,&E,&F);
int from,to,capacity,cost;
for(int loop = 0; loop < E; loop++){
scanf("%d %d %d %d",&from,&to,&capacity,&cost);
add_edge(from,to,capacity,cost);
}
printf("%d\n", min_cost_flow(0,V-1,F));
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>
#define chmin(a, b) ((a)=min((a), (b)))
#define chmax(a, b) ((a)=max((a), (b)))
#define fs first
#define sc second
#define eb emplace_back
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
typedef tuple<int, int, int> T;
const ll MOD=1e9+7;
const ll INF=1e18;
const double pi=acos(-1);
const double eps=1e-10;
int dx[]={1, 0, -1, 0};
int dy[]={0, -1, 0, 1};
const int MAX_V = 110;
struct edge{
int to, cap, cost, rev;
};
int V;
vector<vector<edge>> G(MAX_V);
int h[MAX_V]; // ポテンシャル h(v):=(s-v間の最短距離)
int dist[MAX_V]; // 最短距離
int prevv[MAX_V], preve[MAX_V]; //直前の頂点と辺
// fromからtoへ向かう容量cap, コストcostの辺をグラフに追加する
void add_edge(int from, int to, int cap, int cost){
G[from].eb((edge){to, cap, cost, (int)G[to].size()});
G[to].eb((edge){from, 0, -cost, (int)(G[from].size()-1)});
}
// sからtへの流量fの最小費用流を求める
// 流せない場合は-1を返す
int min_cost_flow(int s, int t, int f){
int res = 0;
fill(h, h+V, 0);
while(f > 0){ // dijkstra
priority_queue<P, vector<P>, greater<P>> que;
fill(dist, dist+V, 1e9);
dist[s] = 0;
que.push(P(0, s));
while(que.size()){
P p = que.top(); que.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(int i=0; i<G[v].size(); i++){
edge &e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]){
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if(dist[t] == 1e9){ // これ以上流せない
return -1;
}
for(int v=0; v<V; v++){
h[v] += dist[v];
}
// s-t間最短路に沿って目一杯流す
int d = f;
for(int v=t; v!=s; v=prevv[v]){
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for(int v=t; v!=s; v=prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main(){
int e, f; cin>>V>>e>>f;
for(int i=0; i<e; i++){
int s, t, c, d; cin>>s>>t>>c>>d;
add_edge(s, t, c, d);
}
cout << min_cost_flow(0, V - 1, f) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
#define vi vector<int>
#define vvi vector<vector<int> >
#define vl vector<ll>
#define vvl vector<vector<ll>>
#define vb vector<bool>
#define vc vector<char>
#define vs vector<string>
using ll = long long;
using ld =long double;
#define int ll
#define INF 1e9
#define EPS 0.0000000001
#define rep(i,n) for(int i=0;i<n;i++)
#define loop(i,s,n) for(int i=s;i<n;i++)
#define all(in) in.begin(), in.end()
template<class T, class S> void cmin(T &a, const S &b) { if (a > b)a = b; }
template<class T, class S> void cmax(T &a, const S &b) { if (a < b)a = b; }
#define MAX 9999999
int dx[]={0,0,1,-1};
int dy[]={1,-1,0,0};
int W,H;
bool inrange(int x,int y){return (0<=x&&x<W)&&(0<=y&&y<H);}
using namespace std;
typedef pair<int, int> pii;
typedef pair<int,pii> piii;
#define MP make_pair
struct Edge{
int to,cap,cost,rev;
Edge(int _to,int _cap,int _cost,int _rev){
to=_to;
cap=_cap;
cost=_cost;
rev=_rev;
}
};
typedef vector<Edge> ve;
typedef vector<ve> vve;
class MCF{ //Minimum Cost Flow
int inf = INF;
public:
int n;
vve G;
vi h,dist,prev,pree;
MCF(int size){
n=size;
G=vve(n);
h=dist=prev=pree=vi(n);
}
void add_edge(int s,int t,int ca,int co){
Edge e=Edge(t,ca,co,G[t].size());
G[s].push_back(e);
Edge ee=Edge(s,0,-co,G[s].size()-1);
G[t].push_back(ee);
}
int mcf(int source,int sink,int f){
int out=0;
h=vi(n);
while(f>0){
priority_queue<pii,vector<pii> >q;
dist=vi(n,inf);
dist[source]=0;
q.push(pii(0,source));
while(!q.empty()){
pii p=q.top();q.pop();
int v=p.second;
if(dist[v]<-p.first)continue;
rep(i,G[v].size()){
Edge &e=G[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prev[e.to]=v;
pree[e.to]=i;
q.push(pii(-dist[e.to],e.to));
}
}
}
if(dist[sink]==inf)return -1;
rep(i,n)h[i]+=dist[i];
int d=f;
for(int v=sink;v!=source;v=prev[v])d=min(d,G[prev[v]][pree[v]].cap);
f-=d;
out+=d*h[sink];
for(int v=sink;v!=source;v=prev[v]){
Edge &e=G[prev[v]][pree[v]];
e.cap-=d;
G[v][e.rev].cap+=d;
}
}
return out;
}
};
signed main(){
int v,e,f; cin>>v>>e>>f;
MCF hoge(v);
rep(i,e){
int a,b,c,d; cin>>a>>b>>c>>d;
hoge.add_edge(a, b, c, d);
}
cout<<hoge.mcf(0, --v, f)<<endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
using namespace std;
#define INF 1e9
struct min_cost_flow
{
struct edge{int to,cap,cost,rev;};
int V;
vector<vector<edge>> g;
public:
min_cost_flow(int n)
{
V=n;
g.resize(n,vector<edge>());
}
void add_edge(int from,int to,int cap ,int cost)
{
g[from].push_back( (edge) { to,cap,cost,(int)g[to].size() } );
g[to].push_back( (edge){from,0, -cost,(int)g[from].size()-1});
}
// s to t minmun flow
// can't reach -1
int run(int s,int t,int f)
{
int res = 0;
int v = (int)g.size();
vector<int> prevv(v),preve(v);
while( f > 0 )
{
//bellmanford s-t周辺最短路を求める
vector<int> dist(v,INF);
dist[s] = 0;
bool update = true;
while(update)
{
update = false;
for(int j= 0;j<v;j++)
{
if(dist[j] == INF) continue;
for(int i= 0;i<g[j].size();i++)
{
edge &e = g[j][i];
if(e.cap > 0 && dist[e.to] > dist[j] + e.cost)
{
dist[e.to] = dist[j] + e.cost;
prevv[e.to] = j;
preve[e.to] = i;
update = true;
}
}
}
}
if(dist[t] == INF ) return -1; //can't reach
//s-t周辺に目いっぱい流す
int d = f;
for(int i = t; i!= s; i = prevv[i]) d = min(d,g[prevv[i]][preve[i]].cap);
f -= d;
res += d*dist[t];
for(int i = t; i!= s; i = prevv[i]){
edge &e = g[prevv[i]][preve[i]];
e.cap -= d;
g[i][e.rev].cap += d;
}
}
return res;
}
};
int main()
{
int v,e,f;
cin>>v>>e>>f;
min_cost_flow solve(v);
for(int i=0;i<e;i++){
int c,d,u,v;
cin>>u>>v>>c>>d;
solve.add_edge(u,v,c,d);
}
cout<<solve.run(0,v-1,f)<<endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <stdio.h>
#include <iostream>
#include <vector>
#include <string>
#include <string.h>
#include <math.h>
#include <algorithm>
#include <queue>
using namespace std;
#define MAX_V 201
#define INF 1000000000
typedef pair<int, int> P;
struct edge{int to, cap, cost, rev;};
int V;
vector<edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V];
int preve[MAX_V];
void ae(int from, int to, int cap, int cost){
G[from].push_back((edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
int minCostFlow(int s, int t, int f){
int res = 0;
memset(h,0,sizeof(h));
while(f > 0){
priority_queue<P, vector<P>, greater<P> > que;
for(int i = 0; i < V; i++){
dist[i] = INF;
}
dist[s] = 0;
que.push(P(0,s));
while(!que.empty()){
P p = que.top(); que.pop();
int v = p.second;
if(dist[v] < p.first)continue;
for(int i = 0; i < (int)G[v].size(); i++){
edge &e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]){
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if(dist[t] == INF){
return -1;
}
for(int v = 0; v < V; v++){
h[v] += dist[v];
}
int d = f;
for(int v = t; v != s; v = prevv[v]){
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for(int v = t; v != s; v = prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main(){
int v,e,f;
cin>>v>>e>>f;
V=v;
edge z;
for(int i=0;i<e;i++){
cin>>z.to>>z.cap>>z.cost>>z.rev;
ae(z.to,z.cap,z.cost,z.rev);
}
cout << minCostFlow(0,v-1,f) << endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
struct Primal_Dual
{
const int INF = 1 << 30;
typedef pair< int, int > Pi;
struct edge
{
int to, cap, cost, rev;
};
vector< vector< edge > > graph;
vector< int > potential, min_cost, prevv, preve;
Primal_Dual(int V) : graph(V) {}
void add_edge(int from, int to, int cap, int cost)
{
graph[from].push_back((edge) {to, cap, cost, (int) graph[to].size()});
graph[to].push_back((edge) {from, 0, -cost, (int) graph[from].size() - 1});
}
int min_cost_flow(int s, int t, int f)
{
int V = graph.size(), ret = 0;
priority_queue< Pi, vector< Pi >, greater< Pi > > que;
potential.assign(V, 0);
preve.assign(V, -1);
prevv.assign(V, -1);
while(f > 0) {
min_cost.assign(V, INF);
que.push(Pi(0, s));
min_cost[s] = 0;
while(!que.empty()) {
Pi p = que.top();
que.pop();
if(min_cost[p.second] < p.first) continue;
for(int i = 0; i < graph[p.second].size(); i++) {
edge &e = graph[p.second][i];
int nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to];
if(e.cap > 0 && min_cost[e.to] > nextCost) {
min_cost[e.to] = nextCost;
prevv[e.to] = p.second, preve[e.to] = i;
que.push(Pi(min_cost[e.to], e.to));
}
}
}
if(min_cost[t] == INF) return -1;
for(int v = 0; v < V; v++) potential[v] += min_cost[v];
int addflow = f;
for(int v = t; v != s; v = prevv[v]) {
addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
}
f -= addflow;
ret += addflow * potential[t];
for(int v = t; v != s; v = prevv[v]) {
edge &e = graph[prevv[v]][preve[v]];
e.cap -= addflow;
graph[v][e.rev].cap += addflow;
}
}
return ret;
}
};
void solve()
{
int V, E, F;
cin >> V >> E >> F;
Primal_Dual graph(V);
for(int i = 0; i < E; i++) {
int a, b, c, d;
cin >> a >> b >> c >> d;
graph.add_edge(a, b, c, d);
}
cout << graph.min_cost_flow(0, V - 1, F) << endl;
}
int main()
{
cin.tie(0);
ios::sync_with_stdio(false);
solve();
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#include <tuple>
#define mkp make_pair
#define mkt make_tuple
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;
template< typename flow_t, typename cost_t >
struct MinCostFlow {
const cost_t INF;
struct edge {
int to;
flow_t cap;
cost_t cost;
int rev;
};
vector<vector<edge>> graph;
vector<cost_t> potential,min_cost;
vector<int> prevv,preve;
MinCostFlow(int V) : graph(V),INF(numeric_limits< cost_t >::max()) {}
void add_edge(int from,int to,flow_t cap,cost_t cost){
graph[from].emplace_back((edge){to,cap,cost,(int)graph[to].size()});
graph[to].emplace_back((edge){from,0,-cost,(int)graph[from].size()-1});
}
cost_t min_cost_flow(int s,int t,flow_t f){
int V=(int)graph.size();
cost_t ret=0;
using Pi = pair<cost_t,int>;
priority_queue<Pi,vector<Pi>,greater<Pi>> PQ;
potential.assign(V,0);
preve.assign(V,-1);
prevv.assign(V,-1);
while(f>0){
min_cost.assign(V,INF);
PQ.emplace(0,s);
min_cost[s]=0;
while(!PQ.empty()){
cost_t d;
int now;
tie(d,now)=PQ.top();
PQ.pop();
if(min_cost[now]<d) continue;
for(int i=0;i<graph[now].size();i++){
edge &e=graph[now][i];
cost_t nextCost=min_cost[now]+(e.cost+potential[now]-potential[e.to]);
if(e.cap>0&&min_cost[e.to]>nextCost){
min_cost[e.to]=nextCost;
prevv[e.to]=now;
preve[e.to]=i;
PQ.emplace(min_cost[e.to],e.to);
}
}
}
if(min_cost[t]==INF) return -1;
for(int v=0;v<V;v++) potential[v]+=min_cost[v];
flow_t addflow=f;
for(int v=t;v!=s;v=prevv[v]){
addflow=min(addflow,graph[prevv[v]][preve[v]].cap);
}
f-=addflow;
ret+=addflow*potential[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e=graph[prevv[v]][preve[v]];
e.cap-=addflow;
graph[v][e.rev].cap+=addflow;
}
}
return ret;
}
};
int N,M,F;
vector<int> A,B,C,D;
int main(){
cin>>N>>M>>F;
A.resize(M);
B.resize(M);
C.resize(M);
D.resize(M);
for(int i=0;i<M;i++) cin>>A[i]>>B[i]>>C[i]>>D[i];
MinCostFlow<int,int> mcf(N);
for(int i=0;i<M;i++){
mcf.add_edge(A[i],B[i],C[i],D[i]);
}
cout<<mcf.min_cost_flow(0,N-1,F)<<endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | #!/usr/bin/env python3
# GRL_6_B: Minimum Cost Flow
WEIGHT_MAX = 10 ** 10
class Edge:
__slots__ = ('src', 'dest', 'capacity', 'flow', 'cost')
def __init__(self, v, w, capacity, cost=0):
self.src = v
self.dest = w
self.capacity = capacity
self.cost = cost
self.flow = 0
def other(self, v):
if v == self.src:
return self.dest
else:
return self.src
def residual_capacity(self, v):
if v == self.src:
return self.capacity - self.flow
else:
return self.flow
def cost_from(self, v):
if v == self.src:
return self.cost
else:
return -self.cost
def add_flow(self, v, f):
if v == self.src:
self.flow += f
else:
self.flow -= f
def __str__(self):
return "{} {} {} {} {}".format(self.src, self.dest, self.capacity,
self.cost, self.flow)
class Network:
def __init__(self, v):
self.v = v
self._edges = [[] for _ in range(v)]
def add(self, edge):
self._edges[edge.src].append(edge)
self._edges[edge.dest].append(edge)
def adj(self, v):
return self._edges[v]
def flow(self, v):
return sum(e.flow for e in self.adj(v) if e.src == v)
def cost(self):
cost = 0
for v in range(self.v):
for e in self.adj(v):
if e.src == v:
cost += e.flow * e.cost
return cost
def __str__(self):
s = ''
for v in range(self.v):
for e in self.adj(v):
s += "{} {}\n".format(v, e)
return s
def min_cost(network, s, t, f):
def augment_path():
def relax(edge, v):
w = edge.other(v)
c = edge.cost_from(v)
if e.residual_capacity(v) > 0 and dists[w] > dists[v] + c:
dists[w] = dists[v] + c
edge_to[w] = e
_nodes.append(w)
dists = [WEIGHT_MAX] * network.v
dists[s] = 0
edge_to = [None] * network.v
nodes = []
nodes.append(s)
for _ in range(network.v):
_nodes = []
for v in nodes:
for e in network.adj(v):
relax(e, v)
nodes = _nodes
if edge_to[t] is None:
return (0, [])
else:
v = t
e = edge_to[v]
cap = f
while e is not None:
v = e.other(v)
_cap = e.residual_capacity(v)
if cap > _cap:
cap = _cap
e = edge_to[v]
return (cap, edge_to)
while f > 0:
cap, path = augment_path()
if cap == 0:
break
f -= cap
v = t
e = path[t]
while e is not None:
v = e.other(v)
e.add_flow(v, cap)
e = path[v]
if f > 0:
return -1
else:
return network.cost()
def run():
v, e, f = [int(i) for i in input().split()]
net = Network(v)
s, t = 0, v-1
for _ in range(e):
v, w, c, d = [int(i) for i in input().split()]
net.add(Edge(v, w, c, d))
print(min_cost(net, s, t, f))
if __name__ == '__main__':
run()
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define all(a) (a).begin(),(a).end()
#define pb push_back
#define INF (1e9+1)
//#define INF (1LL<<59)
#define MAX_V 100
struct edge { int to, cap, cost,rev; };
int V; // ????????°
vector<edge> G[MAX_V];
vector<int> h(MAX_V); //??????????????£???
vector<int> dist(MAX_V);// ???????????¢
int prevv[MAX_V], preve[MAX_V];// ??´??????????????¨???
// from??????to??????????????????cap????????????cost????????????????????????????????????
void add_edge(int from, int to, int cap, int cost) {
G[from].push_back((edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
//?????????????????????????????????????????´????????????
int shortest_path(int s,vector<int> &d){
int v = d.size();
rep(i,d.size())d[i]=INF;
d[s]=0;
rep(loop,v){
bool update = false;
rep(i,MAX_V){
for(auto e:G[i]){
if(d[i]!=INF && d[e.to] > d[i]+e.cost){
d[e.to] = d[i]+e.cost;
update = true;
}
}
}
if(!update)break;
if(loop==v-1)return true; //negative_cycle
}
return false;
}
// s??????t????????????f???????°??????¨???????±???????
// ??????????????´??????-1?????????
int min_cost_flow(int s, int t, int f) {
int res = 0;
rep(i,h.size())h[i]=0;
shortest_path(s, dist);
while (f > 0) {
// ?????????????????????????????¨??????h?????´??°??????
priority_queue<pii, vector<pii>, greater<pii> > que;
rep(i,dist.size())dist[i]=INF;
dist[s] = 0;
que.push(pii(0, s));
while (!que.empty()) {
pii p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (int i = 0; i < G[v].size(); i++) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to]; prevv[e.to] = v;
preve[e.to] = i;
que.push(pii(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) return -1; //????????\???????????????
for (int v = 0; v < V; v++) h[v] += dist[v];
// s-t????????????????????£??????????????????
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]]; e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main(){
int e,f;
cin>>V>>e>>f;
rep(i,e){
int u,v,c,d;
cin>>u>>v>>c>>d;
add_edge(u, v, c, d);
}
cout<<min_cost_flow(0, V-1, f)<<endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
#define pb push_back
using namespace std;
const int INF=0x3f3f3f3f;
const int maxn=105;
const int maxq=1005;
struct edge{int to,cap,cost,rev;};
int n,m,k;
int d[maxn];
int a[maxn];
int p1[maxn];
int p2[maxn];
bool inq[maxn];
vector<edge>G[maxn];
void add_edge(int u,int v,int c,int w) {
G[u].pb(edge{v,c,w,int(G[v].size())});
G[v].pb(edge{u,0,-w,int(G[u].size()-1)});
}
int mcmf(int s,int t) {
int flow=0 , cost=0;
while (1) {
memset(d,0x3f,sizeof(d));
d[s]=0; a[s]=max(0,k-flow);
int qh=0,qt=0,q[maxq];
q[qt++]=s; inq[s]=1;
while (qh<qt) {
int u=q[qh++];
inq[u]=0;
for (int i=0;i<G[u].size();i++) {
edge e=G[u][i];
if (d[e.to]>d[u]+e.cost && e.cap) {
d[e.to]=d[u]+e.cost;
a[e.to]=min(a[u],e.cap);
p1[e.to]=u;
p2[e.to]=i;
if (!inq[e.to]) {
q[qt++]=e.to;
inq[e.to]=1;
}
}
}
}
if (d[t]==INF || !a[t]) break;
flow+=a[t];
cost+=a[t]*d[t];
for (int v=t,u=p1[t];v!=s;v=u,u=p1[u]) {
int id=p2[v];
G[u][id].cap-=a[t];
id=G[u][id].rev;
G[v][id].cap+=a[t];
}
}
if (flow<k) return -1;
else return cost;
}
int main() {
cin>>n>>m>>k;
for (int i=0;i<m;i++) {
int u,v,c,w; cin>>u>>v>>c>>w;
add_edge(u,v,c,w);
}
cout<<mcmf(0,n-1)<<'\n';
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <vector>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <stack>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <bitset>
#include <complex>
using namespace std;
#define REP(i,n) for(int i = 0; i < (int)n; i++)
#define FOR(i,a,b) for(int i = a; i < (int)b; i++)
#define pb push_back
#define mp make_pair
typedef vector<int> vi;
typedef pair<int, int> pi;
typedef long long ll;
typedef unsigned long long ull;
const int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};
const int INF = 1 << 27;
const int MAX_V = 101;
//////////////////////////////
// ????°??????¨???
struct edge { int to, cap, cost, rev; };
int V;
vector<edge> G[MAX_V]; //??°???????????£??\???????????¨???
int h[MAX_V]; //??????????????£???
int dist[MAX_V]; //???????????¢
int prevv[MAX_V], preve[MAX_V]; // ??´??????????????¨???
void add_edge(int from, int to, int cap, int cost){
G[from].push_back((edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((edge){from, 0, -cost, (int)(G[from].size()) - 1});
}
// s??????t????????????f???????°??????¨???
// ??????????????´??????-1?????????
int min_cost_flow(int s, int t, int f){
int res = 0;
fill(h, h + V, 0);
while(f > 0){
priority_queue<pi, vector<pi>, greater<pi> > que;
fill(dist, dist + V, INF);
dist[s] = 0;
que.push(pi(0, s));
while(!que.empty()){
pi p = que.top(); que.pop();
int v = p.second;
if(dist[v] < p.first) continue;
REP(i, G[v].size()){
edge &e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]){
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(pi(dist[e.to], e.to));
}
}
}
if(dist[t] == INF) return -1;
REP(v, V) h[v] += dist[v];
int d = f;
for(int v = t; v != s; v = prevv[v]) d = min(d, G[prevv[v]][preve[v]].cap);
f -= d;
res += d * h[t];
for(int v = t; v != s; v = prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main() {
int E, F; cin >>V >>E >>F;
REP(i, E){
int a,b,c,d; cin >> a >> b >> c >> d;
add_edge(a,b,c,d);
}
cout << min_cost_flow(0, V-1, F) <<endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | java | import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.PriorityQueue;
import java.util.TreeMap;
public class Main {
static ContestScanner in;static Writer out;public static void main(String[] args)
{try{in=new ContestScanner();out=new Writer();Main solve=new Main();solve.solve();
in.close();out.flush();out.close();}catch(IOException e){e.printStackTrace();}}
static void dump(int[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
static void dump(int[]a,int n){for(int i=0;i<a.length;i++)out.printf("%"+n+"d ",a[i]);out.println();}
static void dump(long[]a){for(int i=0;i<a.length;i++)out.print(a[i]+" ");out.println();}
static void dump(char[]a){for(int i=0;i<a.length;i++)out.print(a[i]);out.println();}
static long pow(long a,int n){long r=1;while(n>0){if((n&1)==1)r*=a;a*=a;n>>=1;}return r;}
static String itob(int a,int l){return String.format("%"+l+"s",Integer.toBinaryString(a)).replace(' ','0');}
static void sort(int[]a){m_sort(a,0,a.length,new int[a.length]);}
static void sort(int[]a,int l){m_sort(a,0,l,new int[l]);}
static void sort(int[]a,int l,int[]buf){m_sort(a,0,l,buf);}
static void sort(int[]a,int s,int l,int[]buf){m_sort(a,s,l,buf);}
static void m_sort(int[]a,int s,int sz,int[]b)
{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];
} /* qsort(3.5s)<<msort(9.5s)<<<shuffle+qsort(17s)<Arrays.sort(Integer)(20s) */
static void sort(long[]a){m_sort(a,0,a.length,new long[a.length]);}
static void sort(long[]a,int l){m_sort(a,0,l,new long[l]);}
static void sort(long[]a,int l,long[]buf){m_sort(a,0,l,buf);}
static void sort(long[]a,int s,int l,long[]buf){m_sort(a,s,l,buf);}
static void m_sort(long[]a,int s,int sz,long[]b)
{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];}
static void swap(long[] a,int i,int j){final long t=a[i];a[i]=a[j];a[j]=t;}
static void swap(int[] a,int i,int j){final int t=a[i];a[i]=a[j];a[j]=t;}
static int binarySearchSmallerMax(int[]a,int v)// get maximum index which a[idx]<=v
{int l=-1,r=a.length-1,s=0;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
static int binarySearchSmallerMax(int[]a,int v,int l,int r)
{int s=-1;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
@SuppressWarnings("unchecked")
static List<Integer>[]createGraph(int n)
{List<Integer>[]g=new List[n];for(int i=0;i<n;i++)g[i]=new ArrayList<>();return g;}
@SuppressWarnings("unchecked")
void solve() throws NumberFormatException, IOException{
final int n = in.nextInt();
final int m = in.nextInt();
int f = in.nextInt();
List<Edge>[] node = new List[n];
for(int i=0; i<n; i++) node[i] = new ArrayList<>();
for(int i=0; i<m; i++){
int a = in.nextInt();
int b = in.nextInt();
int c = in.nextInt();
int d = in.nextInt();
Edge e = new Edge(b, c, d);
Edge r = new Edge(a, 0, -d);
e.rev = r;
r.rev = e;
node[a].add(e);
node[b].add(r);
}
final int s = 0, t = n-1;
int[] h = new int[n];
int[] dist = new int[n];
int[] preV = new int[n];
int[] preE = new int[n];
final int inf = Integer.MAX_VALUE;
PriorityQueue<Pos> qu = new PriorityQueue<>();
int res = 0;
while(f>0){
Arrays.fill(dist, inf);
dist[s] = 0;
qu.clear();
qu.add(new Pos(s, 0));
while(!qu.isEmpty()){
Pos p = qu.poll();
if(dist[p.v]<p.d) continue;
final int sz = node[p.v].size();
for(int i=0; i<sz; i++){
Edge e = node[p.v].get(i);
final int nd = e.cost+p.d + h[p.v]-h[e.to];
if(e.cap>0 && nd < dist[e.to]){
preV[e.to] = p.v;
preE[e.to] = i;
dist[e.to] = nd;
qu.add(new Pos(e.to, nd));
}
}
}
if(dist[t]==inf) break;
for(int i=0; i<n; i++) h[i] += dist[i];
int minf = f;
for(int i=t; i!=s; i=preV[i]){
minf = Math.min(minf, node[preV[i]].get(preE[i]).cap);
}
f -= minf;
res += minf*h[t];
for(int i=t; i!=s; i=preV[i]){
node[preV[i]].get(preE[i]).cap -= minf;
node[preV[i]].get(preE[i]).rev.cap += minf;
}
}
if(f>0) res = -1;
System.out.println(res);
}
}
class Pos implements Comparable<Pos>{
int v, d;
public Pos(int v, int d) {
this.v = v;
this.d = d;
}
@Override
public int compareTo(Pos o) {
return d-o.d;
}
}
class Edge{
int to, cap, cost;
Edge rev;
Edge(int t, int c, int co){
to = t;
cap = c;
cost = co;
}
void rev(Edge r){
rev = r;
}
}
@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
public void add(T key,int v){put(key,get(key)+v);}
public void add(T key){put(key,get(key)+1);}
public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
public MultiSet<T> merge(MultiSet<T> set)
{MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}
@SuppressWarnings("serial")
class OrderedMultiSet<T> extends TreeMap<T, Integer>{
@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
public void add(T key,int v){put(key,get(key)+v);}
public void add(T key){put(key,get(key)+1);}
public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
public OrderedMultiSet<T> merge(OrderedMultiSet<T> set)
{OrderedMultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
while(!s.isEmpty()){l.add(s.firstEntry().getKey(),s.pollFirstEntry().getValue());}return l;}
}
class Pair implements Comparable<Pair>{
int a,b;final int hash;Pair(int a,int b){this.a=a;this.b=b;hash=(a<<16|a>>16)^b;}
public boolean equals(Object obj){Pair o=(Pair)(obj);return a==o.a&&b==o.b;}
public int hashCode(){return hash;}
public int compareTo(Pair o){if(a!=o.a)return a<o.a?-1:1;else if(b!=o.b)return b<o.b?-1:1;return 0;}
}
class Timer{
long time;public void set(){time=System.currentTimeMillis();}
public long stop(){return time=System.currentTimeMillis()-time;}
public void print(){System.out.println("Time: "+(System.currentTimeMillis()-time)+"ms");}
@Override public String toString(){return"Time: "+time+"ms";}
}
class Writer extends PrintWriter{
public Writer(String filename)throws IOException
{super(new BufferedWriter(new FileWriter(filename)));}
public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
private BufferedReader in;private int c=-2;
public ContestScanner()throws IOException
{in=new BufferedReader(new InputStreamReader(System.in));}
public ContestScanner(String filename)throws IOException
{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
public String nextToken()throws IOException {
StringBuilder sb=new StringBuilder();
while((c=in.read())!=-1&&Character.isWhitespace(c));
while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
return sb.toString();
}
public String readLine()throws IOException{
StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
return sb.toString();
}
public long nextLong()throws IOException,NumberFormatException
{return Long.parseLong(nextToken());}
public int nextInt()throws NumberFormatException,IOException
{return(int)nextLong();}
public double nextDouble()throws NumberFormatException,IOException
{return Double.parseDouble(nextToken());}
public void close() throws IOException {in.close();}
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <algorithm>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
const ll inf = 1e14;
class min_cost_flow{
private:
int N;
struct edge{int to; ll cap,cost; int rev; bool is_rev;};
vector<vector<edge>> G;
vector<ll> h,dist,prevv,preve;
public:
min_cost_flow(int n){
N = n;
G = vector<vector<edge>>(N);
h = dist = prevv = preve = vector<ll>(N,0);
}
void add_edge(int from,int to,ll cap,ll cost){
G[from].push_back((edge){to,cap,cost,(int) G[to].size(),false});
G[to].push_back((edge){from,0,-cost,(int) G[from].size()-1,true});
}
ll answer(int s,int t,ll f){
ll res = 0;
fill(h.begin(),h.end(),0);
while(f>0){
priority_queue<P,vector<P>,greater<P>> Q;
fill(dist.begin(),dist.end(),inf);
dist[s] = 0;
Q.push(P(0,s));
while(!Q.empty()){
P p = Q.top(); Q.pop();
int v = p.second;
if(dist[v]<p.first) continue;
for(int i=0;i<G[v].size();i++){
edge &e = G[v][i];
if(e.cap>0 && dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to] = dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
Q.push(P(dist[e.to],e.to));
}
}
}
if(dist[t]==inf) return -1;
for(int v=0;v<N;v++) h[v] += dist[v];
ll d = f;
for(int v=t;v!=s; v=prevv[v]){
d = min(d,G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d*h[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
int N,M,F;
int main(){
cin >> N >> M >> F;
min_cost_flow flow(N+1);
int u,v,c,d;
for(int i=0;i<M;i++){
cin >> u >> v >> c >> d;
flow.add_edge(u,v,c,d);
}
cout << flow.answer(0,N-1,F) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, gcd
from itertools import accumulate, permutations, combinations, product, groupby, combinations_with_replacement
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7
class MinCostFlow:
def __init__(self, n):
self.n = n
self.g = [[] for i in range(n)]
def add_edge(self, fr, to, cap, cost):
G = self.g
G[fr].append([to, cap, cost, len(G[to])])
G[to].append([fr, 0, -cost, len(G[fr])-1])
def flow(self, s, t, f):
N = self.n
G = self.g
INF = 10**18
prevv = [0]*N
preve = [0]*N
res = 0
while f > 0:
dist = [INF]*N
dist[s] = 0
update = True
while update:
update = False
for v in range(N):
if dist[v] == INF: continue
for i in range(len(G[v])):
to, cap, cost, rev = G[v][i]
if cap > 0 and dist[to] > dist[v]+cost:
dist[to] = dist[v]+cost
prevv[to] = v
preve[to] = i
update = True
if dist[t] == INF:
return -1
d = f
v = t
while v != s:
d = min(d, G[prevv[v]][preve[v]][1])
v = prevv[v]
f -= d
res += d*dist[t]
v = t
while v != s:
e = G[prevv[v]][preve[v]]
e[1] -= d
G[v][e[3]][1] += d
v = prevv[v]
return res
V, E, F = MAP()
mcf = MinCostFlow(V)
for _ in range(E):
u, v, c, d = MAP()
mcf.add_edge(u, v, c, d)
print(mcf.flow(0, V-1, F))
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
#define int long long // <-----!!!!!!!!!!!!!!!!!!!
#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define printV(v) for(auto&& x : v){cout << x << " ";} cout << endl
#define printVV(vv) for(auto&& v : vv){for(auto&& x : v){cout << x << " ";}cout << endl;}
#define printP(p) cout << p.first << " " << p.second << endl
#define printVP(vp) for(auto&& p : vp) printP(p);
typedef long long ll;
typedef pair<int, int> Pii;
typedef tuple<int, int, int> TUPLE;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<Pii> vp;
const int inf = 1e9;
const int mod = 1e9 + 7;
template<typename T> using Graph = vector<vector<T>>;
struct edge { int to, cap, cost, rev; };
int V;
const int MAX_V = 100;
vector<edge> G[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
void add_edge(int from, int to, int cap, int cost) {
G[from].emplace_back((edge){to, cap, cost, (int)G[to].size()});
G[to].emplace_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
int min_cost_flow(int s, int t, int f) {
int res = 0;
while (f > 0) {
fill(dist, dist + V, inf);
dist[s] = 0;
bool update = true;
while (update) {
update = false;
for (int v = 0; v < V; v++) {
if (dist[v] == inf) continue;
for (int i = 0; i < G[v].size(); i++) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if (dist[t] == inf) {
return -1;
}
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * dist[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
signed main() {
std::ios::sync_with_stdio(false);
std::cin.tie(0);
int E, F;
cin >> V >> E >> F;
rep(i, E) {
int u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
cout << min_cost_flow(0, V - 1, F) << endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | java |
import java.io.*;
import java.util.*;
import java.util.stream.Stream;
/**
* @author baito
*/
@SuppressWarnings("unchecked")
public class Main
{
static StringBuilder sb = new StringBuilder();
static FastScanner sc = new FastScanner(System.in);
static int INF = 1234567890;
static long LINF = 123456789123456789L;
static long MINF = -123456789123456789L;
static long MOD = 1000000007;
static int[] y4 = {0, 1, 0, -1};
static int[] x4 = {1, 0, -1, 0};
static int[] y8 = {0, 1, 0, -1, -1, 1, 1, -1};
static int[] x8 = {1, 0, -1, 0, 1, -1, 1, -1};
static long[] Fa;//factorial
static boolean[] isPrime;
static int[] primes;
static char[][] map;
public static void main(String[] args)
{
V = sc.nextInt();
E = sc.nextInt();
F = sc.nextInt();
edges = Stream.generate(ArrayList::new).limit(V).toArray(ArrayList[]::new);
for (int i = 0; i < E; i++)
{
addEdge(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
}
System.out.println(minCostFlow(0, V - 1, F));
}
public static void addEdge(int f, int t, int ca, int co)
{
edges[f].add(new Edge(t, ca, co, edges[t].size()));
edges[t].add(new Edge(f, 0, -co, edges[f].size()-1));
}
static class P implements Comparable<P>
{
int v;
long dist;
P(long a, int b)
{
dist = a;
v = b;
}
@Override
public boolean equals(Object o)
{
if (this == o) return true;
if (!(o instanceof P)) return false;
P p = (P) o;
return dist == p.dist && v == p.v;
}
@Override
public int hashCode()
{
return Objects.hash(dist, v);
}
@Override
public int compareTo(P p)
{
return dist > p.dist ? 1 : -1; //xで昇順にソート
//return (dist == p.dist ? v - p.v : dist - p.dist) * -1; //xで降順にソート
//return v == p.v ? dist - p.dist : v - p.v;//yで昇順にソート
//return (v == p.v ? dist - p.dist : v - p.v)*-1;//yで降順にソート
}
}
static int V, E, F;
static ArrayList<Edge>[] edges;
static long minCostFlow(int s, int t, int f)
{
int[] prevv = new int[V];
int[] preve = new int[V];
long[] dist = new long[V];
int[] h = new int[V];
long res = 0;
while (f > 0)
{
Arrays.fill(dist, INF);
dist[s] = 0;
PriorityQueue<P> que = new PriorityQueue<>();
que.add(new P(0, s));
while (!que.isEmpty())
{
P p = que.poll();
int v = p.v;
if (dist[v] < p.dist) continue;
for (int i = 0; i < edges[v].size(); i++)
{
Edge e = edges[v].get(i);
if (e.cap > 0 && dist[e.to] > p.dist + e.cost + h[v] - h[e.to])
{
dist[e.to] = p.dist + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.add(new P(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) return -1;
for (int i = 0; i < V; i++) h[i] += dist[i];
long d = f;
for (int v = t; v != s; v = prevv[v])
{
d = Math.min(d, edges[prevv[v]].get(preve[v]).cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v])
{
Edge e = edges[prevv[v]].get(preve[v]);
e.cap -= d;
edges[v].get(e.rev).cap += d;
}
}
return res;
}
static class Edge
{
int to, rev;
long cap, cost;
Edge(int t, long ca, long co, int r)
{
to = t;
cap = ca;
cost = co;
rev = r;
}
}
public static int upper0(int a)
{
if (a < 0) return 0;
return a;
}
public static long upper0(long a)
{
if (a < 0) return 0;
return a;
}
public static Integer[] toIntegerArray(int[] ar)
{
Integer[] res = new Integer[ar.length];
for (int i = 0; i < ar.length; i++)
{
res[i] = ar[i];
}
return res;
}
//k個の次の組み合わせをビットで返す 大きさに上限はない 110110 -> 111001
public static int nextCombSizeK(int comb, int k)
{
int x = comb & -comb; //最下位の1
int y = comb + x; //連続した下の1を繰り上がらせる
return ((comb & ~y) / x >> 1) | y;
}
public static int keta(long num)
{
int res = 0;
while (num > 0)
{
num /= 10;
res++;
}
return res;
}
public static long getHashKey(int a, int b)
{
return (long) a << 32 | b;
}
public static boolean isOutofIndex(int x, int y)
{
if (x < 0 || y < 0) return true;
if (map[0].length <= x || map.length <= y) return true;
return false;
}
public static void setPrimes()
{
int n = 100001;
isPrime = new boolean[n];
List<Integer> prs = new ArrayList<>();
Arrays.fill(isPrime, true);
isPrime[0] = isPrime[1] = false;
for (int i = 2; i * i <= n; i++)
{
if (!isPrime[i]) continue;
prs.add(i);
for (int j = i * 2; j < n; j += i)
{
isPrime[j] = false;
}
}
primes = new int[prs.size()];
for (int i = 0; i < prs.size(); i++)
primes[i] = prs.get(i);
}
public static void revSort(int[] a)
{
Arrays.sort(a);
reverse(a);
}
public static void revSort(long[] a)
{
Arrays.sort(a);
reverse(a);
}
public static int[][] copy(int[][] ar)
{
int[][] nr = new int[ar.length][ar[0].length];
for (int i = 0; i < ar.length; i++)
for (int j = 0; j < ar[0].length; j++)
nr[i][j] = ar[i][j];
return nr;
}
/**
* <h1>指定した値以上の先頭のインデクスを返す</h1>
* <p>配列要素が０のときは、０が返る。</p>
*
* @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
* 値が無ければ、挿入できる最小のインデックス
*/
public static int lowerBound(final int[] arr, final int value)
{
int low = 0;
int high = arr.length;
int mid;
while (low < high)
{
mid = ((high - low) >>> 1) + low; //(low + high) / 2 (オーバーフロー対策)
if (arr[mid] < value)
{
low = mid + 1;
}
else
{
high = mid;
}
}
return low;
}
/**
* <h1>指定した値より大きい先頭のインデクスを返す</h1>
* <p>配列要素が０のときは、０が返る。</p>
*
* @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
* 値が無ければ、挿入できる最小のインデックス
*/
public static int upperBound(final int[] arr, final int value)
{
int low = 0;
int high = arr.length;
int mid;
while (low < high)
{
mid = ((high - low) >>> 1) + low; //(low + high) / 2 (オーバーフロー対策)
if (arr[mid] <= value)
{
low = mid + 1;
}
else
{
high = mid;
}
}
return low;
}
/**
* <h1>指定した値以上の先頭のインデクスを返す</h1>
* <p>配列要素が０のときは、０が返る。</p>
*
* @return<b>int</b> ： 探索した値以上で、先頭になるインデクス
* 値がなければ挿入できる最小のインデックス
*/
public static long lowerBound(final long[] arr, final long value)
{
int low = 0;
int high = arr.length;
int mid;
while (low < high)
{
mid = ((high - low) >>> 1) + low; //(low + high) / 2 (オーバーフロー対策)
if (arr[mid] < value)
{
low = mid + 1;
}
else
{
high = mid;
}
}
return low;
}
/**
* <h1>指定した値より大きい先頭のインデクスを返す</h1>
* <p>配列要素が０のときは、０が返る。</p>
*
* @return<b>int</b> ： 探索した値より上で、先頭になるインデクス
* 値がなければ挿入できる最小のインデックス
*/
public static long upperBound(final long[] arr, final long value)
{
int low = 0;
int high = arr.length;
int mid;
while (low < high)
{
mid = ((high - low) >>> 1) + low; //(low + high) / 2 (オーバーフロー対策)
if (arr[mid] <= value)
{
low = mid + 1;
}
else
{
high = mid;
}
}
return low;
}
//次の順列に書き換える、最大値ならfalseを返す
public static boolean nextPermutation(int A[])
{
int len = A.length;
int pos = len - 2;
for (; pos >= 0; pos--)
{
if (A[pos] < A[pos + 1]) break;
}
if (pos == -1) return false;
//posより大きい最小の数を二分探索
int ok = pos + 1;
int ng = len;
while (Math.abs(ng - ok) > 1)
{
int mid = (ok + ng) / 2;
if (A[mid] > A[pos]) ok = mid;
else ng = mid;
}
swap(A, pos, ok);
reverse(A, pos + 1, len - 1);
return true;
}
//次の順列に書き換える、最小値ならfalseを返す
public static boolean prevPermutation(int A[])
{
int len = A.length;
int pos = len - 2;
for (; pos >= 0; pos--)
{
if (A[pos] > A[pos + 1]) break;
}
if (pos == -1) return false;
//posより小さい最大の数を二分探索
int ok = pos + 1;
int ng = len;
while (Math.abs(ng - ok) > 1)
{
int mid = (ok + ng) / 2;
if (A[mid] < A[pos]) ok = mid;
else ng = mid;
}
swap(A, pos, ok);
reverse(A, pos + 1, len - 1);
return true;
}
//↓nCrをmod計算するために必要。 ***factorial(N)を呼ぶ必要がある***
static long ncr(int n, int r)
{
if (n < r) return 0;
else if (r == 0) return 1;
factorial(n);
return Fa[n] / (Fa[n - r] * Fa[r]);
}
static long ncr2(int a, int b)
{
if (b == 0) return 1;
else if (a < b) return 0;
long res = 1;
for (int i = 0; i < b; i++)
{
res *= a - i;
res /= i + 1;
}
return res;
}
static long ncrdp(int n, int r)
{
if (n < r) return 0;
long[][] dp = new long[n + 1][r + 1];
for (int ni = 0; ni < n + 1; ni++)
{
dp[ni][0] = dp[ni][ni] = 1;
for (int ri = 1; ri < ni; ri++)
{
dp[ni][ri] = dp[ni - 1][ri - 1] + dp[ni - 1][ri];
}
}
return dp[n][r];
}
static long modNcr(int n, int r)
{
if (n < r) return 0;
long result = Fa[n];
result = result * modInv(Fa[n - r]) % MOD;
result = result * modInv(Fa[r]) % MOD;
return result;
}
public static long modSum(long... lar)
{
long res = 0;
for (long l : lar)
res = (res + l % MOD) % MOD;
if (res < 0) res += MOD;
res %= MOD;
return res;
}
public static long modDiff(long a, long b)
{
long res = a % MOD - b % MOD;
if (res < 0) res += MOD;
res %= MOD;
return res;
}
public static long modMul(long... lar)
{
long res = 1;
for (long l : lar)
res = (res * l % MOD) % MOD;
if (res < 0) res += MOD;
res %= MOD;
return res;
}
public static long modDiv(long a, long b)
{
long x = a % MOD;
long y = b % MOD;
long res = (x * modInv(y)) % MOD;
return res;
}
static long modInv(long n)
{
return modPow(n, MOD - 2);
}
static void factorial(int n)
{
Fa = new long[n + 1];
Fa[0] = Fa[1] = 1;
// for (int i = 2; i <= n; i++)
// {
// Fa[i] = (Fa[i - 1] * i) % MOD;
// }
//
for (int i = 2; i <= 100000; i++)
{
Fa[i] = (Fa[i - 1] * i) % MOD;
}
for (int i = 100001; i <= n; i++)
{
Fa[i] = (Fa[i - 1] * i) % MOD;
}
}
static long modPow(long x, long n)
{
long res = 1L;
while (n > 0)
{
if ((n & 1) == 1)
{
res = res * x % MOD;
}
x = x * x % MOD;
n >>= 1;
}
return res;
}
//↑nCrをmod計算するために必要
static int gcd(int n, int r)
{
return r == 0 ? n : gcd(r, n % r);
}
static long gcd(long n, long r)
{
return r == 0 ? n : gcd(r, n % r);
}
static <T> void swap(T[] x, int i, int j)
{
T t = x[i];
x[i] = x[j];
x[j] = t;
}
static void swap(int[] x, int i, int j)
{
int t = x[i];
x[i] = x[j];
x[j] = t;
}
public static void reverse(int[] x)
{
int l = 0;
int r = x.length - 1;
while (l < r)
{
int temp = x[l];
x[l] = x[r];
x[r] = temp;
l++;
r--;
}
}
public static void reverse(long[] x)
{
int l = 0;
int r = x.length - 1;
while (l < r)
{
long temp = x[l];
x[l] = x[r];
x[r] = temp;
l++;
r--;
}
}
public static void reverse(char[] x)
{
int l = 0;
int r = x.length - 1;
while (l < r)
{
char temp = x[l];
x[l] = x[r];
x[r] = temp;
l++;
r--;
}
}
public static void reverse(int[] x, int s, int e)
{
int l = s;
int r = e;
while (l < r)
{
int temp = x[l];
x[l] = x[r];
x[r] = temp;
l++;
r--;
}
}
static int length(int a)
{
int cou = 0;
while (a != 0)
{
a /= 10;
cou++;
}
return cou;
}
static int length(long a)
{
int cou = 0;
while (a != 0)
{
a /= 10;
cou++;
}
return cou;
}
static int cou(boolean[] a)
{
int res = 0;
for (boolean b : a)
{
if (b) res++;
}
return res;
}
static int cou(String s, char c)
{
int res = 0;
for (char ci : s.toCharArray())
{
if (ci == c) res++;
}
return res;
}
static int countC2(char[][] a, char c)
{
int co = 0;
for (int i = 0; i < a.length; i++)
for (int j = 0; j < a[0].length; j++)
if (a[i][j] == c) co++;
return co;
}
static int countI(int[] a, int key)
{
int co = 0;
for (int i = 0; i < a.length; i++)
if (a[i] == key) co++;
return co;
}
static int countI(int[][] a, int key)
{
int co = 0;
for (int i = 0; i < a.length; i++)
for (int j = 0; j < a[0].length; j++)
if (a[i][j] == key) co++;
return co;
}
static void fill(int[][] a, int v)
{
for (int i = 0; i < a.length; i++)
for (int j = 0; j < a[0].length; j++)
a[i][j] = v;
}
static void fill(long[][] a, long v)
{
for (int i = 0; i < a.length; i++)
for (int j = 0; j < a[0].length; j++)
a[i][j] = v;
}
static void fill(int[][][] a, int v)
{
for (int i = 0; i < a.length; i++)
for (int j = 0; j < a[0].length; j++)
for (int k = 0; k < a[0][0].length; k++)
a[i][j][k] = v;
}
static int max(int... a)
{
int res = Integer.MIN_VALUE;
for (int i : a)
{
res = Math.max(res, i);
}
return res;
}
static long min(long... a)
{
long res = Long.MAX_VALUE;
for (long i : a)
{
res = Math.min(res, i);
}
return res;
}
static int max(int[][] ar)
{
int res = Integer.MIN_VALUE;
for (int i[] : ar)
res = Math.max(res, max(i));
return res;
}
static int min(int... a)
{
int res = Integer.MAX_VALUE;
for (int i : a)
{
res = Math.min(res, i);
}
return res;
}
static int min(int[][] ar)
{
int res = Integer.MAX_VALUE;
for (int i[] : ar)
res = Math.min(res, min(i));
return res;
}
static int sum(int[] a)
{
int cou = 0;
for (int i : a)
cou += i;
return cou;
}
static int abs(int a)
{
return Math.abs(a);
}
static class FastScanner
{
private BufferedReader reader = null;
private StringTokenizer tokenizer = null;
public FastScanner(InputStream in)
{
reader = new BufferedReader(new InputStreamReader(in));
tokenizer = null;
}
public String next()
{
if (tokenizer == null || !tokenizer.hasMoreTokens())
{
try
{
tokenizer = new StringTokenizer(reader.readLine());
} catch (IOException e)
{
throw new RuntimeException(e);
}
}
return tokenizer.nextToken();
}
/*public String nextChar(){
return (char)next()[0];
}*/
public String nextLine()
{
if (tokenizer == null || !tokenizer.hasMoreTokens())
{
try
{
return reader.readLine();
} catch (IOException e)
{
throw new RuntimeException(e);
}
}
return tokenizer.nextToken("\n");
}
public long nextLong()
{
return Long.parseLong(next());
}
public int nextInt()
{
return Integer.parseInt(next());
}
public double nextDouble()
{
return Double.parseDouble(next());
}
public int[] nextIntArray(int n)
{
int[] a = new int[n];
for (int i = 0; i < n; i++)
{
a[i] = nextInt();
}
return a;
}
public int[] nextIntArrayDec(int n)
{
int[] a = new int[n];
for (int i = 0; i < n; i++)
{
a[i] = nextInt() - 1;
}
return a;
}
public int[][] nextIntArray2(int h, int w)
{
int[][] a = new int[h][w];
for (int hi = 0; hi < h; hi++)
{
for (int wi = 0; wi < w; wi++)
{
a[hi][wi] = nextInt();
}
}
return a;
}
public int[][] nextIntArray2Dec(int h, int w)
{
int[][] a = new int[h][w];
for (int hi = 0; hi < h; hi++)
{
for (int wi = 0; wi < w; wi++)
{
a[hi][wi] = nextInt() - 1;
}
}
return a;
}
//複数の配列を受け取る
public void nextIntArrays2ar(int[] a, int[] b)
{
for (int i = 0; i < a.length; i++)
{
a[i] = sc.nextInt();
b[i] = sc.nextInt();
}
}
public void nextIntArrays2arDec(int[] a, int[] b)
{
for (int i = 0; i < a.length; i++)
{
a[i] = sc.nextInt() - 1;
b[i] = sc.nextInt() - 1;
}
}
//複数の配列を受け取る
public void nextIntArrays3ar(int[] a, int[] b, int[] c)
{
for (int i = 0; i < a.length; i++)
{
a[i] = sc.nextInt();
b[i] = sc.nextInt();
c[i] = sc.nextInt();
}
}
//複数の配列を受け取る
public void nextIntArrays3arDecLeft2(int[] a, int[] b, int[] c)
{
for (int i = 0; i < a.length; i++)
{
a[i] = sc.nextInt() - 1;
b[i] = sc.nextInt() - 1;
c[i] = sc.nextInt();
}
}
public Integer[] nextIntegerArray(int n)
{
Integer[] a = new Integer[n];
for (int i = 0; i < n; i++)
{
a[i] = nextInt();
}
return a;
}
public char[] nextCharArray(int n)
{
char[] a = next().toCharArray();
return a;
}
public char[][] nextCharArray2(int h, int w)
{
char[][] a = new char[h][w];
for (int i = 0; i < h; i++)
{
a[i] = next().toCharArray();
}
return a;
}
//スペースが入っている場合
public char[][] nextCharArray2s(int h, int w)
{
char[][] a = new char[h][w];
for (int i = 0; i < h; i++)
{
a[i] = nextLine().replace(" ", "").toCharArray();
}
return a;
}
public char[][] nextWrapCharArray2(int h, int w, char c)
{
char[][] a = new char[h + 2][w + 2];
//char c = '*';
int i;
for (i = 0; i < w + 2; i++)
a[0][i] = c;
for (i = 1; i < h + 1; i++)
{
a[i] = (c + next() + c).toCharArray();
}
for (i = 0; i < w + 2; i++)
a[h + 1][i] = c;
return a;
}
//スペースが入ってる時用
public char[][] nextWrapCharArray2s(int h, int w, char c)
{
char[][] a = new char[h + 2][w + 2];
//char c = '*';
int i;
for (i = 0; i < w + 2; i++)
a[0][i] = c;
for (i = 1; i < h + 1; i++)
{
a[i] = (c + nextLine().replace(" ", "") + c).toCharArray();
}
for (i = 0; i < w + 2; i++)
a[h + 1][i] = c;
return a;
}
public long[] nextLongArray(int n)
{
long[] a = new long[n];
for (int i = 0; i < n; i++)
{
a[i] = nextLong();
}
return a;
}
public long[][] nextLongArray2(int h, int w)
{
long[][] a = new long[h][w];
for (int hi = 0; hi < h; hi++)
{
for (int wi = 0; wi < w; wi++)
{
a[hi][wi] = nextLong();
}
}
return a;
}
}
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
#define fst(t) std::get<0>(t)
#define snd(t) std::get<1>(t)
#define thd(t) std::get<2>(t)
#define fth(t) std::get<3>(t)
#define unless(p) if(!(p))
#define until(p) while(!(p))
using ll = long long;
using P = std::tuple<int,int>;
const int dx[8] = {-1, 1, 0, 0, -1, -1, 1, 1}, dy[8] = {0, 0, -1, 1, -1, 1, -1, 1};
int V, E, F;
// to, rev, cap, cost
std::vector<std::tuple<int, int, int, int>> G[200];
void addEdge(int u, int v, int cap, int cost){
G[u].emplace_back(v, G[v].size(), cap, cost);
G[v].emplace_back(u, G[u].size() - 1, 0, -cost);
}
int dist[1500];
tuple<int, int, int> prevs[1500];
const int INF = numeric_limits<int>::max() / 2;
void bellmanFord(int s){
std::fill(dist, dist+V, INF);
std::fill(prevs, prevs+V, std::make_tuple(-1, -1, -1));
dist[s] = 0;
for(int i=0;i<V;++i){
bool updated = false;
for(int u=0;u<V;++u){
for(int k=0;k<G[u].size();++k){
const auto& p = G[u][k];
int v, rev, cap, c;
std::tie(v, rev, cap, c) = p;
if(cap <= 0){continue;}
if(dist[v] > dist[u] + c){
updated = true;
dist[v] = dist[u] + c;
prevs[v] = std::make_tuple(u, k, rev);
}
}
}
if(!updated){break;}
}
}
int f(){
ll res = 0;
while(F > 0){
bellmanFord(0);
if(dist[V-1] == INF){
return -1;
}
int v = V - 1;
int d = F;
while(v != 0){
int pv, e_idx;
tie(pv, e_idx, ignore) = prevs[v];
d = min(d, thd(G[pv][e_idx]));
v = pv;
}
F -= d;
res += 1ll * d * dist[V-1];
v = V - 1;
while(v != 0){
int pv, e_idx, rev;
tie(pv, e_idx, rev) = prevs[v];
thd(G[pv][e_idx]) -= d;
thd(G[v][rev]) += d;
v = pv;
}
}
return res;
}
int main(){
std::cin.tie(nullptr);
std::ios::sync_with_stdio(false);
std::cin >> V >> E >> F;
for(int i=0;i<E;++i){
int u, v, c, d;
std::cin >> u >> v >> c >> d;
addEdge(u, v, c, d);
}
ll res = f();
std::cout << res << std::endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <vector>
#include <queue>
#define rep(i,n) for(int i=0; i<(n); i++)
using namespace std;
typedef long long int ll;
// Primal-Dual Algorithm
// ref: https://tjkendev.github.io/procon-library/python/min_cost_flow/primal-dual.html
class MinCostFlow {
public:
const ll INF = 1e18;
const ll MAX_COST = 1e9+9;
struct edge {
int to;
ll cap;
ll cost;
ll res;
int r_edge;
};
int N;
vector<vector<edge>> G;
MinCostFlow(int n): N(n), G(n) {}
void add_edge(int from, int to, int cap, int cost){
G[from].push_back({to, cap, cost, cap, (int)G[to].size()});
G[to].push_back({from, 0, -cost, 0, (int)G[from].size()-1});
}
ll flow(int S, int T, int flow){
ll res = 0;
vector<ll> H(N); // ポテンシャル
vector<int> pre_v(N), pre_e(N);
while(flow > 0){
vector<ll> D(N, INF);
priority_queue<pair<ll,int>> que;
D[S] = 0;
que.emplace(0, S);
while(!que.empty()){
ll d = que.top().first;
ll i = que.top().second;
que.pop();
if(D[i] < d) continue;
rep(v, G[i].size()) if(G[i][v].res > 0) {
edge &e = G[i][v];
if (D[e.to] > D[i] + e.cost + H[i] - H[e.to]) {
D[e.to] = D[i] + e.cost + H[i] - H[e.to];
pre_v[e.to] = i;
pre_e[e.to] = v;
que.emplace(D[e.to], e.to);
}
}
}
if( D[T] == INF ) return -1;
rep(i,N) H[i] += D[i];
ll f = flow;
for(int i=T; i != S; i = pre_v[i]) f = min(f, G[pre_v[i]][pre_e[i]].res);
flow -= f;
res += f * H[T];
for(int i=T; i != S; i = pre_v[i]){
edge &e = G[pre_v[i]][pre_e[i]];
e.res -= f;
G[i][e.r_edge].res += f;
}
}
return res;
}
void reset(){
for(auto &g: G) for(auto &e: g) e.res = e.cap;
}
};
// verify: AOJ GRL_6_B
#include <iostream>
int main(){
int V, E, F;
cin >> V >> E >> F;
MinCostFlow fl(V);
rep(i,E){
int u, v, c, d;
cin >> u >> v >> c >> d;
fl.add_edge(u, v, c, d);
}
cout << fl.flow(0, V-1, F) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #define DEBUG 1
#include <iostream>
#include <vector>
#include <tuple>
#include <queue>
using namespace std;
typedef long long ll;
// ------------------------------------------------------------
typedef tuple<ll, int> Info;
struct Edge
{
int to;
ll cap, cost;
int rev;
};
class MinCostFlow
{
int N;
vector<Edge> *G;
ll *h, *dist;
int *prev_v, *prev_e;
ll INFTY = 10000000000000010;
public:
MinCostFlow() {}
MinCostFlow(int n) : N(n)
{
G = new vector<Edge>[n];
h = new ll[n];
dist = new ll[n];
prev_v = new int[n];
prev_e = new int[n];
}
void add_edge(int from, int to, ll cap, ll cost)
{
G[from].push_back((Edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((Edge){from, 0, -cost, (int)G[from].size() - 1});
}
ll min_cost_flow(int s, int t, ll f)
{
ll res = 0;
fill(h, h + N, 0);
while (f > 0)
{
priority_queue<Info, vector<Info>, greater<Info>> Q;
fill(dist, dist + N, INFTY);
dist[s] = 0;
Q.push(Info(0, s));
while (!Q.empty())
{
Info p = Q.top();
Q.pop();
int v = get<1>(p);
if (dist[v] < get<0>(p))
{
continue;
}
for (auto i = 0; i < (int)G[v].size(); i++)
{
Edge &e = G[v][i];
ll tmp = dist[v] + e.cost + h[v] - h[e.to];
if (e.cap > 0 && dist[e.to] > tmp)
{
dist[e.to] = tmp;
prev_v[e.to] = v;
prev_e[e.to] = i;
Q.push(Info(dist[e.to], e.to));
}
}
}
if (dist[t] == INFTY)
{
return -1;
}
for (auto v = 0; v < N; v++)
{
h[v] += dist[v];
}
ll d = f;
for (auto v = t; v != s; v = prev_v[v])
{
d = min(d, G[prev_v[v]][prev_e[v]].cap);
}
f -= d;
res += d * h[t];
for (auto v = t; v != s; v = prev_v[v])
{
Edge &e = G[prev_v[v]][prev_e[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
// ------------------------------------------------------------
int N, M;
ll F;
MinCostFlow flow;
int main()
{
cin >> N >> M >> F;
flow = MinCostFlow(N);
for (auto i = 0; i < M; i++)
{
int u, v;
ll c, d;
cin >> u >> v >> c >> d;
flow.add_edge(u, v, c, d);
}
cout << flow.min_cost_flow(0, N - 1, F) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<cstring>
using namespace std;
typedef pair<int,int> P;//shortest pass,vertex number
const int MAX=100;
const int INF=1<<25;
class edge
{
public:
int to,cap,cost,rev;
edge(){}
edge(int to,int cap,int cost,int rev):to(to),cap(cap),cost(cost),rev(rev){}
};
int V;
vector<edge> G[MAX];
int h[MAX];
int dist[MAX];
int prevv[MAX],preve[MAX];
void add_edge(int from,int to,int cap,int cost)
{
G[from].push_back(edge(to,cap,cost,G[to].size()));
G[to].push_back(edge(from,0,-cost,G[from].size()-1));
return;
}
int mincostflow(int s,int t,int f)
{
int res=0;
memset(h,0,sizeof(h));
while(f>0)
{
priority_queue<P> Q;
fill(dist,dist+V,INF);
dist[s]=0;
Q.push(P(0,s));
while(!Q.empty())
{
P p=Q.top();Q.pop();
int v=p.second;
if(dist[v]<p.first*(-1))continue;
for(int i=0;i<G[v].size();i++)
{
edge &e=G[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to])
{
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to]=v;
preve[e.to]=i;
Q.push(P(dist[e.to]*(-1),e.to));
}
}
}
if(dist[t]==INF)return -1;
for(int v=0;v<V;v++)h[v]+=dist[v];
int d=f;
for(int v=t;v!=s;v=prevv[v])d=min(d,G[prevv[v]][preve[v]].cap);
f-=d;
res+=d*h[t];
for(int v=t;v!=s;v=prevv[v])
{
edge &e=G[prevv[v]][preve[v]];
e.cap-=d;
G[v][e.rev].cap+=d;
}
}
return res;
}
int main()
{
int E,F;cin>>V>>E>>F;
int u,v,c,d;
for(int i=0;i<E;i++)
{
cin>>u>>v>>c>>d;
add_edge(u,v,c,d);
}
cout<<mincostflow(0,V-1,F)<<endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<ctime>
using namespace std;
typedef long long ll;
bool debug = false;
const int NIL = -1;
const int INF = 1000000000;
const int NUM = 100010;
clock_t START, END;
int V, E, F;
struct Edge {
int from, to, cap, flow, cost;
Edge(int u, int v, int c, int f, int w) :from(u), to(v), cap(c), flow(f), cost(w) {}
};
struct Graph {
int n, m;
vector<Edge> edges;
vector<int> G[NUM];
int inq[NUM];
int d[NUM];
int a[NUM];
int p[NUM];
void init(int n) {
this->n = n;
for (int i = 0; i < n; i++)
G[i].clear();
edges.clear();
}
void AddEdge(int from, int to, int cap, int cost) {
edges.push_back(Edge(from, to, cap, 0, cost));
edges.push_back(Edge(to, from, 0, 0, -cost));
m = edges.size();
G[from].push_back(m - 2);
G[to].push_back(m - 1);
}
bool BellmanFord(int s, int t, int& flow, ll& cost) {
for (int i = 0; i < n; i++)
d[i] = INF;
memset(inq, 0, sizeof(inq));
d[s] = 0;
inq[s] = 1;
p[s] = 0;
a[s] = INF;
queue<int> Q;
Q.push(s);
while (!Q.empty()) {
int u = Q.front();
Q.pop();
inq[u] = 0;
for (int i = 0; i < G[u].size(); i++) {
Edge& e = edges[G[u][i]];
if (e.cap > e.flow && d[e.to] > d[u] + e.cost) {
d[e.to] = d[u] + e.cost;
p[e.to] = G[u][i];
a[e.to] = min(a[u], e.cap - e.flow);
if (!inq[e.to]) {
Q.push(e.to);
inq[e.to] = 1;
}
}
}
}
if (d[t] == INF)
return false;
flow += a[t];
if (a[t] <= F) {
cost += (ll)d[t] * (ll)a[t];
F -= a[t];
}
else {
cost += (ll)d[t] * (ll)(F);
F = 0;
}
for (int u = t; u != s; u = edges[p[u]].from) {
edges[p[u]].flow += a[t];
edges[p[u] ^ 1].flow -= a[t];
}
return true;
}
int MincostMaxflow(int s, int t, ll& cost) {
int flow = 0;
cost = 0;
while (BellmanFord(s, t, flow, cost));
return flow;
}
};
Graph solve;
int main(void)
{
if (debug) {
START = clock();
freopen("in29.txt", "r", stdin);
freopen("out.txt", "w", stdout);
}
ll COST;
int u, v, c, d, f;
cin >> V >> E >> F;
f = F;
solve.init(V);
for (int i = 0; i < E; i++) {
scanf("%d%d%d%d", &u, &v, &c, &d);
solve.AddEdge(u, v, c, d);
}
if (solve.MincostMaxflow(0, V - 1, COST) >= f)
cout << COST << endl;
else
cout << "-1" << endl;
if (debug) {
END = clock();
double endtime = (double)(END - START) / 1000;
printf("total time = %lf s", endtime);
}
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <algorithm>
#include <iostream>
#include <limits>
#include <vector>
using namespace std;
typedef int T; // cost type
typedef int U; // flow type
T INF = numeric_limits<T>::max(); // <limits>
struct edge {
int to, rev;
T cost;
U cap;
edge(int to, U cap, int rev, T cost) : to(to), rev(rev), cost(cost), cap(cap) {}
};
struct primal_dual {
int N;
vector<vector<edge> > graph;
vector<int> prev_v, prev_e;
vector<T> min_cost;
primal_dual() {}
primal_dual(int _N) { init(_N); }
void init(int _N) {
N = _N;
graph.resize(N);
prev_v.resize(N);
prev_e.resize(N);
min_cost.resize(N);
}
void add_edge(int u, int v, U cap, T cost) {
graph[u].push_back(edge(v, cap, graph[v].size(), cost));
graph[v].push_back(edge(u, 0, graph[u].size()-1, -cost));
}
T min_cost_flow(int s, int t, U F) {
T val = 0;
while (F > 0) {
fill(min_cost.begin(), min_cost.end(), INF);
min_cost[s] = 0;
bool updated = true;
while (updated) {
updated = false;
for (int v = 0; v < N; ++v) {
if (min_cost[v] == INF) continue;
for (int j = 0; j < graph[v].size(); ++j) {
edge& e = graph[v][j];
T cost = min_cost[v] + e.cost;
if (cost < min_cost[e.to] && e.cap > 0) {
updated = true;
min_cost[e.to] = cost;
prev_v[e.to] = v;
prev_e[e.to] = j;
}
}
}
}
if (min_cost[t] == INF) {
return (T)-1; // fail
}
U f = F;
for (int v = t; v != s; v = prev_v[v]) {
f = min(f, graph[prev_v[v]][prev_e[v]].cap);
}
F -= f;
val += (T)f * min_cost[t];
for (int v = t; v != s; v = prev_v[v]) {
edge& e = graph[prev_v[v]][prev_e[v]];
e.cap -= f;
graph[v][e.rev].cap += f;
}
}
return val;
}
};
int V, E, F;
primal_dual pd;
int main() {
cin >> V >> E >> F;
pd.init(V);
for (int j = 0; j < E; ++j) {
int u, v, c, d;
cin >> u >> v >> c >> d;
pd.add_edge(u, v, c, d);
}
cout << pd.min_cost_flow(0, V-1, F) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
const int MAX=100;
const int INF=1<<25;
class edge
{
public:
int to,cap,cost,rev;
edge(){}
edge(int to,int cap,int cost,int rev):to(to),cap(cap),cost(cost),rev(rev){}
};
int V;
vector<edge> G[MAX];
int dist[MAX];
int prevv[MAX],preve[MAX];
void add_edge(int from,int to,int cap,int cost)
{
G[from].push_back(edge(to,cap,cost,G[to].size()));
G[to].push_back(edge(from,0,-cost,G[from].size()-1));
return;
}
int mincostflow(int s,int t,int f)
{
int res=0;
while(f>0)
{
fill(dist,dist+V,INF);
dist[s]=0;
bool update=true;
while(update)
{
update=false;
for(int v=0;v<V;v++)
{
if(dist[v]==INF)continue;
for(int i=0;i<G[v].size();i++)
{
edge &e=G[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost)
{
dist[e.to]=dist[v]+e.cost;
prevv[e.to]=v;
preve[e.to]=i;
update=true;
}
}
}
}
if(dist[t]==INF)return -1;
int d=f;
for(int v=t;v!=s;v=prevv[v])d=min(d,G[prevv[v]][preve[v]].cap);
f-=d;
res+=d*dist[t];
for(int v=t;v!=s;v=prevv[v])
{
edge &e=G[prevv[v]][preve[v]];
e.cap-=d;
G[v][e.rev].cap+=d;
}
}
return res;
}
int main()
{
int E,F;cin>>V>>E>>F;
int u,v,c,d;
for(int i=0;i<E;i++)
{
cin>>u>>v>>c>>d;
add_edge(u,v,c,d);
}
cout<<mincostflow(0,V-1,F)<<endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | import os
import sys
from collections import defaultdict
import heapq
if os.getenv("LOCAL"):
sys.stdin = open("_in.txt", "r")
sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
"""
最小費用流
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B&lang=jp
"""
class MinCostFlow:
"""
最小費用流 ダイクストラ版
Primal Dual
"""
def __init__(self, graph=None, residual=None):
"""
:param list of (list of (int, int, int)) graph: (to, cap, cost) の隣接リスト
:param list of (list of (list of (int|list))) residual: (to, cap, cost, rev) の残余グラフ
"""
assert (graph and not residual) or (not graph and residual)
if graph:
self.graph = self.residual_graph(graph)
else:
self.graph = residual
@staticmethod
def residual_graph(graph):
"""
残余グラフ構築
:param list of (list of (int, int, int)) graph: (to, cap, cost) の隣接リスト
:rtype: list of (list of (list of (int|list)))
:return: (to, cap, cost, rev) の残余グラフ
"""
ret = [[] for _ in range(len(graph))]
for v in range(len(graph)):
for u, cap, cost in graph[v]:
rev = [v, 0, -cost]
edge = [u, cap, cost, rev]
rev.append(edge)
ret[v].append(edge)
ret[u].append(rev)
return ret
def solve(self, from_v, to_v, flow):
"""
:param int from_v:
:param int to_v:
:param int flow:
:rtype: int
"""
res = 0
h = [0] * len(self.graph)
prevv = [-1] * len(self.graph)
preve = [-1] * len(self.graph)
remains = flow
while remains > 0:
dist = [float('inf')] * len(self.graph)
dist[from_v] = 0
heap = [(0, from_v)]
# Dijkstra
while heap:
d, v = heapq.heappop(heap)
if d > dist[v]:
continue
for edge in self.graph[v]:
u, cap, cost, rev = edge
if cap > 0 and dist[v] + cost + h[v] - h[u] < dist[u]:
dist[u] = dist[v] + cost + h[v] - h[u]
prevv[u] = v
preve[u] = edge
heapq.heappush(heap, (dist[u], u))
if dist[to_v] == float('inf'):
# これ以上流せない
return -1
for i, d in enumerate(dist):
h[i] += d
# 最短路に流せる量
flow = remains
v = to_v
while v != from_v:
cap = preve[v][1]
flow = min(cap, flow)
v = prevv[v]
# 最短路に flow だけ流す
v = to_v
while v != from_v:
preve[v][1] -= flow
preve[v][3][1] += flow
v = prevv[v]
remains -= flow
res += flow * h[to_v]
return res
V, E, F = list(map(int, sys.stdin.readline().split()))
UVCD = [list(map(int, sys.stdin.readline().split())) for _ in range(E)]
graph = [[] for _ in range(V)]
for u, v, c, d in UVCD:
graph[u].append((v, c, d))
ans = MinCostFlow(graph=graph).solve(from_v=0, to_v=V - 1, flow=F)
print(ans)
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | import heapq
INF = 10 ** 5
class MinCostFlow:
"""
最小費用流の ダイクストラ版
蟻本 P.203
"""
def __init__(self, V):
self.V = V
self.G = [[] for _ in range(V)]
# 最小コスト見つかったあとに, route を取得するために使用
self.prevv = [INF] * V
self.preve = [INF] * V
self.h = [0] * V # ポテンシャル
def add_edge(self, from_, to_, cap, cost):
"""
from から to へ向かう容量 cap, コスト cost の辺をグラフに追加
"""
self.G[from_].append([to_, cap, cost, len(self.G[to_])])
self.G[to_].append([from_, 0, -cost, len(self.G[from_]) - 1])
def _get_dist(self, s, t, f):
"""
prevv,preve から 最大で流せる量を返す
:param s: 始点
:param t: 終点
:param f: 最大で流したい量
:return:
"""
d = f
v = t
while v != s:
pre_v = self.prevv[v]
pre_edge = self.preve[v]
d = min(d, self.G[pre_v][pre_edge][1]) # 1:cap のindex
v = pre_v
return d
def _update_cap(self, s, t, d):
""" capacity 更新 """
v = t
while v != s:
pre_v = self.prevv[v]
pre_e = self.preve[v]
e = self.G[pre_v][pre_e] # type:list
e[1] -= d # cap 更新
rev = e[3] # type:int
self.G[v][rev][1] += d # 逆辺のcap更新
v = pre_v
def solve(self, s, t, f):
res = 0
self.h = [0] * self.V
dist = [INF] * self.V # 最短経路
while f > 0:
que = [] # priority queue (<最短距離, 頂点の番号>) を要素にもつ. ダイクストラ用
for i in range(self.V):
dist[i] = INF
dist[s] = 0
heapq.heappush(que, (0, s))
while que:
p = heapq.heappop(que)
v = p[1] # 注目する頂点
if (dist[v] < p[0]): continue
for i in range(len(self.G[v])):
e = self.G[v][i]
to_ = e[0]
cap = e[1]
cost = e[2]
if cap <= 0: continue
# u -> v のとき, dist[v] は dist[u] + cost + h(u) -h(v) # p.202
if dist[to_] > dist[v] + cost + self.h[v] - self.h[to_]:
dist[to_] = dist[v] + cost + self.h[v] - self.h[to_]
self.prevv[to_] = v
self.preve[to_] = i
heapq.heappush(que, (dist[to_], to_))
if dist[t] == INF: # 経路なし(これ以上流せない)
return -1
for v in range(self.V):
self.h[v] += dist[v]
# 流せる量を取得
d = self._get_dist(s, t, f)
res += d * self.h[t]
f -= d
# update capacity
self._update_cap(s, t, d)
return res
v,e,f = [int(_) for _ in input().split()]
mcf = MinCostFlow(v)
for i in range(e):
mcf.add_edge( *[int(_) for _ in input().split()])
print(mcf.solve(0,v-1,f))
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | java | import java.util.List;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.lang.*;
class MinCostFlow{
private static final int inf = 1001001000;
static class Edge{
public int to;
public int cap;
public int cost;
public int rev;
public boolean isRev;
public Edge(final int t, final int ca, final int co, final int r, final boolean isrev){
to = t;
cap = ca;
cost = co;
rev = r;
isRev = isrev;
}
};
static class State implements Comparable<State>{
public int dist;
public int node;
public State(int d, int n){
this.dist = d;
this.node = n;
}
@Override
public int compareTo(State other){
return dist - other.dist;
}
};
private int numberOfNodes;
private List<Edge>[] graph;
private int[] h;
private int[] dist;
private int[] prevv;
private int[] preve;
@SuppressWarnings("unchecked")
public MinCostFlow(final int N){
numberOfNodes = N;
graph = new ArrayList[N];
for(int i = 0; i < N; i++){
graph[i] = new ArrayList<Edge>();
}
h = new int[N];
dist = new int[N];
prevv = new int[N];
preve = new int[N];
}
public void AddEdge(final int from, final int to, final int cap, final int cost){
graph[from].add(new Edge(to, cap, cost, graph[to].size(), false));
graph[to].add(new Edge(from, 0, -cost, graph[from].size()-1, true));
}
public int calc(final int s, final int t, final int flow){
int f = flow;
int res = 0;
while(f > 0){
PriorityQueue<State> Q = new PriorityQueue<>();
Arrays.fill(dist,inf);
dist[s] = 0;
Q.offer(new State(0,s));
while(!Q.isEmpty()){
State now = Q.poll();
if(dist[now.node] < now.dist){
continue;
}
for(int i = 0; i < graph[now.node].size(); i++){
Edge e = graph[now.node].get(i);
if(e.cap > 0 && dist[e.to] > dist[now.node] + e.cost + h[now.node] - h[e.to]){
dist[e.to] = dist[now.node] + e.cost + h[now.node] - h[e.to];
prevv[e.to] = now.node;
preve[e.to] = i;
Q.offer(new State(dist[e.to],e.to));
}
}
}
if(dist[t]==inf){
return -1;
}
for(int v = 0; v < numberOfNodes; v++){
h[v] += dist[v];
}
int d = f;
for(int v = t; v != s; v = prevv[v]){
d = Math.min(d, graph[prevv[v]].get(preve[v]).cap);
}
f -= d;
res += d * h[t];
for(int v = t; v != s; v = prevv[v]){
Edge e = graph[prevv[v]].get(preve[v]);
e.cap -= d;
graph[v].get(e.rev).cap += d;
}
}
return res;
}
};
public class Main{
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
int N = Integer.parseInt(sc.next());
int M = Integer.parseInt(sc.next());
int F = Integer.parseInt(sc.next());
MinCostFlow flow = new MinCostFlow(N);
for(int i = 0; i < M; i++){
int u = Integer.parseInt(sc.next());
int v = Integer.parseInt(sc.next());
int c = Integer.parseInt(sc.next());
int d = Integer.parseInt(sc.next());
flow.AddEdge(u, v, c, d);
}
sc.close();
System.out.println(flow.calc(0,N-1,F));
}
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include "bits/stdc++.h"
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int, int> PI;
typedef pair<LL, LL> PLL;
const LL MOD = 1000000007LL;
const int inf = 1e9;
const LL INF = 1e18;
const int MAX_V = 100;
struct edge {
int to, cap, cost, rev;
edge(int to, int cap, int cost, int rev) :to(to), cap(cap), cost(cost), rev(rev) {}
};
vector<edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
int V;
void add_edge(int from, int to, int cap, int cost) {
G[from].emplace_back(to, cap, cost, G[to].size());
G[to].emplace_back(from, 0, -cost, G[from].size() - 1);
}
int min_cost_flow(int s, int t, int f) {
int res = 0;
fill(h, h + V, 0);
while (f > 0) {
priority_queue<PI, vector<PI>, greater<PI>> que;
fill(dist, dist + V, inf);
dist[s] = 0;
que.push(PI(0, s));
while (!que.empty()) {
PI p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (int i = 0; i < G[v].size(); i++) {
edge e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(PI(dist[e.to], e.to));
}
}
}
if (dist[t] == inf) return -1;
for (int v = 0; v < V; v++) h[v] += dist[v];
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d*h[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main() {
cin >> V;
int E, F;
cin >> E >> F;
for (int i = 0; i < E; i++) {
int u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
cout << min_cost_flow(0, V - 1, F) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
using namespace std;
#define MAX_V 10000
#define INF 1000000001
typedef pair<int,int> P;
struct edge { int to,cap,cost,rev; };
int V;
vector<edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V],preve[MAX_V];
void init_edge(){
for(int i=0;i<V;i++)G[i].clear();
}
void add_edge(int from,int to,int cap,int cost){
G[from].push_back((edge){to,cap,cost,(int)G[to].size()});
G[to].push_back((edge){from,0,-cost,(int)G[from].size()-1});
}
int min_cost_flow(int s,int t,int f){
int res = 0;
fill(h,h+V,0);
while(f>0){
priority_queue< P, vector<P>, greater<P> > que;
fill( dist, dist+V , INF );
dist[s]=0;
que.push(P(0,s));
while(!que.empty()){
P p = que.top(); que.pop();
int v = p.second;
if(dist[v]<p.first)continue;
for(int i=0;i<(int)G[v].size();i++){
edge &e = G[v][i];
if(e.cap>0&&dist[e.to] > dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to]=v;
preve[e.to]=i;
que.push(P(dist[e.to],e.to));
}
}
}
if(dist[t]==INF){
return -1;
}
for(int v=0;v<V;v++)h[v]+=dist[v];
int d=f;
for(int v=t;v!=s;v=prevv[v]){
d=min(d,G[prevv[v]][preve[v]].cap);
}
f-=d;
res+=d*h[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main(){
int E,F,a,b,c,d;
cin>>V>>E>>F;
while(E--){
cin>>a>>b>>c>>d;
add_edge(a,b,c,d);
}
cout<<min_cost_flow(0,V-1,F)<<endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<iostream>
#include<vector>
#include<cstring>
using namespace std;
const int MAX_V = 200;
struct edge{
int to, cap, cost, rev;
};
int V;
vector<edge> G[MAX_V];
int dist[MAX_V]; // 頂点にflowを1流すときのコストの総和
int prevv[MAX_V], preve[MAX_V]; // prev_vertex, prev_edge
const int INF = 1<<30;
void add_edge(int from, int to, int cap, int cost){
G[from].push_back((edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((edge){from, 0, -cost, (int)G[from].size()-1});
}
// flow from s to t, the amount of that is f
int min_cost_flow(int s, int t, int f){
int res = 0;
while(f > 0){
for(int i = 0; i < V; i++) dist[i] = INF;
dist[s] = 0;
bool update = true;
// bellman-ford
while(update){
update = false;
for(int v = 0; v < V; v++){
if(dist[v] == INF) continue;
for(int i = 0; i < G[v].size(); i++){
edge &e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost){
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if(dist[t] == INF){
return -1;
}
int d = f;
// 辺を逆に辿る、流せるだけ流す
for(int v = t; v != s; v = prevv[v]){
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * dist[t];
for(int v = t; v != s; v = prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d; // 順方向に流したので-
G[v][e.rev].cap += d; // 逆方向に流したので+
}
}
return res;
}
int main(){
int e, f;
cin >> V >> e >> f;
for(int i = 0; i < e; i++){
int a, b, c, d;
cin >> a >> b >> c >> d;
add_edge(a, b, c, d);
}
cout << min_cost_flow(0, V-1, f) << endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i, a, b) for (int i = (a); i < (int)(b); ++i)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (int)(a); --i)
#define all(c) c.begin(),c.end()
#define sz(x) ((int)x.size())
using pii = pair<int, int>;
using vvi = vector<vector<int>>;
using vi = vector<int>;
constexpr int INF = 1001001001001001001LL;
struct MinCostFlow {
struct edge { int to, cap, cost, rev; };
int V;
vector<vector<edge>> G;
vi dist, prevv, preve;
MinCostFlow(int V) : V(V), G(V), dist(V), prevv(V), preve(V) {}
void add_edge(int from, int to, int cap, int cost) {
G[from].push_back((edge){ to, cap, cost, sz(G[to]) });
G[to ].push_back((edge){ from, 0, -cost, sz(G[from]) - 1 });
}
// 流せない場合は-1を返す
int get(int s, int t, int f) {
int res = 0;
while (f > 0) {
fill(all(dist), INF);
dist[s] = 0;
bool update = true;
while (update) {
update = false;
rep(v, 0, V) {
if (dist[v] == INF) continue;
rep(i, 0, sz(G[v])) {
auto &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if (dist[t] == INF) {
return -1;
}
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * dist[t];
for (int v = t; v != s; v = prevv[v]) {
auto &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
signed main() {
int V, E, F;
cin >> V >> E >> F;
MinCostFlow min_cost_flow(V);
rep(i, 0, E) {
int vs, vt, cap, cost;
cin >> vs >> vt >> cap >> cost;
min_cost_flow.add_edge(vs, vt, cap, cost);
}
cout << min_cost_flow.get(0, V - 1, F) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using Int = int64_t;
using UInt = uint64_t;
using C = std::complex<double>;
#define rep(i, n) for(Int i = 0; i < (Int)(n); ++i)
#define rep2(i, l, r) for(Int i = (Int)(l); i < (Int)(r); ++i)
#define guard(x) if( not (x) ) continue;
#ifndef LOCAL_
#define fprintf if( false ) fprintf
#endif
template<typename T>
using RQ = std::priority_queue<T, std::vector<T>, std::greater<T>>;
int main() {
Int v, e, f;
std::cin >> v >> e >> f;
std::vector<Int> ss(e+1), ts(e+1), cs(e+1), fs(e+1), bs(e+1);
rep2(i,1,e+1) {
Int a, b, c, d;
std::cin >> a >> b >> c >> d;
ss[i] = a, ts[i] = b, cs[i] = d, fs[i] = 0, bs[i] = c;
}
std::vector<std::vector<Int>> es(v);
rep2(i,1,e+1) {
Int s = ss[i], t = ts[i];
es[s].emplace_back(i);
es[t].emplace_back(-i);
}
Int res = 0;
Int source = 0, sink = v-1;
std::vector<Int> hs(v);
while( f > 0 ) {
RQ<std::pair<Int,Int>> q;
q.emplace(0, source);
std::vector<Int> ps(v, -1), xs(v, -1), ys(v);
xs[source] = 0;
ys[source] = f;
while( not q.empty() ) {
Int d, s; std::tie(d, s) = q.top(); q.pop();
guard( d == xs[s] );
for(Int i : es[s]) {
Int k = std::abs(i);
Int t = i > 0 ? ts[k] : ss[k];
Int tf = i > 0 ? bs[k] : fs[k];
guard( tf > 0 );
Int nd = d + (i>0?cs[k]:-cs[k]) + hs[s] - hs[t];
guard( xs[t] == -1 or xs[t] > nd );
xs[t] = nd;
ps[t] = i;
ys[t] = std::min(ys[s], tf);
q.emplace(nd, t);
}
}
Int tf = ys[sink];
f -= tf;
if( f > 0 and tf == 0 ) {
res = -1;
break;
}
rep(i, v) hs[i] += xs[i];
for(Int i=sink, k=ps[i]; i!=source; i=(k>0?ss[k]:ts[-k]), k=ps[i]) {
Int ak = std::abs(k);
if( k > 0 ) {
fs[ak] += tf;
bs[ak] -= tf;
}
else {
fs[ak] -= tf;
bs[ak] += tf;
}
}
res += tf * hs[sink];
if( f == 0 ) break;
}
printf("%ld\n", res);
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
using i64 = long long;
#define rep(i,s,e) for(int (i) = (s);(i) <= (e);(i)++)
#define all(x) x.begin(),x.end()
struct edge {
i64 from;
i64 to;
i64 cap;
i64 cost;
i64 rev;
};
i64 INF = 1e18;
i64 capacity_scaling_bflow(std::vector<std::vector<edge>>& g, std::vector<i64> b) {
i64 ans = 0;
i64 U = *std::max_element(begin(b), end(b));
i64 delta = (1 << ((int)(std::log2(U)) + 1));
int n = g.size();
std::vector<i64> e = b;
std::vector<i64> p(n, 0);
int zero = 0;
for(auto x : e) {
if(x == 0) zero++;
}
for(;delta > 0; delta >>= 1) {
if(zero == n) break;
for(int s = 0;s < n;s++) {
if(!(e[s] >= delta)) continue;
std::vector<std::size_t> pv(n, -1);
std::vector<std::size_t> pe(n, -1);
std::vector<i64> dist(n, INF);
using P = std::pair<i64,i64>;
std::priority_queue<P,std::vector<P>,std::greater<P>> que;
dist[s] = 0;
que.push({dist[s], s});
while(!que.empty()) {
int v = que.top().second;
i64 d = que.top().first;
que.pop();
if(dist[v] < d) continue;
for(std::size_t i = 0;i < g[v].size();i++) {
const auto& e = g[v][i];
std::size_t u = e.to;
if(e.cap == 0) continue;
if(dist[u] > dist[v] + e.cost + p[v] - p[u]) {
dist[u] = dist[v] + e.cost + p[v] - p[u];
pv[u] = v;
pe[u] = i;
que.push({dist[u], u});
}
}
}
for(int i = 0;i < n;i++) {
if(pv[i] != -1) p[i] += dist[i];
}
int t = 0;
for(;t < n;t++) {
if(!(e[s] >= delta)) break;
if(e[t] <= -delta && pv[t] != -1) {
std::size_t u = t;
for(;pv[u] != -1;u = pv[u]) {
ans += delta * g[pv[u]][pe[u]].cost;
g[pv[u]][pe[u]].cap -= delta;
g[u][g[pv[u]][pe[u]].rev].cap += delta;
}
e[u] -= delta;
e[t] += delta;
if(e[u] == 0) zero++;
if(e[t] == 0) zero++;
}
}
}
}
if(zero == n) return ans;
else return -1e18;
}
int main() {
i64 N,M,F;
cin >> N >> M >> F;
vector<vector<edge>> g(N + M);
vector<i64> e(N + M, 0);
int s = 0;
int t = N - 1;
e[s + M] = F;
e[t + M] = -F;
for(int i = 0;i < M;i++) {
i64 a,b,c,d;
cin >> a >> b >> c >> d;
e[i] = c;
e[a + M] -= c;
g[i].push_back({i, a + M, (i64)1e18, 0, (i64)g[a + M].size()});
g[a + M].push_back({a + M, i, 0, 0, (i64)g[i].size() - 1});
g[i].push_back({i, b + M, (i64)1e18, d, (i64)g[b + M].size()});
g[b + M].push_back({b + M, i, 0, -d, (i64)g[i].size() - 1});
}
i64 ans = capacity_scaling_bflow(g, e);
if(ans == -1e18) {
cout << -1 << endl;
}
else {
cout << ans << endl;
}
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | //#define __USE_MINGW_ANSI_STDIO 0
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VL;
typedef vector<VL> VVL;
typedef pair<int, int> PII;
#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)
#define REP(i, n) FOR(i, 0, n)
#define ALL(x) x.begin(), x.end()
#define IN(a, b, x) (a<=x&&x<b)
#define MP make_pair
#define PB push_back
const int INF = (1LL<<30);
const ll LLINF = (1LL<<60);
const double PI = 3.14159265359;
const double EPS = 1e-12;
const int MOD = 1000000007;
//#define int ll
template <typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template <typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }
int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};
#define MAX_V 10000
struct edge { int to, cap, cost, rev; };
int V;
vector<edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
void add_edge(int from, int to, int cap, int cost) {
G[from].PB({to, cap, cost, (int)G[to].size()});
G[to].PB({from, 0, -cost, (int)G[from].size()-1});
}
// s??????t????????????f???????°??????¨???
int min_cost_flow(int s, int t, int f) {
int res = 0;
fill(h, h+V, 0);
while(f > 0) {
priority_queue<PII, vector<PII>, greater<PII>> que;
fill(dist, dist+V, INF);
dist[s] = 0;
que.push({0, s});
while(que.size()) {
PII p = que.top(); que.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(int i=0; i<(int)G[v].size(); ++i) {
edge &e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push({dist[e.to], e.to});
}
}
}
// ????????\???????????????
if(dist[t] == INF) return -1;
REP(v, V) h[v] += dist[v];
int d = f;
for(int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for(int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
signed main(void)
{
int e, f;
cin >> V >> e >> f;
REP(i, e) {
int u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
cout << min_cost_flow(0, V-1, f) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <unordered_map>
#include <queue>
using namespace std;
typedef unordered_map<int,unordered_map<int,int>> double_map;
int dfs(
int now, int end, int flow, int *cost,
vector<bool> &arrived, vector<int> &dp, double_map &g, double_map &costs
) {
if(now==end||flow==0) return flow;
arrived[now] = true;
for(pair<int,int> p : costs[now]) {
int next = p.first;
int next_cost = p.second;
if(arrived[next]) continue;
if(dp[next]-dp[now]==next_cost) {
int res = dfs(next,end,min(flow,g[now][next]),cost,arrived,dp,g,costs);
if(res>0) {
g[now][next] -= res;
g[next][now] += res;
costs[next][now] = -costs[now][next];
if(g[now][next]==0) {
costs[now].erase(next);
}
*cost += res*next_cost;
return res;
}
}
}
return 0;
}
void calc(int v, double_map &costs, vector<int> &dp, int s) {
dp[s] = 0;
vector<int> vf(v,1<<30);
for(int loop = 0; loop < v; loop++) {
for(int now = 0; now < v; now++) {
if(dp[now]==1<<30) continue;
vf[now] = min(vf[now],dp[now]);
for(pair<int,int> p : costs[now]) {
int next = p.first;
int next_cost = p.second;
vf[next] = min(vf[next],dp[now]+next_cost);
}
}
dp.swap(vf);
}
}
int min_cost_flow(int v, double_map &g, double_map &costs, int f, int s, int e) {
int cost = 0;
int ans = 0;
while(ans<f) {
vector<int> dp(v,1<<30);
calc(v,costs,dp,s);
vector<bool> arrived(v);
int flow = dfs(s,e,f-ans,&cost,arrived,dp,g,costs);
if(flow<=0) {
return -1;
}
else ans += flow;
}
return cost;
}
int main() {
int v,e,f;
double_map g,costs;
cin >> v >> e >> f;
for(int i = 0; i < e; i++) {
int u,v2,c,d;
cin >> u >> v2 >> c >> d;
if(c<=0) continue;
g[u][v2] = c;
costs[u][v2] = d;
}
int cost = min_cost_flow(v,g,costs,f,0,v-1);
cout << cost << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | import sys
readline = sys.stdin.readline
from heapq import heappop as hpp, heappush as hp
class MinCostFlowwithDijkstra:
INF = 1<<31
def __init__(self, N):
self.N = N
self.Edge = [[] for _ in range(N)]
def add_edge(self, st, en, cap, cost):
self.Edge[st].append([en, cap, cost, len(self.Edge[en])])
self.Edge[en].append([st, 0, -cost, len(self.Edge[st])-1])
def get_mf(self, so, si, fl):
N = self.N
INF = self.INF
res = 0
Pot = [0]*N
geta = N
prv = [None]*N
prenum = [None]*N
while fl:
dist = [INF]*N
dist[so] = 0
Q = [so]
while Q:
cost, vn = divmod(hpp(Q), geta)
if dist[vn] < cost:
continue
for enum in range(len(self.Edge[vn])):
vf, cap, cost, _ = self.Edge[vn][enum]
cc = dist[vn] + cost - Pot[vn] + Pot[vf]
if cap > 0 and dist[vf] > cc:
dist[vf] = cc
prv[vf] = vn
prenum[vf] = enum
hp(Q, cc*geta + vf)
if dist[si] == INF:
return -1
for i in range(N):
Pot[i] -= dist[i]
cfl = fl
vf = si
while vf != so:
cfl = min(cfl, self.Edge[prv[vf]][prenum[vf]][1])
vf = prv[vf]
fl -= cfl
res -= cfl*Pot[si]
vf = si
while vf != so:
e = self.Edge[prv[vf]][prenum[vf]]
e[1] -= cfl
self.Edge[vf][e[3]][1] += cfl
vf = prv[vf]
return res
N, M, F = map(int, readline().split())
T = MinCostFlowwithDijkstra(N)
for _ in range(M):
u, v, cap, cost = map(int, readline().split())
T.add_edge(u, v, cap, cost)
print(T.get_mf(0, N-1, F))
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
using lint = long long;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> struct PrimalDual {
struct Edge {
int to, rev;
T cap, cost;
};
const int n;
const T inf = numeric_limits<T>::max();
VV<Edge> g;
V<T> pot, dist;
V<> pv, pe;
PrimalDual(int n) : n(n), g(n), pot(n), dist(n), pv(n), pe(n) {}
void add_edge(int from, int to, T cap, T cost) {
assert(from != to);
assert(cap >= 0);
assert(cost >= 0);
g[from].emplace_back(Edge{to, (int) g[to].size(), cap, cost});
g[to].emplace_back(Edge{from, (int) g[from].size() - 1, 0, -cost});
}
void dijkstra(int s) {
using P = pair<T, int>;
priority_queue< P, V<P>, greater<P> > pque;
fill(begin(dist), end(dist), inf);
pque.emplace(dist[s] = 0, s);
while (!pque.empty()) {
T d; int v;
tie(d, v) = pque.top(); pque.pop();
if (d > dist[v]) continue;
for (int i = 0; i < g[v].size(); ++i) {
const Edge& e = g[v][i];
if (e.cap <= 0 or dist[e.to] <= dist[v] + e.cost - (pot[e.to] - pot[v])) continue;
pv[e.to] = v;
pe[e.to] = i;
pque.emplace(dist[e.to] = dist[v] + e.cost - (pot[e.to] - pot[v]), e.to);
}
}
}
T min_cost_flow(int s, int t, T f) {
assert(s != t);
assert(f >= 0);
T res = 0;
fill(begin(pot), end(pot), 0);
while (f > 0) {
dijkstra(s);
if (dist[t] == inf) return -1;
for (int v = 0; v < n; ++v) pot[v] += dist[v];
T d = f;
for (int v = t; v != s; v = pv[v]) {
d = min(d, g[pv[v]][pe[v]].cap);
}
f -= d;
res += d * pot[t];
for (int v = t; v != s; v = pv[v]) {
Edge& e = g[pv[v]][pe[v]];
e.cap -= d;
g[v][e.rev].cap += d;
}
}
return res;
}
};
int main() {
cin.tie(nullptr); ios::sync_with_stdio(false);
int n, m, f; cin >> n >> m >> f;
PrimalDual<int> pd(n);
for (int i = 0; i < m; ++i) {
int from, to, cap, cost; cin >> from >> to >> cap >> cost;
pd.add_edge(from, to, cap, cost);
}
cout << pd.min_cost_flow(0, n - 1, f) << '\n';
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
using namespace std;
using UL=unsigned int;
using LL=long long;
using ULL=unsigned long long;
#define rep(i,n) for(UL i=0; i<(n); i++)
template<class T>
using nega_queue = priority_queue<T,vector<T>,greater<T>>;
struct Edge{ UL u,v; UL c; int d; UL r; };
UL N,M;
Edge J[2000];
vector<UL> E[100];
UL F;
int fAns = 0;
UL fD[100];
UL fPE[100];
UL fP[100]={};
void fDijkstra(){
rep(i,N) fD[i]=fPE[i]=~0u;
nega_queue<pair<UL,pair<UL,UL>>> Q; Q.push({0,{0,~0u}});
while(Q.size()){
UL d=Q.top().first;
UL p=Q.top().second.first;
UL pre=Q.top().second.second;
Q.pop();
if(fD[p]!=~0u) continue;
fD[p]=d;
fPE[p]=pre;
for(UL j:E[p]){
if(J[j].c==0)continue;
Q.push({d+J[j].d+fP[p]-fP[J[j].v],{J[j].v,j}});
}
}
rep(i,N) fP[i]+=fD[i];
}
void flow(){
fDijkstra();
if(fD[N-1]==~0u){ F=0; fAns=-1; return; }
UL p=N-1;
UL c=F;
while(p!=0){
c=min(c,J[fPE[p]].c);
p=J[fPE[p]].u;
}
p=N-1;
while(p!=0){
J[fPE[p]].c-=c;
J[J[fPE[p]].r].c+=c;
fAns += (int)c * J[fPE[p]].d;
p=J[fPE[p]].u;
}
F-=c;
}
int main(){
scanf("%u%u%u",&N,&M,&F);
rep(i,M){
UL u,v,c; int d; scanf("%u%u%u%d",&u,&v,&c,&d);
E[u].push_back(i);
E[v].push_back(M+i);
J[i]=Edge{u,v,c,d,M+i};
J[M+i]=Edge{v,u,0,-d,i};
}
while(F) flow();
printf("%d\n",fAns);
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define all(a) (a).begin(),(a).end()
typedef long long ll;
typedef pair<int, int> P;
typedef vector<int> vi;
typedef vector<P> vp;
typedef vector<ll> vll;
const int INF = 99999999;
const int MAX_V = 100000;
struct edge { int to, cap, cost, rev; };
int V, E, F;
vector<edge> G[MAX_V];
int h[MAX_V]; // potential
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V]; // privious vertex, edge
void add_edge(int from, int to, int cap, int cost) {
G[from].emplace_back((edge){to, cap, cost, (int)G[to].size()});
G[to].emplace_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
// get min cost flow from s to t
// if we cannot flow f, then return -1
int min_cost_flow(int s, int t, int f) {
int res = 0;
fill(h, h + V, 0);
while (f > 0) {
// update h by dijkstra
priority_queue<P, vector<P>, greater<P>> que;
fill(dist, dist + V, INF);
dist[s] = 0;
que.push(P(0, s));
while (!que.empty()) {
P p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
rep(i, G[v].size()) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) {
// no more flow
return -1;
}
rep(v, V) h[v] += dist[v];
// flow as much as possible along the minimum path from s to t
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, (int)G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
signed main() {
cin >> V >> E >> F;
rep(i, E) {
int u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
cout << min_cost_flow(0, V - 1, F) << endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define all(x) (x).begin(),(x).end()
const int mod=1000000007,MAX=103,INF=1<<30;
typedef pair<int,int> P;
struct edge{int to,cap,cost,rev;};
int V;
vector<edge> G[MAX];
int h[MAX];
int dist[MAX];
int prevv[MAX],preve[MAX];
void add_edge(int from,int to,int cap,int cost){
G[from].push_back((edge){to,cap,cost,int(G[to].size())});
G[to].push_back((edge){from,0,-cost,int(G[from].size()-1)});
}
int min_cost_flow(int s,int t,int f){
int res=0;
fill(h,h+V,0);
while(f>0){
priority_queue<P,vector<P>,greater<P>> que;
fill(dist,dist+V,INF);
dist[s]=0;
que.push(P(0,s));
while(!que.empty()){
P p=que.top();que.pop();
int v=p.second;
if(dist[v]<p.first) continue;
for(int i=0;i<G[v].size();i++){
edge &e=G[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to]=v;
preve[e.to]=i;
que.push(P(dist[e.to],e.to));
}
}
}
if(dist[t]==INF){
return -1;
}
for(int v=0;v<V;v++){
h[v]+=dist[v];
}
int d=f;
for(int v=t;v!=s;v=prevv[v]){
d=min(d,G[prevv[v]][preve[v]].cap);
}
f-=d;
res+=d*h[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e=G[prevv[v]][preve[v]];
e.cap-=d;
G[v][e.rev].cap+=d;
}
}
return res;
}//sからtへの流量fの最小費用流、流せない場合は-1
int main(){
int E,F;cin>>V>>E>>F;
for(int i=0;i<E;i++){
int a,b,c,d;cin>>a>>b>>c>>d;
add_edge(a,b,c,d);
}
int ans=min_cost_flow(0,V-1,F);
cout<<ans<<endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | import heapq
class edge:
def __init__(self, to, cap, cost, rev):
self.to: int = to
self.cap: int = cap
self.cost: int = cost
self.rev: int = rev
class min_cost_flow:
def __init__(self, N):
self.N: int = N
self.INF: int = 1000000000000000000
self.G = [[] for i in range(N)]
def add_edge(self, fro, to, cap, cost):
self.G[fro].append(edge(to, cap, int(cost), int(len(self.G[to]))))
self.G[to].append(edge(fro, 0, -int(cost), int(len(self.G[fro]) - 1)))
def solve(self, s, t, f):
N = self.N
prevv = [0 for i in range(N)]
preve = [0 for i in range(N)]
ret = 0
while 0 < f:
dist = [self.INF for i in range(N)]
dist[s] = 0
hq = [(0, s)]
heapq.heapify(hq)
while hq:
d, v = heapq.heappop(hq)
for i in range(len(self.G[v])):
e = self.G[v][i]
if 0 < e.cap and dist[v] + e.cost < dist[e.to]:
dist[e.to] = dist[v] + e.cost
prevv[e.to] = v
preve[e.to] = i
heapq.heappush(hq, (dist[e.to], e.to))
# 流せない
if dist[t] == self.INF:
return self.INF
d = f
v = t
while v != s:
d = min(d, self.G[prevv[v]][preve[v]].cap)
v = prevv[v]
f -= d
ret += d * dist[t]
v = t
while v != s:
e = self.G[prevv[v]][preve[v]]
e.cap -= d
self.G[v][e.rev].cap += d
v = prevv[v]
return ret
# http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B
v, e, f = map(int, input().split())
mcf = min_cost_flow(v)
for i in range(e):
ui, vi, ci, di = map(int, input().split())
mcf.add_edge(ui, vi, ci, di)
ans = mcf.solve(0, v-1, f)
if ans == mcf.INF:
print(-1)
else:
print(ans)
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
#define INF 1000000000
using namespace std;
typedef pair<int, int> pii;
class MinimumCostFlow {
struct edge {
int to, cap, cost, rev;
edge(int to_, int cap_, int cost_, int rev_)
: to(to_), cap(cap_), cost(cost_), rev(rev_) {}
};
int V;
vector<vector<edge>> G;
vector<int> h, dist, prevv, preve;
public:
MinimumCostFlow(int _V) : V(_V), G(_V), h(_V), dist(_V), prevv(_V), preve(_V) {}
void add(int from, int to, int cap, int cost) {
G[from].push_back(edge(to, cap, cost, G[to].size()));
G[to].push_back(edge(from, 0, -cost, G[from].size() - 1));
}
int calc(int s, int t, int f) {
int res = 0;
fill(h.begin(), h.end(), 0);
while (f > 0) {
priority_queue<pii, vector<pii>, greater<pii>> que;
fill(dist.begin(), dist.end(), INF);
dist[s] = 0;
que.push(pii(0, s));
while (!que.empty()) {
pii p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (size_t i = 0; i < G[v].size(); i++) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(pii(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) return -1;
for (int v = 0; v < V; v++)
h[v] += dist[v];
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
int main()
{
int V, E, F;
cin >> V >> E >> F;
MinimumCostFlow mcf(V);
for (int i = 0, u, v, c, d; i < E; i++) {
cin >> u >> v >> c >> d;
mcf.add(u, v, c, d);
}
cout << mcf.calc(0, V - 1, F) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <algorithm>
#include <vector>
#include <utility>
#include <queue>
#include <limits>
using namespace std;
//BEGIN
template <typename T, typename E>
struct PrimalDual {
struct edge {
int to, rev;
T cap;
E cost;
edge() {}
edge(int to, T cap, E cost, int rev) :to(to), cap(cap), cost(cost), rev(rev) {}
};
const E INF = numeric_limits<E>::max();
vector<vector<edge> > G;
vector<E> h, dist;
vector<int> prevv, preve;
PrimalDual() {}
PrimalDual(int n) :G(n), h(n), dist(n), prevv(n), preve(n) {}
void add_edge(int from, int to, T cap, E cost) {
G[from].emplace_back(to, cap, cost, G[to].size());
G[to].emplace_back(from, 0, -cost, G[from].size() - 1);
}
E min_cost_flow(int s, int t, T f) {
E res = 0;
priority_queue<pair<E, int>, vector<pair<E, int> >, greater<pair<E, int> > > pq;
while (f > 0) {
fill(dist.begin(), dist.end(), INF);
pq.emplace(0, s);
dist[s] = 0;
while (!pq.empty()) {
pair<E, int> p = pq.top();
pq.pop();
if (dist[p.second] < p.first) continue;
for (int i = 0; i < G[p.second].size(); ++i) {
edge& e = G[p.second][i];
E ncost = dist[p.second] + e.cost + h[p.second] - h[e.to];
if (e.cap > 0 && dist[e.to] > ncost) {
dist[e.to] = ncost;
prevv[e.to] = p.second; preve[e.to] = i;
pq.emplace(dist[e.to], e.to);
}
}
}
if (dist[t] == INF) return -1;
for (int v = 0; v < h.size(); ++v)
if (dist[v] < INF) h[v] += dist[v];
T d = f;
for (int v = t; v != s; v = prevv[v]) d = min(d, G[prevv[v]][preve[v]].cap);
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
edge& e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
//END
int main() {
int V, E, F; cin >> V >> E >> F;
PrimalDual<int, int> G(V);
for (int i = 0; i < E; ++i) {
int u, v, c, d; cin >> u >> v >> c >> d;
G.add_edge(u, v, c, d);
}
cout << G.min_cost_flow(0, V - 1, F) << endl;
return 0;
}
/*
created: 2020-01-06
https://onlinejudge.u-aizu.ac.jp/courses/library/5/GRL/6/GRL_6_B
*/
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
typedef unsigned long long ull;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<double, double> pdd;
const ull mod = 1e9 + 7;
#define REP(i,n) for(int i=0;i<(int)n;++i)
//debug
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
template < typename T >
void vprint(T &v){
REP(i, v.size()){
cout << v[i] << " ";
}
cout << endl;
}
struct edge{
ll to, cap, cost, rev;
edge(ll to, ll cap, ll cost, ll rev): to(to), cap(cap), cost(cost), rev(rev) {}
};
typedef vector<edge> edges;
typedef vector<edges> graph;
ll INF= LLONG_MAX/3;
void add_edge(graph &G, ll from, ll to, ll cap, ll cost){
G[from].push_back(edge(to, cap, cost, G[to].size()));
G[to].push_back(edge(from, 0, -cost, G[from].size()-1));
}
ll SSC(graph &G, vector<ll> &excess){
ll V = G.size();
map<ll, ll> E, D;
REP(i, V){
if(excess[i]>0) E[i] = excess[i];
if(excess[i]<0) D[i] = excess[i];
}
ll total_cost = 0;
vector<ll> pot(V, 0);
vector<ll> prevv(V);
vector<ll> preve(V);
while(!E.empty()){
ll s, t;
s = E.begin()->first;
// dijkstra
priority_queue< pll, vector<pll>, greater<pll> > pq;
bool feasibility_flag = false;
vector<ll> dist(V, INF);
vector<bool> visited(V, false);
dist[s] = 0;
pq.push(pll(0, s));
while(!pq.empty()){
pll p = pq.top();
pq.pop();
ll v = p.second;
visited[v] = true;
if(excess[v]<0){
t = v;
feasibility_flag = true;
break;
}
if(dist[v]<p.first) continue;
for(int i=0;i<G[v].size();i++){
edge &e = G[v][i];
if(e.cap>0 && dist[e.to]>dist[v]+e.cost+pot[v]-pot[e.to]){
dist[e.to] = dist[v] + e.cost + pot[v] - pot[e.to];
prevv[e.to] = v;
preve[e.to] = i;
pq.push(pll(dist[e.to], e.to));
}
}
}
// check fesibility
if(!feasibility_flag) return -1;
for(auto itr=D.begin();itr!=D.end();itr++)
// update potential
for(int i=0;i<V;i++) pot[i] += (visited[i] ? dist[i] : dist[t]);
// get flow amount
ll f = min(E[s], -D[t]);
ll d = f;
for(int v=t;v!=s;v=prevv[v]){
d = min(d, G[prevv[v]][preve[v]].cap);
}
// update excess and deficit
E[s] -= d;
if(E[s]==0) E.erase(s);
D[t] += d;
if(D[t]==0) D.erase(t);
// update total cost
total_cost += pot[t]*d;
// update residual graph
for(int v=t;v!=s;v=prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return total_cost;
}
int main(){
ll V, E, F;
cin >> V >> E >> F;
graph G(V);
REP(i, E){
ll u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(G, u, v, c, d);
}
vector<ll> excess(V, 0);
excess[0] = F;
excess[V-1] = -F;
ll res = SSC(G, excess);
cout << res << endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | java | import java.io.IOException;
import java.io.InputStream;
import java.util.*;
import java.math.BigInteger;
public class Main implements Runnable {
static int mod = 1000000007;
public static void main(String[] args) {
new Thread(null, new Main(), "", 1024 * 1024 * 1024).start();
}
public void run() {
FastScanner sc = new FastScanner();
int V = sc.nextInt();
int E = sc.nextInt();
int f = sc.nextInt();
CostedFlowGraph g = new CostedFlowGraph(V);
for(int i=0;i<E;i++){
g.addEdge(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
}
System.out.println(g.minCostFlow(0, V-1, f));
}
}
class CostedFlowGraph {
int V;
CFEdgeList[] elist;
int[] h;
int[] dd;
int[] preV;
int[] preEid;
public CostedFlowGraph(int V){
elist = new CFEdgeList[V];
for(int i=0;i<V;i++){
elist[i] = new CFEdgeList();
}
this.V = V;
h = new int[V]; //その頂点までにかかる費用の合計の最小値
dd = new int[V];
preV = new int[V];
preEid = new int[V];
}
void addEdge(int from, int to, int cap, int d){
CFEdge e = new CFEdge(to,cap,d);
CFEdge rev = new CFEdge(from,0,-d);
e.setRevEdge(rev);
rev.setRevEdge(e);
elist[from].add(e);
elist[to].add(rev);
}
//流量fのフローを流すための最小コストをDijkstraを用いた最短路反復で返す。不可能なら-1。
int minCostFlow(int s, int t, int f){
PriorityQueue<Node> q = new PriorityQueue<>();
int cost = 0;
while(f>0){
Arrays.fill(dd, Integer.MAX_VALUE);
dd[s] = 0;
q.clear();
q.add(new Node(s,0));
while(!q.isEmpty()){
Node now = q.poll();
if(dd[now.v] < now.d){ //既に展開済み
continue;
}
for(int i=0;i<elist[now.v].size();i++){
CFEdge e = elist[now.v].get(i);
int ddash = e.d + now.d + h[now.v] - h[e.to];
if(e.res() >0 && ddash < dd[e.to]){
preV[e.to] = now.v;
preEid[e.to] = i;
dd[e.to] = ddash;
q.add(new Node(e.to, ddash));
}
}
}
if(dd[t] == Integer.MAX_VALUE){ //不可能
break;
}
for(int i=0;i<V;i++){
h[i] += dd[i];
}
int minf = f;
for(int i=t;i!=s;i=preV[i]){
minf = Math.min(minf, elist[preV[i]].get(preEid[i]).res());
}
cost += minf * h[t];
f -= minf;
for(int i=t; i!=s; i=preV[i]){
elist[preV[i]].get(preEid[i]).f += minf;
elist[preV[i]].get(preEid[i]).rev.f -= minf;
}
}
if(f>0){ //不可能
cost = -1;
}
return cost;
}
//for Dijkstra
class Node implements Comparable<Node>{
int v;
int d;
public Node(int v, int d){
this.v = v;
this.d = d;
}
@Override
public int compareTo(Node o){
return Integer.compare(d, o.d);
}
}
public class CFEdgeList extends ArrayList<CFEdge>{
private static final long serialVersionUID = 8880792963612434406L;
}
public class CFEdge{
public int to;
public int cap; //容量
public int d; //コスト
public int f; //流量
public CFEdge rev;
public CFEdge(int to, int cap, int d){
this.to = to;
this.cap = cap;
this.d = d;
this.f = 0;
}
public void setRevEdge(CFEdge e){
this.rev = e;
}
//残余グラフで流せる量
int res(){
return cap - f;
}
}
}
class FastScanner {
private final InputStream in = System.in;
private final byte[] buffer = new byte[1024];
private int ptr = 0;
private int buflen = 0;
private boolean hasNextByte() {
if (ptr < buflen) {
return true;
} else {
ptr = 0;
try {
buflen = in.read(buffer);
} catch (IOException e) {
e.printStackTrace();
}
if (buflen <= 0) {
return false;
}
}
return true;
}
private int readByte() {
if (hasNextByte())
return buffer[ptr++];
else
return -1;
}
private static boolean isPrintableChar(int c) {
return 33 <= c && c <= 126;
}
public boolean hasNext() {
while (hasNextByte() && !isPrintableChar(buffer[ptr]))
ptr++;
return hasNextByte();
}
public String next() {
if (!hasNext())
throw new NoSuchElementException();
StringBuilder sb = new StringBuilder();
int b = readByte();
while (isPrintableChar(b)) {
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
public long nextLong() {
if (!hasNext())
throw new NoSuchElementException();
long n = 0;
boolean minus = false;
int b = readByte();
if (b == '-') {
minus = true;
b = readByte();
}
if (b < '0' || '9' < b) {
throw new NumberFormatException();
}
while (true) {
if ('0' <= b && b <= '9') {
n *= 10;
n += b - '0';
} else if (b == -1 || !isPrintableChar(b)) {
return minus ? -n : n;
} else {
throw new NumberFormatException();
}
b = readByte();
}
}
public int nextInt() {
long nl = nextLong();
if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
throw new NumberFormatException();
return (int) nl;
}
public int[] nextintArray(int n){
int[] a = new int[n];
for(int i=0;i<n;i++){
a[i] = nextInt();
}
return a;
}
public long[] nextlongArray(int n){
long[] a = new long[n];
for(int i=0;i<n;i++){
a[i] = nextLong();
}
return a;
}
public Integer[] nextIntegerArray(int n){
Integer[] a = new Integer[n];
for(int i=0;i<n;i++){
a[i] = nextInt();
}
return a;
}
public double nextDouble() {
return Double.parseDouble(next());
}
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
#define rep(i,j,k) for(int i = (int)j;i <= (int)k;i ++)
#define debug(x) cerr<<#x<<":"<<x<<endl
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;
#define NUM 100
struct Edge{
Edge(int arg_to,int arg_capacity,int arg_cost,int arg_rev_index){
to = arg_to;
capacity = arg_capacity;
cost = arg_cost;
rev_index = arg_rev_index;
}
int to,capacity,cost,rev_index;
};
int V;
vector<Edge> G[NUM];
int dist[NUM];
int pre_node[NUM],pre_edge[NUM];
void add_edge(int from,int to,int capacity,int cost){
G[from].push_back(Edge(to,capacity,cost,G[to].size()));
G[to].push_back(Edge(from,0,-cost,G[from].size()-1));
}
int min_cost_flow(int source,int sink,int flow){
int ret = 0;
while(flow > 0){
for(int i = 0; i < V; i++)dist[i] = BIG_NUM;
dist[source] = 0;
bool update = true;
while(update){
update = false;
for(int node_id = 0; node_id < V; node_id++){
if(dist[node_id] == BIG_NUM)continue;
for(int i = 0; i < G[node_id].size(); i++){
Edge &e = G[node_id][i];
if(e.capacity > 0 && dist[e.to] > dist[node_id]+e.cost){
dist[e.to] = dist[node_id]+e.cost;
pre_node[e.to] = node_id;
pre_edge[e.to] = i;
update = true;
}
}
}
}
if(dist[sink] == BIG_NUM){
return -1;
}
int tmp_flow = flow;
for(int node_id = sink; node_id != source; node_id = pre_node[node_id]){
tmp_flow = min(tmp_flow,G[pre_node[node_id]][pre_edge[node_id]].capacity);
}
flow -= tmp_flow;
ret += tmp_flow*dist[sink];
for(int node_id = sink; node_id != source; node_id = pre_node[node_id]){
Edge &e = G[pre_node[node_id]][pre_edge[node_id]];
e.capacity -= tmp_flow;
G[node_id][e.rev_index].capacity += tmp_flow;
}
}
return ret;
}
int main(){
int E,F;
scanf("%d %d %d",&V,&E,&F);
int from,to,capacity,cost;
for(int loop = 0; loop < E; loop++){
scanf("%d %d %d %d",&from,&to,&capacity,&cost);
add_edge(from,to,capacity,cost);
}
printf("%d\n", min_cost_flow(0,V-1,F));
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | // AOJ GRL_6_B: Network Flow - Minimum Cost Flow
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using Pi = pair<int, int>;
using Pl = pair<ll, ll>;
using Ti = tuple<int, int, int>;
using Tl = tuple<ll, ll, ll>;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define F first
#define S second
#define Get(t, i) get<(i)>((t))
#define all(v) (v).begin(), (v).end()
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define reps(i, f, n) for(int i = (int)(f); i < (int)(n); i++)
#define each(a, b) for(auto& a : b)
const int inf = 1 << 25;
const ll INF = 1LL << 55;
struct edge
{
int to, capacity, cost, rev;
edge(){}
edge(int to, int capacity, int cost, int rev):to(to), capacity(capacity), cost(cost), rev(rev){}
};
struct PrimalDual
{
vector< vector<edge> > graph;
vector<int> potential, mincost, prevv, preve;
PrimalDual(int V):graph(V), potential(V), mincost(V), prevv(V), preve(V){}
void add_edge(int from, int to, int capacity, int cost)
{
graph[from].push_back(edge(to, capacity, cost, (int)graph[to].size()));
graph[to].push_back(edge(from, 0, -cost, (int)graph[from].size()-1));
}
int min_cost_flow(int source, int sink, int f)
{
int ret = 0;
fill(potential.begin(), potential.end(), 0);
fill(prevv.begin(), prevv.end(), -1);
fill(preve.begin(), preve.end(), -1);
while(f > 0) {
priority_queue<Pi, vector<Pi>, greater<Pi> > que;
fill(mincost.begin(), mincost.end(), inf);
mincost[source] = 0;
que.push(Pi(0, source));
while(!que.empty()) {
Pi p = que.top(); que.pop();
int v = p.second;
if(mincost[v] < p.first) continue;
for(int i = 0; i < (int)graph[v].size(); i++) {
edge& e = graph[v][i];
int dual_cost = mincost[v] + e.cost + potential[v] - potential[e.to];
if(e.capacity > 0 && dual_cost < mincost[e.to]) {
mincost[e.to] = dual_cost;
prevv[e.to] = v; preve[e.to] = i;
que.push(Pi(mincost[e.to], e.to));
}
}
}
if(mincost[sink] == inf) return -1;
for(int v = 0; v < (int)graph.size(); v++) potential[v] += mincost[v];
int d = f;
for(int v = sink; v != source; v = prevv[v]) d = min(d, graph[prevv[v]][preve[v]].capacity);
f -= d;
ret += d * potential[sink];
for(int v = sink; v != source; v = prevv[v]) {
edge& e = graph[prevv[v]][preve[v]];
e.capacity -= d;
graph[v][e.rev].capacity += d;
}
}
return ret;
}
};
int main()
{
int V, E, F;
cin >> V >> E >> F;
PrimalDual mnf(V);
while(E--) {
int u, v, c, d;
cin >> u >> v >> c >> d;
mnf.add_edge(u, v, c, d);
}
cout << mnf.min_cost_flow(0, V-1, F) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <cstdio>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
using Weight=long long;
static const Weight INF=1LL<<57;
template <class T>
using gp_queue=priority_queue<T, deque<T>, less<T>>;
struct Arc {
// accessible to the reverse edge
size_t src, dst;
Weight capacity, cost, flow;
size_t rev;
Arc() {}
Arc(size_t src, size_t dst, Weight capacity, Weight cost=0):
src(src), dst(dst), capacity(capacity), cost(cost), flow(0), rev(-1)
{}
Weight residue() const {
return capacity - flow;
}
};
bool operator<(const Arc &e, const Arc &f) {
if (e.cost != f.cost) {
return e.cost > f.cost;
} else if (e.capacity != f.capacity) {
return e.capacity > f.capacity;
} else {
return e.src!=f.src? e.src<f.src : e.dst<f.dst;
}
}
using Arcs=vector<Arc>;
using Node=vector<Arc>;
using FlowNetwork=vector<Node>;
void connect(FlowNetwork &g, size_t s, size_t d, Weight c=1, Weight k=0) {
g[s].push_back(Arc(s, d, c, k));
g[d].push_back(Arc(d, s, 0, -k));
g[s].back().rev = g[d].size()-1;
g[d].back().rev = g[s].size()-1;
}
void join(FlowNetwork &g, size_t s, size_t d, Weight c=1, Weight k=0) {
g[s].push_back(Arc(s, d, c, k));
g[d].push_back(Arc(d, s, c, k));
g[s].back().rev = g[d].size()-1;
g[d].back().rev = g[s].size()-1;
}
Weight mincost_flow(FlowNetwork &g, size_t s, size_t t, Weight F=INF) {
size_t V=g.size();
vector<Arc *> prev(V, NULL);
Weight mcost=0;
while (F > 0) {
vector<Weight> d(V, INF); d[s]=0;
for (bool updated=true; updated;) {
updated = false;
for (size_t v=0; v<V; ++v) {
if (d[v] == INF) continue;
for (Arc &e: g[v]) {
if (e.capacity <= 0) continue;
if (d[e.dst] > d[e.src] + e.cost) {
d[e.dst] = d[e.src] + e.cost;
prev[e.dst] = &e;
updated = true;
}
}
}
}
if (d[t] == INF)
return -1;
Weight f=F;
for (Arc *e=prev[t]; e!=NULL; e=prev[e->src])
f = min(f, e->capacity);
F -= f;
mcost += f * d[t];
for (Arc *e=prev[t]; e!=NULL; e=prev[e->src]) {
e->capacity -= f;
g[e->dst][e->rev].capacity += f;
}
}
return mcost;
}
int main() {
size_t V, E;
Weight F;
scanf("%zu %zu %lld", &V, &E, &F);
FlowNetwork g(V);
for (size_t i=0; i<E; ++i) {
size_t u, v;
Weight c, d;
scanf("%zu %zu %lld %lld", &u, &v, &c, &d);
connect(g, u, v, c, d);
}
printf("%lld\n", mincost_flow(g, 0, V-1, F));
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
struct min_cost_flow_graph {
struct edge {
int from, to;
T cap, f;
U cost;
};
vector<edge> edges;
vector<vector<int>> g;
int n, st, fin;
T required_flow, flow;
U cost;
min_cost_flow_graph(int n, int st, int fin, T required_flow)
: n(n), st(st), fin(fin), required_flow(required_flow) {
assert(0 <= st && st < n && 0 <= fin && fin < n && st != fin);
g.resize(n);
flow = 0;
cost = 0;
}
void clear_flow() {
for (const edge &e : edges) {
e.f = 0;
}
flow = 0;
cost = 0;
}
void add(int from, int to, T cap = 1, T rev_cap = 0, U cost = 1) {
assert(0 <= from && from < n && 0 <= to && to < n);
g[from].emplace_back(edges.size());
edges.push_back({from, to, cap, 0, cost});
g[to].emplace_back(edges.size());
edges.push_back({to, from, rev_cap, 0, -cost});
}
U min_cost_flow() {
vector<U> h(n, 0);
while (flow < required_flow) {
vector<int> preve(n);
vector<U> dist(n, numeric_limits<U>::max() / 2);
priority_queue<pair<U, int>, vector<pair<U, int>>, greater<pair<U, int>>> pq;
dist[st] = 0;
pq.emplace(dist[st], st);
while (!pq.empty()) {
U expected = pq.top().first;
int i = pq.top().second;
pq.pop();
if (expected != dist[i]) {
continue;
}
for (int id : g[i]) {
const edge &e = edges[id];
if (0 < e.cap - e.f && dist[e.from] + e.cost + h[e.from] - h[e.to] < dist[e.to]) {
dist[e.to] = dist[e.from] + e.cost + h[e.from] - h[e.to];
preve[e.to] = id;
pq.emplace(dist[e.to], e.to);
}
}
}
if (dist[fin] == numeric_limits<U>::max() / 2) {
return -1;
}
for (int i = 0; i < n; i++) {
h[i] += dist[i];
}
T d = required_flow - flow;
for (int v = fin; v != st; v = edges[preve[v]].from) {
d = min(d, edges[preve[v]].cap - edges[preve[v]].f);
}
flow += d;
cost += d * h[fin];
for (int v = fin; v != st; v = edges[preve[v]].from) {
edges[preve[v]].f += d;
edges[preve[v] ^ 1].f -= d;
}
}
return cost;
}
};
int main() {
int n, m, f;
cin >> n >> m >> f;
min_cost_flow_graph<int, int> g(n, 0, n - 1, f);
for (int i = 0; i < m; i++) {
int from, to, cap, cost;
cin >> from >> to >> cap >> cost;
g.add(from, to, cap, 0, cost);
}
cout << g.min_cost_flow() << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <algorithm>
#include <functional>
#include <iostream>
#include <queue>
#include <vector>
using namespace std;
namespace Flow {
struct Edge {
int to, capacity, cost, reverse;
Edge(int to, int capacity, int cost, int reverse) :
to(to), capacity(capacity), cost(cost), reverse(reverse) {}
};
template <int MaxN> class PrimalDual {
int n = MaxN;
vector<Edge> g[MaxN];
public:
void clear(int n) {
this->n = n;
for (int i = 0; i < n; ++i)
g[i].clear();
}
void push(int from, int to, int capacity = 1, int cost = 0) {
g[from].emplace_back(to, capacity, cost, g[to].size());
g[to].emplace_back(from, 0, -cost, g[from].size() - 1);
}
pair<int, int> flow(int s, int t, int f = 1 << 30) {
int flow = f, cost = 0;
static int prevv[MaxN], preve[MaxN], dist[MaxN], h[MaxN];
fill(h, h + n, 0);
while (flow > 0) {
fill(dist, dist + n, 1 << 30);
dist[s] = 0;
using P = pair<int, int>;
priority_queue<P, vector<P>, greater<P>> q;
for (q.emplace(0, s); q.size(); ) {
auto p = q.top();
q.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (auto& e : g[v]) {
int d = dist[v] + e.cost + h[v] - h[e.to];
if (e.capacity > 0 && dist[e.to] > d) {
dist[e.to] = d;
prevv[e.to] = v;
preve[e.to] = &e - &g[v][0];
q.emplace(d, e.to);
}
}
}
if (dist[t] == 1 << 30) break;
for (int v = 0; v < n; ++v)
h[v] += dist[v];
int d = flow;
for (int v = t; v != s; v = prevv[v])
d = min(d, g[prevv[v]][preve[v]].capacity);
flow -= d;
cost += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
auto& e = g[prevv[v]][preve[v]];
e.capacity -= d;
g[v][e.reverse].capacity += d;
}
}
return { f - flow, cost };
}
};
}
int main() {
int n, m, f;
cin >> n >> m >> f;
Flow::PrimalDual<100> pd;
pd.clear(n);
for (int i = 0; i < m; ++i) {
int a, b, c, d;
cin >> a >> b >> c >> d;
pd.push(a, b, c, d);
}
auto p = pd.flow(0, n - 1, f);
cout << (p.first == f ? p.second : -1) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | //最短経路長が短い経路に流せるだけ流す。
//ただし、順辺のコストをcとしたときに逆辺のコストは-cにする (フローを押し戻すとき、コストも押し戻すため）。
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
const int VMAX = 100;
struct Edge {
int from, to, flow, cost, rev;
Edge(int from, int to, int flow, int cost, int rev) {
this->from = from;
this->to = to;
this->flow = flow;
this->cost = cost;
this->rev = rev;
}
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &g, int from, int to, int flow, int cost) {
g[from].push_back(Edge(from, to, flow, cost, g[to].size()));
g[to].push_back(Edge(to, from, 0, -cost, g[from].size() - 1));
}
int dfs(Graph &g, int s, int t, int flow, bool yet[], int level[]) {
yet[s] = false;
if (s == t) return flow;
for (int i = 0; i < g[s].size(); i++) {
int v = g[s][i].to;
if (g[s][i].flow > 0 && yet[v] && level[v] == level[s] + g[s][i].cost) {
int res = dfs(g, v, t, min(flow, g[s][i].flow), yet, level);
if (res > 0) {
int r = g[s][i].rev;
g[s][i].flow -= res;
g[v][r].flow += res;
return res;
}
}
}
return 0;
}
int minCostflow(Graph &g, int s, int t, int flow) {
const int INF_DIST = 11451419;
const int INF_FLOW = 11451419;
const int ERROR_RETURN = -1;
int level[VMAX];
bool yet[VMAX];
queue<int> que;
int i;
int ret = 0;
while (true) {
for (i = 0; i < g.size(); i++) level[i] = INF_DIST;
que.push(s); level[s] = 0;
while (!que.empty()) {
int v = que.front(); que.pop();
for (i = 0; i < g[v].size(); i++) {
int nv = g[v][i].to;
if (g[v][i].flow > 0 && level[nv] > level[v] + g[v][i].cost) {
level[nv] = level[v] + g[v][i].cost;
que.push(nv);
}
}
}
if (level[t] >= INF_DIST) break;
while (true) {
for (i = 0; i < g.size(); i++) yet[i] = true;
int f = dfs(g, s, t, INF_FLOW, yet, level);
if (f == 0) break;
flow -= f;
ret += f * level[t];
if (flow <= 0) {
ret += flow * level[t];
return ret;
}
}
}
return -1;
}
int n, m, f;
int u, v, c, d;
Graph g;
int main() {
cin >> n >> m >> f;
g.resize(n);
for (int i = 0; i < m; i++) {
cin >> u >> v >> c >> d;
add_edge(g, u, v, c, d);
}
cout << minCostflow(g, 0, n - 1, f) << endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
using namespace std;
struct PrimalDual{
const int INF = 1<<28;
typedef pair<int,int> P;
struct edge{
int to,cap,cost,rev;
edge(){}
edge(int to,int cap,int cost,int rev):to(to),cap(cap),cost(cost),rev(rev){}
};
int V;
vector<vector<edge> > G;
vector<int> h,dist,prevv,preve;
PrimalDual(){}
PrimalDual(int V):V(V){init();}
void init(){
for(int i=0;i<(int)G.size();i++) G[i].clear();
G.clear();
h.clear();
dist.clear();
prevv.clear();
preve.clear();
G.resize(V);
h.resize(V);
dist.resize(V);
prevv.resize(V);
preve.resize(V);
}
void add_edge(int from,int to,int cap,int cost){
G[from].push_back(edge(to,cap,cost,G[to].size()));
G[to].push_back(edge(from,0,-cost,G[from].size()-1));
}
int min_cost_flow(int s,int t,int f){
int res=0;
fill(h.begin(),h.begin()+V,0);
while(f>0){
priority_queue<P,vector<P>,greater<P> > que;
fill(dist.begin(),dist.begin()+V,INF);
dist[s]=0;
que.push(P(0,s));
while(!que.empty()){
P p=que.top();que.pop();
int v=p.second;
if(dist[v]<p.first) continue;
for(int i=0;i<(int)G[v].size();i++){
edge &e=G[v][i];
if(e.cap>0&&dist[e.to]>dist[v]+e.cost+h[v]-h[e.to]){
dist[e.to]=dist[v]+e.cost+h[v]-h[e.to];
prevv[e.to]=v;
preve[e.to]=i;
que.push(P(dist[e.to],e.to));
}
}
}
if(dist[t]==INF){
return -1;
}
for(int v=0;v<V;v++) h[v]+=dist[v];
int d=f;
for(int v=t;v!=s;v=prevv[v]){
d=min(d,G[prevv[v]][preve[v]].cap);
}
f-=d;
res+=d*h[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e=G[prevv[v]][preve[v]];
e.cap-=d;
G[v][e.rev].cap+=d;
}
}
return res;
}
};
int main(){
int v,e,f;
cin>>v>>e>>f;
PrimalDual pd(v);
for(int i=0;i<e;i++){
int u,v,c,d;
cin>>u>>v>>c>>d;
pd.add_edge(u,v,c,d);
}
cout<<pd.min_cost_flow(0,v-1,f)<<endl;
return 0;
}
/*
verified on 2017/06/29
http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_6_B
*/ |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <numeric>
#include <queue>
#include <algorithm>
#include <utility>
#include <functional>
using namespace std;
//template<typename Int = int>
using Int = int;
struct PrimalDual {
struct Edge {
int dst;
Int cap, flow, cost;
int rev;
bool isRev;
Edge(int dst, Int cap, Int flow, Int cost, int rev, bool isRev)
:dst(dst), cap(cap), flow(flow), cost(cost), rev(rev), isRev(isRev) {
}
};
int n;
vector<vector<Edge>> g;
PrimalDual(int n_) : n(n_), g(vector<vector<Edge>>(n_)) {}
void addEdge(int src, int dst, Int cap, Int cost) {
g[src].emplace_back(dst, cap, 0, cost, g[dst].size(), false);
g[dst].emplace_back(src, cap, cap, -cost, g[src].size() - 1, true);
}
vector<Int> h, dist;
vector<int> prevv, preve;
Int solve(int s, int t, Int f) {
Int res = 0;
h.assign(n, 0);
dist.assign(n, 0);
prevv.assign(n, 0);
preve.assign(n, 0);
while (f > 0) {
if (!dijkstra(s,t)) return -1;
for (int i = 0; i < n; ++i) h[i] += dist[i];
Int d = f;
for (int v = t; v != s; v = prevv[v]) {
Edge &e = g[prevv[v]][preve[v]];
d = min(d, residue(e));
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
Edge &e = g[prevv[v]][preve[v]];
e.flow += d;
g[v][e.rev].flow -= d;
}
}
return res;
}
bool dijkstra(int s, int t) {
constexpr Int INF = numeric_limits<Int>::max();
dist.assign(n, INF);
dist[s] = 0;
priority_queue<pair<Int, int>> q;
fill(dist.begin(), dist.end(), INF);
dist[s] = 0;
q.emplace(0, s);
while (q.size()) {
int d, v;
tie(d, v) = q.top();
q.pop();
d = -d;
if (dist[v] < d) continue;
for (int i = 0; i < (int)g[v].size(); ++i) {
Edge &e = g[v][i];
if (residue(e) > 0 && dist[e.dst] > dist[v] + e.cost + h[v] - h[e.dst]) {
dist[e.dst] = dist[v] + e.cost + h[v] - h[e.dst];
prevv[e.dst] = v;
preve[e.dst] = i;
q.emplace(-dist[e.dst], e.dst);
}
}
}
return dist[t] != INF;
}
Int residue(const Edge& e) { return e.cap - e.flow; }
};
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int n, m, f;
cin >> n >> m >> f;
PrimalDual pd(n);
for (int i = 0; i < m; i++) {
int u, v, c, d;
cin >> u >> v >> c >> d;
pd.addEdge(u, v, c, d);
}
cout << pd.solve(0, n - 1, f) << endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<stack>
#include<map>
#include<set>
#include<bitset>
using namespace std;
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; ++i )
#define rep(i,n) REP(i,0,n)
typedef long long ll;
typedef pair<int,int> pint;
typedef pair<ll,int> pli;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;
template<typename F,typename C>
struct MinCostFlow{
struct Edge{
int to;
F cap;
C cost;
int rev;
};
const C INF;
vector<vector<Edge>> v;
vector<C> pot,dist;
vector<int> prevv,preve;
MinCostFlow(int n):v(n),INF(numeric_limits<C>::max()){}
void add_edge(int from,int to,F cap,C cost){
v[from].emplace_back((Edge){to,cap,cost,(int)v[to].size()});
v[to].emplace_back((Edge){from,0,-cost,(int)v[from].size()-1});
}
C min_cost_flow(int s,int t,F f){
int n=v.size();
C ret=0;
using P = pair<C,int>;
priority_queue<P,vector<P>,greater<P>> que;
pot.assign(n, 0);
prevv.assign(n, -1);
preve.assign(n, -1);
while(f>0){
dist.assign(n, INF);
que.emplace(0,s);
dist[s]=0;
while(!que.empty()){
int cur=que.top().second;
C d=que.top().first;
que.pop();
if(dist[cur]<d)continue;
rep(i,v[cur].size()){
Edge &e = v[cur][i];
C next_cost = dist[cur]+e.cost+pot[cur]-pot[e.to];
if(e.cap>0 && dist[e.to]>next_cost){
dist[e.to]=next_cost;
prevv[e.to]=cur;
preve[e.to]=i;
que.emplace(dist[e.to],e.to);
}
}
}
if(dist[t]==INF)return -1;
rep(i,n)pot[i]+=dist[i];
F add_flow = f;
for(int u=t;u!=s;u=prevv[u]){
add_flow=min(add_flow,v[prevv[u]][preve[u]].cap);
}
f-=add_flow;
ret+=add_flow*pot[t];
for(int u=t;u!=s;u=prevv[u]){
Edge& e=v[prevv[u]][preve[u]];
e.cap -=add_flow;
v[e.to][e.rev].cap += add_flow;
}
}
return ret;
}
};
int main(){
int n,m,f;
cin>>n>>m>>f;
MinCostFlow<int,int> mcf(n);
rep(i,m){
int a,b,c,d;
cin>>a>>b>>c>>d;
mcf.add_edge(a, b, c, d);
}
cout<<mcf.min_cost_flow(0, n-1, f)<<endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using Int = int64_t;
using UInt = uint64_t;
using C = std::complex<double>;
#define rep(i, n) for(Int i = 0; i < (Int)(n); ++i)
#define rep2(i, l, r) for(Int i = (Int)(l); i < (Int)(r); ++i)
#define guard(x) if( not (x) ) continue;
#ifndef LOCAL_
#define fprintf if( false ) fprintf
#endif
template<typename T>
using RQ = std::priority_queue<T, std::vector<T>, std::greater<T>>;
int main() {
Int v, e, f;
std::cin >> v >> e >> f;
std::vector<Int> ss(e+1), ts(e+1), cs(e+1), fs(e+1), bs(e+1);
rep2(i,1,e+1) {
Int a, b, c, d;
std::cin >> a >> b >> c >> d;
ss[i] = a, ts[i] = b, cs[i] = d, fs[i] = 0, bs[i] = c;
}
std::vector<std::vector<Int>> es(v);
rep2(i,1,e+1) {
Int s = ss[i], t = ts[i];
es[s].emplace_back(i);
es[t].emplace_back(-i);
}
Int res = 0;
Int source = 0, sink = v-1;
std::vector<Int> hs(v);
while( f > 0 ) {
RQ<std::pair<Int,Int>> q;
q.emplace(0, source);
std::vector<Int> ps(v, -1), xs(v, -1), ys(v);
xs[source] = 0;
ys[source] = f;
std::vector<bool> visited(v);
while( not q.empty() ) {
Int d, s; std::tie(d, s) = q.top(); q.pop();
guard( d == xs[s] );
assert( not visited[s] );
visited[s] = true;
for(Int i : es[s]) {
Int k = std::abs(i);
Int t = i > 0 ? ts[k] : ss[k];
Int tf = i > 0 ? bs[k] : fs[k];
guard( tf > 0 );
Int nd = d + (i>0?cs[k]:-cs[k]) + hs[s] - hs[t];
guard( xs[t] == -1 or xs[t] > nd );
assert( nd >= 0 );
xs[t] = nd;
ps[t] = i;
ys[t] = std::min(ys[s], tf);
assert( not visited[t] );
q.emplace(nd, t);
}
}
Int tf = ys[sink];
fprintf(stderr, "tf = %ld\n", tf);
f -= tf;
if( f > 0 and tf == 0 ) {
res = -1;
break;
}
rep(i, v) hs[i] += xs[i];
for(Int i=sink, k=ps[i]; i!=source; i=(k>0?ss[k]:ts[-k]), k=ps[i]) {
Int ak = std::abs(k);
fprintf(stderr, "i=%ld, k=%ld\n", i, k);
if( k > 0 ) {
fs[ak] += tf;
bs[ak] -= tf;
}
else {
fs[ak] -= tf;
bs[ak] += tf;
}
}
res += tf * hs[sink];
if( f == 0 ) break;
rep2(i,1,e+1) {
fprintf(stderr, "%ld -> %ld : cost=%ld : ->=%ld : <-=%ld\n", ss[i], ts[i], cs[i], fs[i], bs[i]);
}
}
printf("%ld\n", res);
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | from typing import List, Iterator, Optional, Tuple
def trace_back(sink: int,
predecessors: List[Optional[Tuple[int, int]]]) -> Iterator[List[int]]:
p = predecessors[sink]
while p is not None:
v, i = p
yield edges[v][i]
p = predecessors[v]
def min_cost_flow(source: int, sink: int, required_flow: int) -> int:
res = 0
while required_flow:
dist = [float('inf')] * n
dist[source] = 0
predecessors: List[Optional[Tuple[int, int]]] = [None] * n
while True:
updated = False
for v in range(n):
if dist[v] == float('inf'):
continue
for i, (remain, target, cost, _) in enumerate(edges[v]):
new_dist = dist[v] + cost
if remain and dist[target] > new_dist:
dist[target] = new_dist
predecessors[target] = (v, i)
updated = True
if not updated:
break
if dist[sink] == float('inf'):
return -1
aug = min(required_flow, min(e[0] for e in trace_back(sink, predecessors)))
required_flow -= aug
res += int(aug * dist[sink])
for e in trace_back(sink, predecessors):
remain, target, cost, idx = e
e[0] -= aug
edges[target][idx][0] += aug
return res
if __name__ == "__main__":
n, m, f = map(int, input().split())
edges = [[] for _ in range(n)] # type: ignore
for _ in range(m):
s, t, c, d = map(int, input().split())
es, et = edges[s], edges[t]
ls, lt = len(es), len(et)
es.append([c, t, d, lt])
et.append([0, s, -d, ls])
print(min_cost_flow(0, n - 1, f))
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define all(a) (a).begin(),(a).end()
typedef long long ll;
typedef pair<int, int> P;
typedef vector<int> vi;
typedef vector<P> vp;
typedef vector<ll> vll;
const int INF = 99999999;
const int MAX_V = 100000;
struct edge { int to, cap, cost, rev; };
int V, E, F;
vector<edge> G[MAX_V];
int h[MAX_V]; // potential
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V]; // privious vertex, edge
void add_edge(int from, int to, int cap, int cost) {
G[from].emplace_back((edge){to, cap, cost, (int)G[to].size()});
G[to].emplace_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
// get min cost flow from s to t
// if we can flow f, then return -1
int min_cost_flow(int s, int t, int f) {
int res = 0;
fill(h, h + V, 0);
while (f > 0) {
// update h by dijkstra
priority_queue<P, vector<P>, greater<P>> que;
fill(dist, dist + V, INF);
dist[s] = 0;
que.push(P(0, s));
while (!que.empty()) {
P p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
rep(i, G[v].size()) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) {
// no more flow
return -1;
}
rep(v, V) h[v] += dist[v];
// flow as much as possible along the minimum path from s to t
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, (int)G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
signed main() {
cin >> V >> E >> F;
rep(i, E) {
int u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
cout << min_cost_flow(0, V - 1, F) << endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <functional>
#include <vector>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#include <set>
#include <bitset>
#include <tuple>
#include <cassert>
#include <exception>
#include <iomanip>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> P;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<string> vs;
typedef vector<P> vp;
#define rep(i,a,n) for(ll i = (a);i < (n);i++)
#define per(i,a,n) for(ll i = (a);i > (n);i--)
#define lep(i,a,n) for(ll i = (a);i <= (n);i++)
#define pel(i,a,n) for(ll i = (a);i >= (n);i--)
#define clr(a,b) memset((a),(b),sizeof(a))
#define pb push_back
#define mp make_pair
#define all(c) (c).begin(),(c).end()
#define sz size()
#define print(X) cout << (X) << endl
#define fprint(NUM,X) cout << fixed << setprecision(NUM) << (X) << endl
#define fprints(NUM,X,Y) cout << fixed << setprecision(NUM) << (X) << " " << (Y) << endl
static const int INF = 1e+9+7;
ll n,m,l;
string s,t;
ll d[200010],dp[1010][1010];
double w[1000],v[1000];
double box[200010];
struct edge{ int to,cap,cost,rev; };
static const int MAX = 100000;
int V;
vector<edge> graph[MAX];
int dist[MAX];
int prevv[MAX],preve[MAX];
void add_edge(int from,int to,int cap,int cost){
graph[from].push_back((edge){ to,cap,cost,(int)graph[to].size() });
graph[to].push_back((edge){ from,0,-cost,(int)graph[from].size()-1 });
}
int min_cost_flow(int s,int t,int f){
int res = 0;
while(f > 0){
fill(dist,dist + V,INF);
dist[s] = 0;
bool update = true;
while(update){
update = false;
for(int v = 0;v < V;v++){
if(dist[v] == INF)continue;
for(int i = 0;i < graph[v].size();i++){
edge &e = graph[v][i];
if(e.cap > 0 && dist[e.to] > dist[v] + e.cost){
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if(dist[t] == INF)return -1;
int d = f;
for(int v = t;v != s;v = prevv[v]){
d = min(d,graph[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * dist[t];
for(int v = t;v != s;v = prevv[v]){
edge &e = graph[prevv[v]][preve[v]];
e.cap -= d;
graph[v][e.rev].cap += d;
}
}
return res;
}
int main(){
cin >> V >> n >> m;
rep(i,0,n){
int a,b,c,e;
cin >> a >> b >> c >> e;
add_edge(a,b,c,e);
}
print(min_cost_flow(0,V-1,m));
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
struct min_cost_flow_graph {
struct edge {
int from, to;
T cap, f;
U cost;
};
vector<edge> edges;
vector<vector<int>> g;
int n, st, fin;
T required_flow, flow;
U cost;
min_cost_flow_graph(int n, int st, int fin, T required_flow)
: n(n), st(st), fin(fin), required_flow(required_flow) {
assert(0 <= st && st < n && 0 <= fin && fin < n && st != fin);
g.resize(n);
flow = 0;
cost = 0;
}
void clear_flow() {
for (const edge &e : edges) {
e.f = 0;
}
flow = 0;
cost = 0;
}
void add(int from, int to, T cap = 1, T rev_cap = 0, U cost = 1) {
assert(0 <= from && from < n && 0 <= to && to < n);
g[from].emplace_back(edges.size());
edges.push_back({from, to, cap, 0, cost});
g[to].emplace_back(edges.size());
edges.push_back({to, from, rev_cap, 0, -cost});
}
U min_cost_flow() {
while (flow < required_flow) {
vector<int> prevv(n), preve(n);
vector<U> dist(n, numeric_limits<U>::max() / 4);
dist[st] = 0;
for (bool update = true; update; ) {
update = false;
for (int i = 0; i < n; i++) {
for (int id : g[i]) {
const edge &e = edges[id];
if (0 < e.cap - e.f && dist[e.from] + e.cost < dist[e.to]) {
dist[e.to] = dist[e.from] + e.cost;
prevv[e.to] = e.from;
preve[e.to] = id;
update = true;
}
}
}
}
if (dist[fin] == numeric_limits<U>::max() / 4) {
return -1;
}
T d = required_flow - flow;
for (int v = fin; v != st; v = prevv[v]) {
d = min(d, edges[preve[v]].cap - edges[preve[v]].f);
}
flow += d;
cost += d * dist[fin];
for (int v = fin; v != st; v = prevv[v]) {
edges[preve[v]].f += d;
edges[preve[v] ^ 1].f -= d;
}
}
return cost;
}
};
int main() {
int n, m, f;
cin >> n >> m >> f;
min_cost_flow_graph<int, int> g(n, 0, n - 1, f);
for (int i = 0; i < m; i++) {
int from, to, cap, cost;
cin >> from >> to >> cap >> cost;
g.add(from, to, cap, 0, cost);
}
cout << g.min_cost_flow() << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
/*
* 最小費用流
* O(FVE)
*/
struct MinCostFlow{
const int inf = std::numeric_limits<int>::max()/3;
struct edge{
int to,cap,cost,rev;
edge(){}
edge(int t,int ca,int co,int r) : to(t),cap(ca),cost(co),rev(r){}
};
int V; // # of node
vector<vector<edge>> G;
MinCostFlow(){}
MinCostFlow(int V_){ init(V_); }
void init(int V_){
V = V_;
G.resize(V);
}
void add_edge(int from,int to,int cap,int cost){
G[from].emplace_back(to,cap,cost,G[to].size());
G[to].emplace_back(from,0,-cost,G[from].size()-1);
}
// s->tに向かって流量f流すときの最小費用
// もしs->tに向かってf流せない場合は-1
int min_cost_flow(int s,int t,int f){
int res=0;
vector<int> dist(V,inf);
vector<int> prevv(V),preve(V);
while(f>0){
dist.assign(V,inf);
dist[s] = 0;
bool update=true;
while(update){
update=false;
for(int v=0;v<V;v++){
if(dist[v]==inf) continue;
for(int i=0;i<(int)G[v].size();i++){
edge &e = G[v][i];
if(e.cap>0 and dist[e.to] > dist[v]+e.cost){
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if(dist[t] == inf) return -1; // 流量fを流すことは不可能
int d = f;
for(int v=t;v!=s;v=prevv[v]) d = min(d,G[prevv[v]][preve[v]].cap);
f -= d;
res += d * dist[t];
for(int v=t;v!=s;v=prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
int main(){
int V,E,F; cin >> V >> E >> F;
MinCostFlow graph(V);
for(int i=0;i<E;i++){
int u,v,c,d;
cin >> u >> v >> c >> d;
graph.add_edge(u,v,c,d);
}
cout << graph.min_cost_flow(0,V-1,F) << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <functional>
#include <cassert>
typedef long long ll;
using namespace std;
#define debug(x) cerr << #x << " = " << x << endl;
#define mod 1000000007 //1e9+7(prime number)
#define INF 1000000000 //1e9
#define LLINF 2000000000000000000LL //2e18
#define SIZE 100010
/* Minimum Cost Flow */
struct MinimumCostFlow{
typedef pair<int,int> P;
struct edge {
int to, cap, cost, rev;
edge(int a, int b, int c, int d):to(a),cap(b),cost(c),rev(d){}
};
vector<vector<edge> > G;
vector<int> h, dist, prevv, preve;
int V;
MinimumCostFlow(int v):G(v,vector<edge>()),prevv(v,0),preve(v,0),V(v){}
int add_edge(int from,int to,int cap, int cost){
int id = G[from].size();
G[from].push_back(edge(to,cap,cost,G[to].size()));
G[to].push_back(edge(from,0,-cost,G[from].size() - 1));
return id;
}
int solve(int s, int t, int f){
int res = 0;
h.assign(V,0);
while(f > 0){
priority_queue<P, vector<P>, greater<P> > pq;
dist.assign(V, INF);
dist[s] = 0;
pq.push(P(0, s));
while(pq.size()){
P p = pq.top(); pq.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(int i = 0; i < G[v].size(); i++){
edge &e = G[v][i];
int d = dist[v] + e.cost + h[v] - h[e.to];
if(e.cap > 0 && dist[e.to] > d){
dist[e.to] = d;
prevv[e.to] = v;
preve[e.to] = i;
pq.push(P(dist[e.to], e.to));
}
}
}
if(dist[t] == INF) return -1;
for(int v = 0; v < V; v++) h[v] += dist[v];
int d = f;
for(int v = t; v != s; v = prevv[v])
d = min(d, G[prevv[v]][preve[v]].cap);
f -= d;
res += d * h[t];
for(int v = t; v != s; v = prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
};
int main(){
int v,e,f;
int a,b,c,d;
scanf("%d%d%d",&v,&e,&f);
MinimumCostFlow flow(v);
for(int i=0;i<e;i++){
scanf("%d%d%d%d",&a,&b,&c,&d);
flow.add_edge(a,b,c,d);
}
cout << flow.solve(0, v-1, f) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <fstream>
#include <cassert>
#include <typeinfo>
#include <vector>
#include <stack>
#include <cmath>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <cstdio>
#include <queue>
#include <iomanip>
#include <cctype>
#include <random>
#include <complex>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<P,int> pip;
typedef vector<pip> vip;
const int inf=1<<29;
const ll INF=1ll<<50;
const double pi=acos(-1);
const double eps=1e-8;
const ll mod=1e9+7;
const int dx[4]={0,1,0,-1},dy[4]={1,0,-1,0};
class Network{
private:
int V;
struct edge{
int to,cap,cost,rev;
};
vector<vector<edge> > g;
vi h,d,pv,pe;
public:
Network(int v){
V=v;
g=vector<vector<edge> >(v);
}
void add_edge(int s,int t,int cap,int cost){
g[s].push_back(edge{t,cap,cost,(int)g[t].size()});
g[t].push_back(edge{s,0,-cost,(int)g[s].size()-1});
}
int min_cost_flow(int s,int t,int f){
int res=0;
h=pv=pe=vi(V);
while(f>0){
priority_queue<P> q;
d=vi(V,inf);
d[s]=0;
q.push({0,s});
while(!q.empty()){
P p=q.top();
q.pop();
int v=p.second;
if(d[v]<-p.first) continue;
for(int i=0;i<g[v].size();i++){
edge &e=g[v][i];
if(e.cap>0&&d[e.to]>d[v]+e.cost+h[v]-h[e.to]){
d[e.to]=d[v]+e.cost+h[v]-h[e.to];
pv[e.to]=v;
pe[e.to]=i;
q.push({-d[e.to],e.to});
}
}
}
if(d[t]==inf) return -1;
for(int i=0;i<V;i++) h[i]+=d[i];
int D=f;
for(int i=t;i!=s;i=pv[i]) D=min(D,g[pv[i]][pe[i]].cap);
f-=D;
res+=D*h[t];
for(int i=t;i!=s;i=pv[i]){
edge &e=g[pv[i]][pe[i]];
e.cap-=D;
g[i][e.rev].cap+=D;
}
}
return res;
}
};
int n,m,f;
int main(){
cin>>n>>m>>f;
Network net(n);
for(int i=0;i<m;i++){
int v,u,c,d;
cin>>v>>u>>c>>d;
net.add_edge(v,u,c,d);
}
cout<<net.min_cost_flow(0,n-1,f)<<endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <utility>
#include <queue>
#define llint long long
#define inf 1e18
using namespace std;
typedef pair<llint, llint> P;
struct edge{
llint to, cap, cost, rev;
edge(){}
edge(llint a, llint b, llint c, llint d){
to = a, cap = b, cost = c, rev = d;
}
};
llint n, m, F;
llint S, T;
vector<edge> G[205];
llint dist[205];
llint prevv[205], preve[205];
llint h[205];
void BellmanFord()
{
for(int i = 0; i <= T; i++) dist[i] = inf;
dist[S] = 0, prevv[S] = -1;
bool update = true;
while(update){
update = false;
for(int i = 0; i <= T; i++){
for(int j = 0; j < G[i].size(); j++){
if(G[i][j].cap == 0) continue;
if(dist[G[i][j].to] > dist[i] + G[i][j].cost){
dist[G[i][j].to] = dist[i] + G[i][j].cost;
prevv[G[i][j].to] = i;
preve[G[i][j].to] = j;
update = true;
}
}
}
}
}
void Dijkstra()
{
for(int i = 0; i <= T; i++) dist[i] = inf;
dist[S] = 0, prevv[S] = -1;
priority_queue< P, vector<P>, greater<P> > Q;
Q.push( make_pair(0, S) );
llint v, d;
while(Q.size()){
d = Q.top().first;
v = Q.top().second;
Q.pop();
if(dist[v] < d) continue;
for(int i = 0; i < G[v].size(); i++){
if(G[v][i].cap == 0) continue;
llint u = G[v][i].to, c = h[v] - h[u] + G[v][i].cost;
if(dist[u] > d + c){
dist[u] = d + c;
prevv[u] = v;
preve[u] = i;
Q.push( make_pair(dist[u], u) );
}
}
}
}
void add_edge(llint from, llint to, llint cap, llint cost)
{
G[from].push_back( edge(to, cap, cost, G[to].size()) );
G[to].push_back( edge(from, 0, -cost, G[from].size()-1) );
}
int main()
{
cin >> n >> m >> F;
llint u, v, c, d;
for(int i = 1; i <= m; i++){
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
S = 0, T = n-1;
BellmanFord();
for(int i = 0; i <= T; i++) h[i] = dist[i];
llint f = F, ans = 0;
while(f > 0){
Dijkstra();
if(dist[T] >= inf) break;
llint p = T, flow = f;
while(prevv[p] != -1){
flow = min(flow, G[prevv[p]][preve[p]].cap);
p = prevv[p];
}
p = T;
while(prevv[p] != -1){
G[prevv[p]][preve[p]].cap -= flow;
G[p][G[prevv[p]][preve[p]].rev].cap += flow;
p = prevv[p];
}
f -= flow;
ans += (dist[T] + h[T] - h[S]) * flow;
for(int i = 0; i <= T; i++) h[i] += dist[i];
}
if(f > 0) ans = -1;
cout << ans << endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <vector>
#include <cstring>
#include <string>
#include <algorithm>
#include <iomanip>
#include <queue>
#include <functional>
using namespace std;
const int MAX_V = 100010;
using Capacity = int;
using Cost = int;
const auto inf = numeric_limits<Capacity>::max() / 8;
struct Edge {
int dst;
Capacity cap, cap_orig;
Cost cost;
int revEdge; bool isRev;
Edge(int dst, Capacity cap, Cost cost, int revEdge, bool isRev)
:dst(dst), cap(cap), cap_orig(cap), cost(cost), revEdge(revEdge), isRev(isRev) {
}
};
struct PrimalDual {
int n;
vector<vector<Edge> > g;
PrimalDual(int n_) : n(n_), g(vector<vector<Edge> >(n_)) {}
void add_edge(int src, int dst, Capacity cap, Cost cost) { // ?????????
g[src].emplace_back(dst, cap, cost, g[dst].size(), false);
g[dst].emplace_back(src, 0, -cost, g[src].size() - 1, true);
}
Cost solve(int s, int t, int f) {
Cost res = 0;
// vector<Cost> h(g.size()), dist(g.size());
// vector<int> prevv(g.size()), preve(g.size());
static Cost h[MAX_V], dist[MAX_V];
static int prevv[MAX_V], preve[MAX_V];
for(int i = 0; i < n; i++) {
h[i] = 0;
}
while(f > 0) {
typedef pair<Cost, int> pcv;
priority_queue<pcv, vector<pcv>, greater<pcv> > q;
for(int i = 0; i < n; i++) {
dist[i] = inf;
}
dist[s] = 0;
q.emplace(pcv(0, s));
while(q.size()) {
pcv p = q.top(); q.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(int i = 0; i < g[v].size(); i++) {
Edge &e = g[v][i];
if(e.cap > 0 && dist[e.dst] > dist[v] + e.cost + h[v] - h[e.dst]) {
dist[e.dst] = dist[v] + e.cost + h[v] - h[e.dst];
prevv[e.dst] = v;
preve[e.dst] = i;
q.emplace(pcv(dist[e.dst], e.dst));
}
}
}
if(dist[t] == inf) {
return -1;
}
for(int v = 0; v < n; v++) {
h[v] += dist[v];
}
// s-t ????????????????????£??????????????????
int d = f;
for(int v = t; v != s; v = prevv[v]) {
d = min(d, g[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for(int v = t; v != s; v = prevv[v]) {
Edge &e = g[prevv[v]][preve[v]];
e.cap -= d;
g[v][e.revEdge].cap += d;
}
}
return res;
}
// ??????????????????=???????????????-?????¨??????????????¨???
void view() {
for(int i = 0; i < g.size(); i++) {
for(int j = 0; j < g[i].size(); j++) {
if(!g[i][j].isRev) {
Edge& e = g[i][j];
printf("%3d->%3d (flow:%d)\n", i, e.dst, e.cap_orig - e.cap);
}
}
}
}
};
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
int V, E, F;
cin >> V >> E >> F;
PrimalDual pd(V);
for(int i = 0; i < E; i++) {
int u, v, c, d;
cin >> u >> v >> c >> d;
pd.add_edge(u, v, c, d);
}
int res = pd.solve(0, V - 1, F);
if(res == inf) {
cout << -1 << endl;
}
else {
cout << res << endl;
}
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <queue>
#include <vector>
using namespace std;
constexpr int INF = 1000000001;
constexpr int MAX = 10000;
typedef pair<int, int> P;
struct Edge {
int to;
int cap;
int cost;
int rev;
Edge(int to, int cap, int cost, int rev)
: to(to), cap(cap), cost(cost), rev(rev) {}
};
int V, E, F;
vector<Edge> G[MAX];
int h[MAX];
int dist[MAX];
int prevv[MAX], preve[MAX];
auto add_edge(int from, int to, int cap, int cost) -> void {
G[from].push_back(Edge(to, cap, cost, G[to].size()));
G[to].push_back(Edge(from, 0, -cost, G[from].size() - 1));
}
auto min_cost_flow(int s, int t, int f) -> int {
auto res = 0;
fill(h, h + V, 0);
while(f > 0) {
priority_queue<P, vector<P>, greater<P>> que;
fill(dist, dist + V, INF);
dist[s] = 0;
que.push(P(0, s));
while(!que.empty()) {
P p = que.top();
que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (auto i = 0; i < G[v].size(); i++) {
Edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) {
return -1;
}
for (int v = 0; v < V; v++) {
h[v] += dist[v];
}
int d = f;
for (auto v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (auto v = t; v != s; v = prevv[v]) {
Edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
auto main(int argc, char const *argv[]) -> int {
int n;
cin>>V>>E>>F;
while(E--){
int u, v, c, d;
cin>>u>>v>>c>>d;
add_edge(u,v,c,d);
}
cout<<min_cost_flow(0, V - 1, F)<<endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
#define _overload(_1,_2,_3,name,...) name
#define _rep(i,n) _range(i,0,n)
#define _range(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload(__VA_ARGS__,_range,_rep,)(__VA_ARGS__)
#define _rrep(i,n) _rrange(i,n,0)
#define _rrange(i,a,b) for(int i=int(a)-1;i>=int(b);--i)
#define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__)
#define _all(arg) begin(arg),end(arg)
#define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg))
#define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary)
#define clr(a,b) memset((a),(b),sizeof(a))
#define bit(n) (1LL<<(n))
#define popcount(n) (__builtin_popcountll(n))
template<class T>bool chmax(T &a, const T &b) { return (a<b)?(a=b,1):0;}
template<class T>bool chmin(T &a, const T &b) { return (b<a)?(a=b,1):0;}
using namespace std;
const int dx[8]={1,0,-1,0,1,-1,-1,1};
const int dy[8]={0,1,0,-1,1,1,-1,-1};
using edge=struct {int to,cap,cost,rev;};
using G=vector<vector<edge>>;
const int inf=1<<29;
void add_edge(G &graph,int a,int b,int c,int d){
graph[a].push_back({b,c,d,int(graph[b].size())});
graph[b].push_back({a,0,-d,int(graph[a].size()-1)});
}
int min_cost_flow(G &graph,int s,int t,int f){
int res=0;
while(f){
int n=graph.size(),update;
vector<int> dist(n,inf),pv(n,0),pe(n,0);
dist[s]=0;
rep(loop,n){
update=false;
rep(v,n)rep(i,graph[v].size()){
edge &e=graph[v][i];
if(e.cap>0 && chmin(dist[e.to],dist[v]+e.cost)){
pv[e.to]=v,pe[e.to]=i;
update=true;
}
}
if(!update) break;
}
if(dist[t]==inf) return -1;
int d=f;
for(int v=t;v!=s;v=pv[v]) chmin(d,graph[pv[v]][pe[v]].cap);
f-=d,res+=d*dist[t];
for(int v=t;v!=s;v=pv[v]){
edge &e=graph[pv[v]][pe[v]];
e.cap-=d;
graph[v][e.rev].cap+=d;
}
}
return res;
}
int main(void){
int n,m,f;
cin >> n >> m >> f;
G graph(n);
rep(i,m){
int a,b,c,d;
cin >> a >> b >> c >> d;
add_edge(graph,a,b,c,d);
}
cout << min_cost_flow(graph,0,n-1,f) << endl;
return 0;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
using FLOW = int;
using COST = int;
const int MAX_V = 100;
const COST INF = 1000000000;
struct Edge {
int rev, from, to;
FLOW cap, icap;
COST cost;
Edge(int r, int f, int t, FLOW cp, COST cs)
: rev(r), from(f), to(t), cap(cp), icap(cp), cost(cs) {}
};
struct Graph {
int V;
vector<Edge> list[MAX_V];
Graph(int n = 0) { init(n); }
void init(int n = 0) {
V = n;
for(auto &&v : list)
v.clear();
}
void resize(int n = 0) { V = n; }
void reset() {
for(auto &&v : list)
for(auto &&e : v)
e.cap = e.icap;
}
inline vector<Edge> &operator[](int i) { return list[i]; }
Edge &redge(Edge &e) { return list[e.to][e.rev + (e.from == e.to)]; }
void addedge(int from, int to, FLOW cap, COST cost) {
list[from].emplace_back(list[to].size(), from, to, cap, cost);
list[to].emplace_back(list[from].size() - 1, to, from, 0, -cost);
}
};
COST MinCostFlow(Graph &G, int s, int t, FLOW f) {
COST dist[MAX_V];
int prevv[MAX_V];
int preve[MAX_V];
COST res = 0;
COST h[MAX_V];
memset(h, 0, sizeof(h));
using P = pair<COST, int>;
priority_queue<P, vector<P>, greater<P>> que;
while(f > 0) {
fill(dist, dist + G.V, INF);
dist[s] = 0;
que.emplace(0, s);
while(!que.empty()) {
P p = que.top();
que.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(int i = 0; i < (int)G[v].size(); i++) {
Edge &e = G[v][i];
if(e.cap > 0 &&
dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.emplace(dist[e.to], e.to);
}
}
}
if(dist[t] == INF) return -1;
for(int v = 0; v < G.V; v++)
h[v] += dist[v];
FLOW d = f;
for(int v = t; v != s; v = prevv[v])
d = min(d, G[prevv[v]][preve[v]].cap);
f -= d;
res += h[t] * d;
for(int v = t; v != s; v = prevv[v]) {
Edge &e = G[prevv[v]][preve[v]];
Edge &re = G.redge(e);
e.cap -= d;
re.cap += d;
}
}
return res;
}
int main() {
int n, m;
FLOW f;
cin >> n >> m >> f;
Graph G(n);
for(int i = 0; i < m; i++) {
int a, b, c, d;
cin >> a >> b >> c >> d;
G.addedge(a, b, c, d);
}
cout << MinCostFlow(G, 0, n - 1, f) << "\n";
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
#define INF 1e9
#define llINF 1e18
#define MOD 1000000007
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define ll long long
#define ull unsigned long long
#define vi vector<ll>
#define vvi vector<vi>
#define BITLE(n) (1LL<<((ll)n))
#define BITCNT(n) (__builtin_popcountll(n))
#define SUBS(s,f,t) ((s).substr((f)-1,(t)-(f)+1))
#define ALL(a) (a).begin(),(a).end()
using namespace std;
struct MinCostFlow{
struct edge{
ll to,cap,cost,rev;
};
const ll MAX_V=200100;
const ll Inf=1e18;
ll V;
vector<vector<edge>>E;
vi dist,h,prevv,preve;
MinCostFlow(ll V):V(V),E(V),dist(V),h(V),prevv(V),preve(V){}
void addEdge(ll from, ll to, ll cap, ll cost){
E[from].pb({to,cap,cost,(ll)E[to].size()});
E[to].pb({from,0,-cost,(ll)E[from].size()-1});
}
void dijkstra(ll s){
priority_queue<pair<ll,ll>,vector<pair<ll,ll>>,greater<pair<ll,ll>>>que;
fill(ALL(dist),Inf);
dist[s] = 0;
que.push(pair<ll,ll>(0,s));
while(!que.empty()){
pair<ll,ll> p = que.top();
que.pop();
ll v = p.second;
if(dist[v] < p.first)continue;
for(int j = 0;j < E[v].size();j++){
edge t = E[v][j];
if(t.cap > 0&&dist[t.to] > dist[v] + t.cost + h[v] - h[t.to]){
dist[t.to] = dist[v] + t.cost + h[v] - h[t.to];
prevv[t.to] = v;preve[t.to] = j;
que.push(pair<ll,ll>(dist[t.to],t.to));
}
}
}
}
ll execution(ll s,ll t,ll f){
ll ret = 0;
fill(ALL(h),0);
while(f>0){
dijkstra(s);
if(dist[t] == Inf)return -1;
for(ll v = 0;v < V;v++)h[v] += dist[v];
ll d = f;
for(ll v = t; v != s; v = prevv[v]){
d = min(d, E[prevv[v]][preve[v]].cap);
}
f -= d;
ret += d * h[t];
for(int v = t; v != s; v = prevv[v]){
edge &e = E[prevv[v]][preve[v]];
e.cap -= d;
E[v][e.rev].cap += d;
}
}
return ret;
}
};
int main(){
cin.tie(0);
ios::sync_with_stdio(false);
ll v,e,f;cin>>v>>e>>f;
MinCostFlow mcf(v);
for(int i=0;i<e;i++){
ll f,t,c,d;cin>>f>>t>>c>>d;
mcf.addEdge(f,t,c,d);
}
cout<<mcf.execution(0,v-1,f)<<endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define INF 1<<30
#define LINF 1LL<<60
#define MAX_V 100000
struct edge{
int to;
int cap;
int cost;
int rev;
edge(){}
edge(int to,int cap,int cost,int rev):to(to),cap(cap),cost(cost),rev(rev){}
};
int V;
vector<edge> G[MAX_V];
int dist[MAX_V];
int prevv[MAX_V],preve[MAX_V];
void add_edge(int from,int to,int cap,int cost){
G[from].push_back(edge(to,cap,cost,(int)G[to].size()));
G[to].push_back(edge(from,0,-cost,(int)G[from].size()-1));
}
int min_cost_flow(int s,int t,int f){
int res=0;
while(f>0){
fill(dist,dist+V,INF);
dist[s]=0;
bool update = true;
while(update){
update = false;
for(int v=0; v<V ;v++){
if(dist[v]==INF) continue;
for(int i=0; i<G[v].size(); i++){
edge &e = G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v]+e.cost) {
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if(dist[t]==INF) return -1;
int d = f;
for(int v=t; v!=s; v=prevv[v])d=min(d,G[prevv[v]][preve[v]].cap);
f -= d;
res += d*dist[t];
for(int v=t; v!=s; v=prevv[v]){
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main() {
int E, F; cin >> V >> E >> F;
for (int i = 0; i < E;i++) {
int u, v, c, d; cin >> u >> v >> c >> d;
add_edge(u,v,c,d);
}
cout << min_cost_flow(0,V-1,F) << endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <vector>
#include <queue>
#include <set>
using namespace std;
struct Graph {
struct edge {
int to;
int cap;
int cost;
int rev;
};
int n;
vector<vector<edge>> edges;
Graph(int N) {
n = N;
edges.resize(n, vector<edge>());
}
int size() const { return n; }
vector<edge> &operator[](int v) { return edges[v]; }
};
int minimumCostFlow(Graph& g,int s,int t,int f)
{
const int n = g.size();
using Pi = pair<int,int>;
priority_queue<Pi,vector<Pi>,greater<Pi>> que;
vector<int> prevv(n,-1);
vector<int> preve(n,-1);
vector<int> potential(n,0);
int res = 0;
while(f > 0){
vector<int> dist(n,1e9);
que.push({0,s});
dist[s] = 0;
while(!que.empty()){
Pi p = que.top();
que.pop();
if(dist[p.second] < p.first) continue;
for(int i = 0;i < g[p.second].size();i++){
auto& e = g[p.second][i];
int next = dist[p.second] + e.cost + potential[p.second] - potential[e.to];
if(e.cap > 0 && dist[e.to] > next){
dist[e.to] = next;
prevv[e.to] = p.second;
preve[e.to] = i;
que.push({dist[e.to],e.to});
}
}
}
if(dist[t] == 1e9) return -1;
for(int v = 0;v < n;v++){
potential[v] += dist[v];
}
int d = f;
for(int v = t;v != s;v = prevv[v]){
d = min(d,g[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * potential[t];
for(int v = t;v != s;v = prevv[v]){
auto& e = g[prevv[v]][preve[v]];
e.cap -= d;
g[v][e.rev].cap += d;
}
}
return res;
}
#include <iostream>
int main()
{
int v;int e;int f;
cin >> v >> e >> f;
Graph g(v);
for(int i = 0;i < e;i++)
{
int u,v,c,d;
cin >> u >> v >> c >> d;
g[u].push_back({v,c,d,(int)g[v].size()});
g[v].push_back({u,0,-d,(int)g[u].size() - 1});
}
int ans = minimumCostFlow(g,0,v - 1,f);
cout << ans << endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int MAX_V = 100;
const int INF = 1e9;
struct edge
{
int to,cap,cost,rev;
};
int V;
vector<edge> G[MAX_V];
int dist[MAX_V];
int prevv[MAX_V],preve[MAX_V];
void add_edge(int from,int to, int cap, int cost)
{
G[from].push_back((edge){to,cap,cost,(int)G[to].size()});
G[to].push_back((edge){from,0,-cost,(int)G[from].size()-1});
}
int min_cost_frow(int s,int t,int f)
{
int res = 0;
while(f>0)
{
fill(dist,dist+V,INF);
dist[s] = 0;
bool update = true;
while(update)
{
update = false;
for(int v = 0;v<V;v++)
{
if(dist[v] == INF)continue;
for(int i = 0;i<G[v].size();i++)
{
edge &e = G[v][i];
if(e.cap>0&&dist[e.to]>dist[v] + e.cost)
{
dist[e.to] = dist[v]+e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if(dist[t]==INF)
{
return -1;
}
int d = f;
for(int v = t;v != s;v = prevv[v])
{
d = min(d,G[prevv[v]][preve[v]].cap);
}
f -=d;
res += d*dist[t];
for(int v= t;v !=s;v=prevv[v])
{
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main()
{
int E,F;
cin >> V >> E >> F;
for(int i = 0;i<E;i++)
{
int u,v,c,d;
cin >> u >> v >> c >> d;
add_edge(u,v,c,d);
}
cout<<min_cost_frow(0,V-1,F)<<endl;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define all(a) (a).begin(),(a).end()
typedef long long ll;
typedef pair<int, int> P;
typedef vector<int> vi;
typedef vector<P> vp;
typedef vector<ll> vll;
const int INF = 99999999;
const int MAX_V = 100000;
struct edge { int to, cap, cost, rev; };
int V, E, F;
vector<edge> G[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V]; // privious vertex, edge
void add_edge(int from, int to, int cap, int cost) {
G[from].emplace_back((edge){to, cap, cost, (int)G[to].size()});
G[to].emplace_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
// get min cost flow from s to t
// if we can flow not at all, then return -1
int min_cost_flow(int s, int t, int f) {
int res = 0;
while (f > 0) {
fill(dist, dist + V, INF);
dist[s] = 0;
bool update = true;
while (update) {
update = false;
rep(v, V) {
if (dist[v] == INF) continue;
rep(i, G[v].size()) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if (dist[t] == INF) {
// no more flow
return -1;
}
// flow as much as possible along minimum path from s to t
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, (int)G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * dist[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
signed main() {
cin >> V >> E >> F;
rep(i, E) {
int u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
cout << min_cost_flow(0, V - 1, F) << endl;
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <iostream>
#include <cstdio>
#include <vector>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long ll;
#define rep(i,n) for(int i=0;i<(n);i++)
const int INF = 1e9;
struct edge { int to, cap, cost, rev; };
int V;
const int MAX_V = 100;
vector<edge> G[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];
void add_edge(int from, int to, int cap, int cost) {
G[from].push_back((edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
int min_cost_flow(int s, int t, int f) {
int res = 0;
while (f > 0) {
fill(dist, dist + V, INF);
dist[s] = 0;
bool update = true;
while (update) {
update = false;
for (int v = 0; v < V; v++) {
if (dist[v] == INF) continue;
for (int i = 0; i < G[v].size(); i++) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
prevv[e.to] = v;
preve[e.to] = i;
update = true;
}
}
}
}
if (dist[t] == INF) {
return -1;
}
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * dist[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main(void){
cin >> V;
int e, f; cin >> e >> f;
rep(i, e){
int u, v, c, d;
cin >> u >> v >> c >> d;
add_edge(u, v, c, d);
}
printf("%d\n", min_cost_flow(0, V - 1, f));
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | python3 | #!usr/bin/env python3
from collections import defaultdict
from collections import deque
from heapq import heappush, heappop
import sys
import math
import bisect
import random
def LI(): return list(map(int, sys.stdin.readline().split()))
def I(): return int(sys.stdin.readline())
def LS():return list(map(list, sys.stdin.readline().split()))
def S(): return list(sys.stdin.readline())[:-1]
def IR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = I()
return l
def LIR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = LI()
return l
def SR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = S()
return l
def LSR(n):
l = [None for i in range(n)]
for i in range(n):l[i] = SR()
return l
mod = 1000000007
# 1:shortest path
# 1_A
"""
from heapq import heappush, heappop
def dijkstra(num, start):
dist = [float("inf") for i in range(num)]
dist[start] = 0
q = [[dist[start], start]]
while q:
du, u = heappop(q)
for j, k in adj[u]:
if dist[j] > du + k:
dist[j] = du + k
heappush(q, [dist[j], j])
print(dist, q)
return dist
v,e,r = map(int, input().split(" "))
adj = [[] for i in range(v)]
for i in range(e):
s,t,d = map(int, input().split(" "))
adj[s].append([t, d])
lis = dijkstra(v, r)
print(lis)
for i in lis:
print(str(i).upper())
"""
# 1_B
"""
def bellman_ford(num, start):
dist = [float("inf")]*num
dist[start] = 0
for i in range(num):
update = False
for fro, to, cost in e:
d = dist[fro] + cost
if dist[to] > d:
dist[to] = d
update = True
if i == num-1:
return False
if not update:
break
return dist
v,E,r = map(int, input().split(" "))
e = []
for i in range(E):
s,t,d = map(int, input().split(" "))
e.append([s, t, d])
lis = bellman_ford(v, r)
if not lis:
print("NEGATIVE CYCLE")
else:
for i in lis:
print(str(i).upper())
"""
# 1_C
"""
def warshallfloyd(n):
for i in range(n):
for j in range(n):
for k in range(n):
d[j][k] = min(d[j][k], d[j][i]+d[i][k])
v,e = map(int, input().split())
d = [[float("inf") for j in range(v)] for i in range(v)]
for i in range(v):
d[i][i] = 0
for i in range(e):
s, t, c = map(int, input().split())
d[s][t] = c
warshallfloyd(v)
for i in range(v):
if d[i][i] < 0:
print("NEGATIVE CYCLE")
quit()
for i in d:
for j in range(v):
if j < v-1:
print(str(i[j]).upper(), end = " ")
else:
print(str(i[j]).upper())
"""
# 2:spanning tree
# 2_A
"""
def root(x):
if par[x] == x:
return x
par[x] = root(par[x])
return par[x]
def same(x,y):
return root(x) == root(y)
def unite(x,y):
x = root(x)
y = root(y)
if rank[x] < rank[y]:
par[x] = y
else:
par[y] = x
if rank[x] == rank[y]:
rank[x] += 1
v,e = LI()
c = LIR(e)
c.sort(key = lambda x:x[2])
par = [i for i in range(v)]
rank = [0 for i in range(v)]
k = 0
ans = 0
for a,b,w in c:
if not same(a,b):
k += 1
unite(a,b)
ans += w
if k == v-1:
break
print(ans)
"""
#2_B
"""
def root(x):
if par[x] == x:
return x
par[x] = root(par[x])
return par[x]
def same(x,y):
return root(x) == root(y)
def unite(x,y):
x = root(x)
y = root(y)
if rank(x) < rank(y):
par[x] = y
else:
par[y] = x
if rank(x) == rank(y):
rank[x] += 1
"""
#3:connected components
#3_A
#3_B
#3_C
#4:path/cycle
#4_A
"""
def bellman_ford(num, start):
dist = [float("inf") for i in range(num)]
dist[start] = 0
for i in range(num):
update = False
for j, k, l in adj:
if dist[k] > dist[j] + l:
dist[k] = dist[j] + l
update = True
if i == num-1:
return False
if not update:
break
return True
v, e = map(int, input().split(" "))
adj = []
for i in range(e):
s,t = map(int, input().split(" "))
adj.append([s, t, -1])
for i in range(v):
if not bellman_ford(v,i):
print(1)
quit()
print(0)
"""
#4_B
"""
def visit(s):
if f[s]:
f[s] = 0
for t in v[s]:
visit(t)
l.append(s)
n,e = LI()
v = [[] for i in range(n)]
for i in range(e):
s,t = LI()
v[s].append(t)
l = []
f = [1 for i in range(n)]
for i in range(n):
visit(i)
l = l[::-1]
for i in l:
print(i)
"""
#5:tree
#5_A
"""
from heapq import heappush, heappop
def dijkstra(num, start):
dist = [float("inf") for i in range(num)]
dist[start] = 0
q = [[dist[start], start]]
while q:
du, u = heappop(q)
for j, k in adj[u]:
if dist[j] > du + k:
dist[j] = du + k
heappush(q, [dist[j], j])
return dist
n = II()
adj = [[] for i in range(n)]
for i in range(n-1):
s,t,w = LI()
adj[s].append([t, w])
adj[t].append([s, w])
d = dijkstra(n,0)
i = d.index(max(d))
d2 = dijkstra(n,i)
print(max(d2))
"""
#5_B
"""
from heapq import heappush, heappop
def dijkstra(num, start):
dist = [float("inf") for i in range(num)]
dist[start] = 0
q = [[dist[start], start]]
while q:
du, u = heappop(q)
for j, k in adj[u]:
if dist[j] > du + k:
dist[j] = du + k
heappush(q, [dist[j], j])
return dist
n = int(input())
adj = [[] for i in range(n)]
for i in range(n-1):
s, t, w = map(int, input().split(" "))
adj[s].append([t, w])
adj[t].append([s, w])
for i in range(n):
s = dijkstra(n,i)
print(max(s))
"""
#5_C
#5_D
#5_E
#6
#6_A_maximum_flow
"""
def bfs(s,g,n):
bfs_map = [-1 for i in range(n)]
bfs_map[s] = 0
q = deque()
q.append(s)
fin = False
while q:
x = q.popleft()
for y in v[x]:
if c[x][y] > 0 and bfs_map[y] < 0:
bfs_map[y] = bfs_map[x]+1
if y == g:
fin = True
break
q.append(y)
if fin:
break
if bfs_map[g] == -1:
return None,0
path = [None]*(bfs_map[g]+1)
m = float("inf")
path[bfs_map[g]] = g
y = g
for i in range(bfs_map[g])[::-1]:
for x in v[y]:
if c[x][y] > 0 and bfs_map[x] == bfs_map[y]-1:
path[i] = x
if c[x][y] < m:
m = c[x][y]
y = x
break
return path,m
def ford_fulkerson(s,g,c,n):
f = 0
while 1:
p,m = bfs(s,g,n)
if not m:break
f += m
for i in range(len(p)-1):
c[p[i]][p[i+1]] -= m
c[p[i+1]][p[i]] += m
return f
n,e = LI()
c = [defaultdict(lambda : 0) for j in range(n)]
v = [[] for i in range(n)]
for i in range(e):
a,b,w = LI()
c[a][b] = w
v[a].append(b)
v[b].append(a)
print(ford_fulkerson(0,n-1,c,n))
"""
#6_B
def dijkstra(s,h):
dist = [float("inf")]*n
prev = [-1]*n
dist[s] = 0
q = [(0,s)]
while q:
dx,x = heappop(q)
for y in v[x]:
if cap[x][y] <= 0:
continue
dy = dx+cost[x][y]+h[x]-h[y]
if dy < dist[y]:
dist[y] = dy
prev[y] = x
heappush(q,(dy,y))
return (dist,prev)
def minimim_flow(s,g,f):
res = 0
h = [0]*n
while f > 0:
dist,prev = dijkstra(s,h)
if dist[g] == float("inf"):
return -1
for i in range(n):
h[i] += dist[i]
flow = f
y = g
while y != s:
x = prev[y]
if cap[x][y] < flow:
flow = cap[x][y]
y = x
f -= flow
res += flow*h[g]
y = g
while y != s:
x = prev[y]
cap[x][y] -= flow
cap[y][x] += flow
y = x
return res
n,m,f = LI()
v = [[] for i in range(n)]
cap = [defaultdict(lambda : 0) for i in range(n)]
cost = [defaultdict(lambda : 0) for i in range(n)]
for i in range(m):
a,b,c,d = LI()
v[a].append(b)
v[b].append(a)
cost[a][b] = d
cost[b][a] = -d
cap[a][b] = c
print(minimim_flow(0,n-1,f))
#7
#7_A
"""
def bfs(s,g,n):
bfs_map = [-1 for i in range(n)]
bfs_map[s] = 0
q = deque()
q.append(s)
fin = False
while q:
x = q.popleft()
for y in range(n):
if c[x][y] > 0 and bfs_map[y] < 0:
bfs_map[y] = bfs_map[x]+1
if y == g:
fin = True
break
q.append(y)
if fin:
break
if bfs_map[g] == -1:
return [None,0]
path = [None for i in range(bfs_map[g]+1)]
m = float("inf")
path[bfs_map[g]] = g
y = g
for i in range(bfs_map[g])[::-1]:
for x in range(n+1):
if c[x][y] > 0 and bfs_map[x] == bfs_map[y]-1:
path[i] = x
if c[x][y] < m:
m = c[x][y]
y = x
break
return [path,m]
def ford_fulkerson(s,g,c,n):
while 1:
p,m = bfs(s,g,n)
if not m:break
for i in range(len(p)-1):
c[p[i]][p[i+1]] -= m
c[p[i+1]][p[i]] += m
return sum(c[g])
x,y,e = LI()
c = [[0 for i in range(x+y+2)] for j in range(x+y+2)]
for i in range(x):
c[0][i+1] = 1
for i in range(y):
c[x+i+1][x+y+1] = 1
for i in range(e):
a,b = LI()
c[a+1][x+b+1] = 1
print(ford_fulkerson(0,x+y+1,c,x+y+2))
"""
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <math.h>
#include <bits/stdc++.h>//一括で読み込み
using namespace std;
#define MAX_V 500
typedef long long ll;
typedef pair<int,int> P;
struct edge{int to, cap, cost, rev;};
int V;
vector<edge> G[MAX_V];
int h[MAX_V];
int dist[MAX_V];
int prevv[MAX_V],preve[MAX_V];
void add_edge(int from, int to, int cap, int cost)
{
G[from].push_back((edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((edge){from, 0, -cost, (int)G[from].size()-1});
}
int min_cost_flow(int s, int t, int f)
{
int res = 0;
fill(h, h+V, 0);
while(f > 0)
{
priority_queue<P,vector<P>,greater<P>> que;
fill(dist, dist+V, 1<<28);
dist[s] = 0;
que.push(P(0,s));
while(!que.empty())
{
P p = que.top();
que.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(int i = 0; i < G[v].size(); i++)
{
edge &e=G[v][i];
if(e.cap > 0 && dist[e.to] > dist[v]+e.cost+h[v]-h[e.to])
{
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
que.push(P(dist[e.to], e.to));
}
}
}
if(dist[t] == (1 << 28))
{
return -1;
}
for(int v = 0; v < V; v++) h[v] += dist[v];
int d = f;
for(int v = t; v != s; v = prevv[v])
{
d = min(d,G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d*h[t];
for(int v = t; v != s; v = prevv[v])
{
edge &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main()
{
int e,f,u,v,c,d,i;
cin >> V;//Vは頂点数（500以下）
cin >> e >> f;
for(i = 0; i < e; i++)
{
cin >> u >> v >> c >> d;
add_edge(u,v,c,d);//辺の追加（開始、終了頂点と容量、コスト）
}
cout << min_cost_flow(0, V-1, f) << endl;//最小費用流(開始、終了頂点と流量)
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <bits/stdc++.h>
#define fread_siz 1024
inline int get_c(void)
{
static char buf[fread_siz];
static char *head = buf + fread_siz;
static char *tail = buf + fread_siz;
if (head == tail)
fread(head = buf, 1, fread_siz, stdin);
return *head++;
}
inline int get_i(void)
{
register int ret = 0;
register int neg = false;
register int bit = get_c();
for (; bit < 48; bit = get_c())
if (bit == '-')neg ^= true;
for (; bit > 47; bit = get_c())
ret = ret * 10 + bit - 48;
return neg ? -ret : ret;
}
template <class T>
inline T min(T a, T b)
{
return a < b ? a : b;
}
const int inf = 2e9;
const int maxn = 2005;
int n, m;
int s, t;
int flow;
int edges;
int hd[maxn];
int nt[maxn];
int to[maxn];
int vl[maxn];
int fl[maxn];
inline void add(int u, int v, int f, int w)
{
nt[edges] = hd[u]; to[edges] = v; fl[edges] = f; vl[edges] = +w; hd[u] = edges++;
nt[edges] = hd[v]; to[edges] = u; fl[edges] = 0; vl[edges] = -w; hd[v] = edges++;
}
int dis[maxn];
int pre[maxn];
inline bool spfa(void)
{
static int que[maxn];
static int inq[maxn];
static int head, tail;
memset(dis, 0x3f, sizeof(dis));
head = 0, tail = 0;
que[tail++] = s;
pre[s] = -1;
inq[s] = 1;
dis[s] = 0;
while (head != tail)
{
int u = que[head++], v; inq[u] = 0;
for (int i = hd[u]; ~i; i = nt[i])
if (dis[v = to[i]] > dis[u] + vl[i] && fl[i])
{
dis[v] = dis[u] + vl[i];
pre[v] = i ^ 1;
if (!inq[v])
inq[v] = 1, que[tail++] = v;
}
}
return dis[t] < 0x3f3f3f3f;
}
inline int expend(void)
{
int newFlow = inf;
for (int i = pre[t]; ~i; i = pre[to[i]])
newFlow = min(newFlow, fl[i ^ 1]);
for (int i = pre[t]; ~i; i = pre[to[i]])
fl[i] += newFlow, fl[i^1] -= newFlow;
return flow -= newFlow, newFlow * dis[t];
}
inline int mcmf(void)
{
int ret = 0;
while (spfa())
ret += expend();
return flow ? -1 : ret;
}
signed main(void)
{
n = get_i();
m = get_i();
flow = get_i();
memset(hd, -1, sizeof(hd));
for (int i = 1; i <= m; ++i)
{
int u = get_i();
int v = get_i();
int f = get_i();
int w = get_i();
add(u, v, f, w);
}
s = n, t = n - 1;
add(s, 0, flow, 0);
printf("%d\n", mcmf());
} |
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | //#include "bits/stdc++.h"
#define _USE_MATH_DEFINES
#include <cmath>
#include <cstdlib>
#include <deque>
#include <algorithm>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <iterator>
using namespace std;
#define rep(i,a,b) for(int i=(a), i##_len=(b);i<i##_len;i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(c) begin(c),end(c)
//#define int long long
#define SZ(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
typedef long long ll;
//typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef pair<ll, int> pli;
typedef pair<double, double> pdd;
typedef vector<vector<int>> mat;
template<class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; }
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)1e9 + 7;
const double EPS = 1e-9;
struct edge
{
int s, t, c, d,rev;
edge(int s, int t, int c, int d,int rev) :s(s), t(t), c(c),d(d), rev(rev) {}
edge() { s = -1, t = -1, c = -1, rev = -1; d = -1; }
};
vector<vector<edge>> G;
int dist[101];
int prevv[101], preve[101];
int min_cost_flow(int s, int t, int f)
{
int res = 0;
while (f > 0)
{
rep(i, 0, 101)dist[i] = INF;
dist[s] = 0;
while (true)
{
bool update = false;
rep(i, 0, SZ(G))
{
if (dist[i] == INF)
{
continue;
}
rep(j, 0, SZ(G[i]))
{
edge e = G[i][j];
if (e.c > 0 && dist[e.t] > dist[i] + e.d)
{
dist[e.t] = dist[i] + e.d;
prevv[e.t] = i;
preve[e.t] = j;
update = true;
}
}
}
if (!update)
{
break;
}
}
if (dist[t] == INF)
{
return -1;
}
int tf = f;
for (int i = t; i != s; i = prevv[i])
{
chmin(tf, G[prevv[i]][preve[i]].c);
}
f -= tf;
res += tf*dist[t];
for (int i = t; i != s; i = prevv[i])
{
G[prevv[i]][preve[i]].c -= tf;
G[i][G[prevv[i]][preve[i]].rev].c += tf;
}
}
return res;
}
signed main()
{
cin.tie(0);
ios::sync_with_stdio(false);
int V, E, F,s, t, c, d;
cin >> V >> E >> F;
G.resize(V);
rep(i, 0, E)
{
cin >> s >> t >> c >> d;
G[s].push_back(edge(s, t, c, d,SZ(G[t])));
G[t].push_back(edge(t, s, 0, -d,SZ(G[s]) - 1));
}
cout << min_cost_flow(0,V-1,F) << endl;
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include <algorithm>
#include <iostream>
#include <iomanip>
#include <cstring>
#include <string>
#include <vector>
#include <random>
#include <bitset>
#include <queue>
#include <cmath>
#include <stack>
#include <set>
#include <map>
typedef long long ll;
using namespace std;
const ll MOD = 1000000007LL;
typedef pair <int, int> P;
class PrimalDual {
const int INF = 1 << 30;
struct Edge {
int to, cap, cost, rev;
};
int n;
vector<vector<Edge>> G;
vector<int> potential; // ポテンシャル
vector<int> dist; // 最短距離
vector<int> prevv, preve; // 直前の頂点と辺
void dijkstra(int s) {
fill(dist.begin(), dist.end(), INF);
priority_queue<P, vector<P>, greater<P>> q;
dist[s] = 0;
q.push(P(0, s));
while (!q.empty()) {
P p = q.top();
q.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (int i = 0; i < G[v].size(); i++) {
Edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] + potential[e.to] > dist[v] + e.cost + potential[v]) {
dist[e.to] = dist[v] + e.cost + potential[v] - potential[e.to];
prevv[e.to] = v;
preve[e.to] = i;
q.push(P(dist[e.to], e.to));
}
}
}
}
public:
PrimalDual(int n) : n(n), G(n), potential(n), dist(n), prevv(n), preve(n) {}
void add_edge(int from, int to, int cap, int cost) {
G[from].push_back({to, cap, cost, (int)G[to].size()});
G[to].push_back({from, 0, -cost, (int)G[from].size() - 1});
}
int min_cost_flow(int s, int t, int flow) {
fill(potential.begin(), potential.end(), 0);
int ret = 0;
while (flow) {
dijkstra(s);
if (dist[t] == INF) return -1;
for (int v = 0; v < n; v++) potential[v] += dist[v];
int f = flow;
for (int v = t; v != s; v = prevv[v]) f = min(f, G[prevv[v]][preve[v]].cap);
flow -= f;
ret += f * potential[t];
for (int v = t; v != s; v = prevv[v]) {
Edge &e = G[prevv[v]][preve[v]];
e.cap -= f;
G[v][e.rev].cap += f;
}
}
return ret;
}
};
int main() {
int V, E, F;
cin >> V >> E >> F;
PrimalDual pd(V);
for (int e = 0; e < E; e++) {
int u, v, c, d;
cin >> u >> v >> c >> d;
pd.add_edge(u, v, c, d);
}
cout << pd.min_cost_flow(0, V - 1, F) << "\n";
return 0;
}
|
p02377 Minimum Cost Flow | Examples
Input
4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1
Output
6
Input
Output | {
"input": [
"4 5 2\n0 1 2 1\n0 2 1 2\n1 2 1 1\n1 3 1 3\n2 3 2 1",
""
],
"output": [
"6",
""
]
} | {
"input": [],
"output": []
} | CORRECT | cpp | #include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
#define rep(i,n) for(ll i=0;i<(ll)(n);i++)
#define all(a) (a).begin(),(a).end()
#define pb push_back
#define INF (1e9+1)
//#define INF (1LL<<59)
#define MAX_V 100
struct edge { int to, cap, cost,rev; };
int V; // ????????°
vector<edge> G[MAX_V];
int h[MAX_V]; //??????????????£???
int dist[MAX_V];// ???????????¢
int prevv[MAX_V], preve[MAX_V];// ??´??????????????¨???
// from??????to??????????????????cap????????????cost????????????????????????????????????
void add_edge(int from, int to, int cap, int cost) {
G[from].push_back((edge){to, cap, cost, (int)G[to].size()});
G[to].push_back((edge){from, 0, -cost, (int)G[from].size() - 1});
}
// s??????t????????????f???????°??????¨???????±???????
// ??????????????´??????-1?????????
int min_cost_flow(int s, int t, int f) {
int res = 0;
fill(h, h + V, 0); // h????????????
while (f > 0) {
// ?????????????????????????????¨??????h?????´??°??????
priority_queue<pii, vector<pii>, greater<pii> > que; fill(dist, dist + V, INF);
dist[s] = 0;
que.push(pii(0, s));
while (!que.empty()) {
pii p = que.top(); que.pop();
int v = p.second;
if (dist[v] < p.first) continue;
for (int i = 0; i < G[v].size(); i++) {
edge &e = G[v][i];
if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
dist[e.to] = dist[v] + e.cost + h[v] - h[e.to]; prevv[e.to] = v;
preve[e.to] = i;
que.push(pii(dist[e.to], e.to));
}
}
}
if (dist[t] == INF) return -1; //????????\???????????????
for (int v = 0; v < V; v++) h[v] += dist[v];
// s-t????????????????????£??????????????????
int d = f;
for (int v = t; v != s; v = prevv[v]) {
d = min(d, G[prevv[v]][preve[v]].cap);
}
f -= d;
res += d * h[t];
for (int v = t; v != s; v = prevv[v]) {
edge &e = G[prevv[v]][preve[v]]; e.cap -= d;
G[v][e.rev].cap += d;
}
}
return res;
}
int main(){
int e,f;
cin>>V>>e>>f;
rep(i,e){
int u,v,c,d;
cin>>u>>v>>c>>d;
add_edge(u, v, c, d);
}
cout<<min_cost_flow(0, V-1, f)<<endl;
} |
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