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def is_square_form(num: int) -> bool:
digit = 9
while num > 0:
if num % 10 != digit:
return False
num //= 100
digit -= 1
return True | project_euler |
def solution() -> int:
num = 138902663
while not is_square_form(num * num):
if num % 10 == 3:
num -= 6 # (3 - 6) % 10 = 7
else:
num -= 4 # (7 - 4) % 10 = 3
return num * 10 | project_euler |
def sum_of_digit_factorial(n: int) -> int:
return sum(DIGIT_FACTORIAL[d] for d in str(n)) | project_euler |
def solution() -> int:
limit = 7 * factorial(9) + 1
return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i) | project_euler |
def solution(n: int = 4000000) -> int:
if n <= 1:
return 0
a = 0
b = 2
count = 0
while 4 * b + a <= n:
a, b = b, 4 * b + a
count += a
return count + b | project_euler |
def solution(n: int = 4000000) -> int:
even_fibs = []
a, b = 0, 1
while b <= n:
if b % 2 == 0:
even_fibs.append(b)
a, b = b, a + b
return sum(even_fibs) | project_euler |
def solution(n: int = 4000000) -> int:
i = 1
j = 2
total = 0
while j <= n:
if j % 2 == 0:
total += j
i, j = j, i + j
return total | project_euler |
def solution(n: int = 4000000) -> int:
fib = [0, 1]
i = 0
while fib[i] <= n:
fib.append(fib[i] + fib[i + 1])
if fib[i + 2] > n:
break
i += 1
total = 0
for j in range(len(fib) - 1):
if fib[j] % 2 == 0:
total += fib[j]
return total | project_euler |
def solution(n: int = 4000000) -> int:
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
getcontext().prec = 100
phi = (Decimal(5) ** Decimal(0.5) + 1) / Decimal(2)
index = (math.floor(math.log(n * (phi + 2), phi) - 1) // 3) * 3 + 2
num = Decimal(round(phi ** Decimal(index + 1))) / (phi + 2)
total = num // 2
return int(total) | project_euler |
def greatest_common_divisor(x: int, y: int) -> int:
return x if y == 0 else greatest_common_divisor(y, x % y) | project_euler |
def lcm(x: int, y: int) -> int:
return (x * y) // greatest_common_divisor(x, y) | project_euler |
def solution(n: int = 20) -> int:
g = 1
for i in range(1, n + 1):
g = lcm(g, i)
return g | project_euler |
def solution(n: int = 20) -> int:
try:
n = int(n)
except (TypeError, ValueError):
raise TypeError("Parameter n must be int or castable to int.")
if n <= 0:
raise ValueError("Parameter n must be greater than or equal to one.")
i = 0
while 1:
i += n * (n - 1)
nfound = 0
for j in range(2, n):
if i % j != 0:
nfound = 1
break
if nfound == 0:
if i == 0:
i = 1
return i
return None | project_euler |
def solution(min_block_length: int = 50) -> int:
fill_count_functions = [1] * min_block_length
for n in count(min_block_length):
fill_count_functions.append(1)
for block_length in range(min_block_length, n + 1):
for block_start in range(n - block_length):
fill_count_functions[n] += fill_count_functions[
n - block_start - block_length - 1
]
fill_count_functions[n] += 1
if fill_count_functions[n] > 1_000_000:
break
return n | project_euler |
def check_bouncy(n: int) -> bool:
if not isinstance(n, int):
raise ValueError("check_bouncy() accepts only integer arguments")
str_n = str(n)
sorted_str_n = "".join(sorted(str_n))
return sorted_str_n != str_n and sorted_str_n[::-1] != str_n | project_euler |
def solution(percent: float = 99) -> int:
if not 0 < percent < 100:
raise ValueError("solution() only accepts values from 0 to 100")
bouncy_num = 0
num = 1
while True:
if check_bouncy(num):
bouncy_num += 1
if (bouncy_num / num) * 100 >= percent:
return num
num += 1 | project_euler |
def sieve() -> Generator[int, None, None]:
factor_map: dict[int, int] = {}
prime = 2
while True:
factor = factor_map.pop(prime, None)
if factor:
x = factor + prime
while x in factor_map:
x += factor
factor_map[x] = factor
else:
factor_map[prime * prime] = prime
yield prime
prime += 1 | project_euler |
def solution(limit: float = 1e10) -> int:
primes = sieve()
n = 1
while True:
prime = next(primes)
if (2 * prime * n) > limit:
return n
# Ignore the next prime as the reminder will be 2.
next(primes)
n += 2 | project_euler |
def is_palindrome(n: int) -> bool:
if n % 10 == 0:
return False
s = str(n)
return s == s[::-1] | project_euler |
def solution() -> int:
answer = set()
first_square = 1
sum_squares = 5
while sum_squares < LIMIT:
last_square = first_square + 1
while sum_squares < LIMIT:
if is_palindrome(sum_squares):
answer.add(sum_squares)
last_square += 1
sum_squares += last_square**2
first_square += 1
sum_squares = first_square**2 + (first_square + 1) ** 2
return sum(answer) | project_euler |
def choose(n: int, r: int) -> int:
ret = 1.0
for i in range(1, r + 1):
ret *= (n + 1 - i) / i
return round(ret) | project_euler |
def non_bouncy_exact(n: int) -> int:
return choose(8 + n, n) + choose(9 + n, n) - 10 | project_euler |
def non_bouncy_upto(n: int) -> int:
return sum(non_bouncy_exact(i) for i in range(1, n + 1)) | project_euler |
def solution(num_digits: int = 100) -> int:
return non_bouncy_upto(num_digits) | project_euler |
def solution(length: int = 50) -> int:
ways_number = [1] * (length + 1)
for row_length in range(3, length + 1):
for block_length in range(3, row_length + 1):
for block_start in range(row_length - block_length):
ways_number[row_length] += ways_number[
row_length - block_start - block_length - 1
]
ways_number[row_length] += 1
return ways_number[length] | project_euler |
def solution(limit: int = 100) -> int:
singles: list[int] = [*list(range(1, 21)), 25]
doubles: list[int] = [2 * x for x in range(1, 21)] + [50]
triples: list[int] = [3 * x for x in range(1, 21)]
all_values: list[int] = singles + doubles + triples + [0]
num_checkouts: int = 0
double: int
throw1: int
throw2: int
checkout_total: int
for double in doubles:
for throw1, throw2 in combinations_with_replacement(all_values, 2):
checkout_total = double + throw1 + throw2
if checkout_total < limit:
num_checkouts += 1
return num_checkouts | project_euler |
def __init__(self, vertices: set[int], edges: Mapping[EdgeT, int]) -> None:
self.vertices: set[int] = vertices
self.edges: dict[EdgeT, int] = {
(min(edge), max(edge)): weight for edge, weight in edges.items()
} | project_euler |
def add_edge(self, edge: EdgeT, weight: int) -> None:
self.vertices.add(edge[0])
self.vertices.add(edge[1])
self.edges[(min(edge), max(edge))] = weight | project_euler |
def prims_algorithm(self) -> Graph:
subgraph: Graph = Graph({min(self.vertices)}, {})
min_edge: EdgeT
min_weight: int
edge: EdgeT
weight: int
while len(subgraph.vertices) < len(self.vertices):
min_weight = max(self.edges.values()) + 1
for edge, weight in self.edges.items():
if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
if weight < min_weight:
min_edge = edge
min_weight = weight
subgraph.add_edge(min_edge, min_weight)
return subgraph | project_euler |
def solution(filename: str = "p107_network.txt") -> int:
script_dir: str = os.path.abspath(os.path.dirname(__file__))
network_file: str = os.path.join(script_dir, filename)
edges: dict[EdgeT, int] = {}
data: list[str]
edge1: int
edge2: int
with open(network_file) as f:
data = f.read().strip().split("\n")
adjaceny_matrix = [line.split(",") for line in data]
for edge1 in range(1, len(adjaceny_matrix)):
for edge2 in range(edge1):
if adjaceny_matrix[edge1][edge2] != "-":
edges[(edge2, edge1)] = int(adjaceny_matrix[edge1][edge2])
graph: Graph = Graph(set(range(len(adjaceny_matrix))), edges)
subgraph: Graph = graph.prims_algorithm()
initial_total: int = sum(graph.edges.values())
optimal_total: int = sum(subgraph.edges.values())
return initial_total - optimal_total | project_euler |
def solution(min_total: int = 10**12) -> int:
prev_numerator = 1
prev_denominator = 0
numerator = 1
denominator = 1
while numerator <= 2 * min_total - 1:
prev_numerator += 2 * numerator
numerator += 2 * prev_numerator
prev_denominator += 2 * denominator
denominator += 2 * prev_denominator
return (denominator + 1) // 2 | project_euler |
def _calculate(days: int, absent: int, late: int) -> int:
# if we are absent twice, or late 3 consecutive days,
# no further prize strings are possible
if late == 3 or absent == 2:
return 0
# if we have no days left, and have not failed any other rules,
# we have a prize string
if days == 0:
return 1
# No easy solution, so now we need to do the recursive calculation
# First, check if the combination is already in the cache, and
# if yes, return the stored value from there since we already
# know the number of possible prize strings from this point on
key = (days, absent, late)
if key in cache:
return cache[key]
# now we calculate the three possible ways that can unfold from
# this point on, depending on our attendance today
# 1) if we are late (but not absent), the "absent" counter stays as
# it is, but the "late" counter increases by one
state_late = _calculate(days - 1, absent, late + 1)
# 2) if we are absent, the "absent" counter increases by 1, and the
# "late" counter resets to 0
state_absent = _calculate(days - 1, absent + 1, 0)
# 3) if we are on time, this resets the "late" counter and keeps the
# absent counter
state_ontime = _calculate(days - 1, absent, 0)
prizestrings = state_late + state_absent + state_ontime
cache[key] = prizestrings
return prizestrings | project_euler |
def solution(days: int = 30) -> int:
return _calculate(days, absent=0, late=0) | project_euler |
def solve(matrix: Matrix, vector: Matrix) -> Matrix:
size: int = len(matrix)
augmented: Matrix = [[0 for _ in range(size + 1)] for _ in range(size)]
row: int
row2: int
col: int
col2: int
pivot_row: int
ratio: float
for row in range(size):
for col in range(size):
augmented[row][col] = matrix[row][col]
augmented[row][size] = vector[row][0]
row = 0
col = 0
while row < size and col < size:
# pivoting
pivot_row = max((abs(augmented[row2][col]), row2) for row2 in range(col, size))[
1
]
if augmented[pivot_row][col] == 0:
col += 1
continue
else:
augmented[row], augmented[pivot_row] = augmented[pivot_row], augmented[row]
for row2 in range(row + 1, size):
ratio = augmented[row2][col] / augmented[row][col]
augmented[row2][col] = 0
for col2 in range(col + 1, size + 1):
augmented[row2][col2] -= augmented[row][col2] * ratio
row += 1
col += 1
# back substitution
for col in range(1, size):
for row in range(col):
ratio = augmented[row][col] / augmented[col][col]
for col2 in range(col, size + 1):
augmented[row][col2] -= augmented[col][col2] * ratio
# round to get rid of numbers like 2.000000000000004
return [
[round(augmented[row][size] / augmented[row][row], 10)] for row in range(size)
] | project_euler |
def interpolated_func(var: int) -> int:
return sum(
round(coeffs[x_val][0]) * (var ** (size - x_val - 1))
for x_val in range(size)
) | project_euler |
def question_function(variable: int) -> int:
return (
1
- variable
+ variable**2
- variable**3
+ variable**4
- variable**5
+ variable**6
- variable**7
+ variable**8
- variable**9
+ variable**10
) | project_euler |
def solution(func: Callable[[int], int] = question_function, order: int = 10) -> int:
data_points: list[int] = [func(x_val) for x_val in range(1, order + 1)]
polynomials: list[Callable[[int], int]] = [
interpolate(data_points[:max_coeff]) for max_coeff in range(1, order + 1)
]
ret: int = 0
poly: Callable[[int], int]
x_val: int
for poly in polynomials:
x_val = 1
while func(x_val) == poly(x_val):
x_val += 1
ret += poly(x_val)
return ret | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def solution(a_limit: int = 1000, b_limit: int = 1000) -> int:
longest = [0, 0, 0] # length, a, b
for a in range((a_limit * -1) + 1, a_limit):
for b in range(2, b_limit):
if is_prime(b):
count = 0
n = 0
while is_prime((n**2) + (a * n) + b):
count += 1
n += 1
if count > longest[0]:
longest = [count, a, b]
ans = longest[1] * longest[2]
return ans | project_euler |
def solution():
script_dir = os.path.dirname(os.path.realpath(__file__))
triangle = os.path.join(script_dir, "triangle.txt")
with open(triangle) as f:
triangle = f.readlines()
a = [[int(y) for y in x.rstrip("\r\n").split(" ")] for x in triangle]
for i in range(1, len(a)):
for j in range(len(a[i])):
number1 = a[i - 1][j] if j != len(a[i - 1]) else 0
number2 = a[i - 1][j - 1] if j > 0 else 0
a[i][j] += max(number1, number2)
return max(a[-1]) | project_euler |
def solution(num: int = 100) -> int:
return sum(map(int, str(factorial(num)))) | project_euler |
def solution(num: int = 100) -> int:
return sum(int(x) for x in str(factorial(num))) | project_euler |
def factorial(num: int) -> int:
sum_of_digits = 0
while number > 0:
last_digit = number % 10
sum_of_digits += last_digit
number = number // 10 # Removing the last_digit from the given number
return sum_of_digits | project_euler |
def solution(num: int = 100) -> int:
nfact = factorial(num)
result = split_and_add(nfact)
return result | project_euler |
def solution(num: int = 100) -> int:
fact = 1
result = 0
for i in range(1, num + 1):
fact *= i
for j in str(fact):
result += int(j)
return result | project_euler |
def solution(power: int = 1000) -> int:
n = 2**power
r = 0
while n:
r, n = r + n % 10, n // 10
return r | project_euler |
def solution(power: int = 1000) -> int:
num = 2**power
string_num = str(num)
list_num = list(string_num)
sum_of_num = 0
for i in list_num:
sum_of_num += int(i)
return sum_of_num | project_euler |
def solution(n: int = 100) -> int:
collect_powers = set()
current_pow = 0
n = n + 1 # maximum limit
for a in range(2, n):
for b in range(2, n):
current_pow = a**b # calculates the current power
collect_powers.add(current_pow) # adds the result to the set
return len(collect_powers) | project_euler |
def solution():
with open(os.path.dirname(__file__) + "/grid.txt") as f:
l = [] # noqa: E741
for _ in range(20):
l.append([int(x) for x in f.readline().split()])
maximum = 0
# right
for i in range(20):
for j in range(17):
temp = l[i][j] * l[i][j + 1] * l[i][j + 2] * l[i][j + 3]
if temp > maximum:
maximum = temp
# down
for i in range(17):
for j in range(20):
temp = l[i][j] * l[i + 1][j] * l[i + 2][j] * l[i + 3][j]
if temp > maximum:
maximum = temp
# diagonal 1
for i in range(17):
for j in range(17):
temp = l[i][j] * l[i + 1][j + 1] * l[i + 2][j + 2] * l[i + 3][j + 3]
if temp > maximum:
maximum = temp
# diagonal 2
for i in range(17):
for j in range(3, 20):
temp = l[i][j] * l[i + 1][j - 1] * l[i + 2][j - 2] * l[i + 3][j - 3]
if temp > maximum:
maximum = temp
return maximum | project_euler |
def largest_product(grid):
n_columns = len(grid[0])
n_rows = len(grid)
largest = 0
lr_diag_product = 0
rl_diag_product = 0
# Check vertically, horizontally, diagonally at the same time (only works
# for nxn grid)
for i in range(n_columns):
for j in range(n_rows - 3):
vert_product = grid[j][i] * grid[j + 1][i] * grid[j + 2][i] * grid[j + 3][i]
horz_product = grid[i][j] * grid[i][j + 1] * grid[i][j + 2] * grid[i][j + 3]
# Left-to-right diagonal (\) product
if i < n_columns - 3:
lr_diag_product = (
grid[i][j]
* grid[i + 1][j + 1]
* grid[i + 2][j + 2]
* grid[i + 3][j + 3]
)
# Right-to-left diagonal(/) product
if i > 2:
rl_diag_product = (
grid[i][j]
* grid[i - 1][j + 1]
* grid[i - 2][j + 2]
* grid[i - 3][j + 3]
)
max_product = max(
vert_product, horz_product, lr_diag_product, rl_diag_product
)
if max_product > largest:
largest = max_product
return largest | project_euler |
def solution():
grid = []
with open(os.path.dirname(__file__) + "/grid.txt") as file:
for line in file:
grid.append(line.strip("\n").split(" "))
grid = [[int(i) for i in grid[j]] for j in range(len(grid))]
return largest_product(grid) | project_euler |
def hexagonal_num(n: int) -> int:
return n * (2 * n - 1) | project_euler |
def is_pentagonal(n: int) -> bool:
root = (1 + 24 * n) ** 0.5
return ((1 + root) / 6) % 1 == 0 | project_euler |
def solution(start: int = 144) -> int:
n = start
num = hexagonal_num(n)
while not is_pentagonal(num):
n += 1
num = hexagonal_num(n)
return num | project_euler |
def parse_roman_numerals(numerals: str) -> int:
total_value = 0
index = 0
while index < len(numerals) - 1:
current_value = SYMBOLS[numerals[index]]
next_value = SYMBOLS[numerals[index + 1]]
if current_value < next_value:
total_value -= current_value
else:
total_value += current_value
index += 1
total_value += SYMBOLS[numerals[index]]
return total_value | project_euler |
def generate_roman_numerals(num: int) -> str:
numerals = ""
m_count = num // 1000
numerals += m_count * "M"
num %= 1000
c_count = num // 100
if c_count == 9:
numerals += "CM"
c_count -= 9
elif c_count == 4:
numerals += "CD"
c_count -= 4
if c_count >= 5:
numerals += "D"
c_count -= 5
numerals += c_count * "C"
num %= 100
x_count = num // 10
if x_count == 9:
numerals += "XC"
x_count -= 9
elif x_count == 4:
numerals += "XL"
x_count -= 4
if x_count >= 5:
numerals += "L"
x_count -= 5
numerals += x_count * "X"
num %= 10
if num == 9:
numerals += "IX"
num -= 9
elif num == 4:
numerals += "IV"
num -= 4
if num >= 5:
numerals += "V"
num -= 5
numerals += num * "I"
return numerals | project_euler |
def solution(roman_numerals_filename: str = "/p089_roman.txt") -> int:
savings = 0
with open(os.path.dirname(__file__) + roman_numerals_filename) as file1:
lines = file1.readlines()
for line in lines:
original = line.strip()
num = parse_roman_numerals(original)
shortened = generate_roman_numerals(num)
savings += len(original) - len(shortened)
return savings | project_euler |
def solution():
script_dir = os.path.dirname(os.path.realpath(__file__))
words_file_path = os.path.join(script_dir, "words.txt")
words = ""
with open(words_file_path) as f:
words = f.readline()
words = [word.strip('"') for word in words.strip("\r\n").split(",")]
words = [
word
for word in [sum(ord(x) - 64 for x in word) for word in words]
if word in TRIANGULAR_NUMBERS
]
return len(words) | project_euler |
def solution() -> int:
answer = 0
decimal_context = decimal.Context(prec=105)
for i in range(2, 100):
number = decimal.Decimal(i)
sqrt_number = number.sqrt(decimal_context)
if len(str(sqrt_number)) > 1:
answer += int(str(sqrt_number)[0])
sqrt_number_str = str(sqrt_number)[2:101]
answer += sum(int(x) for x in sqrt_number_str)
return answer | project_euler |
def digit_factorial_sum(number: int) -> int:
if not isinstance(number, int):
raise TypeError("Parameter number must be int")
if number < 0:
raise ValueError("Parameter number must be greater than or equal to 0")
# Converts number in string to iterate on its digits and adds its factorial.
return sum(DIGIT_FACTORIAL[digit] for digit in str(number)) | project_euler |
def solution(chain_length: int = 60, number_limit: int = 1000000) -> int:
if not isinstance(chain_length, int) or not isinstance(number_limit, int):
raise TypeError("Parameters chain_length and number_limit must be int")
if chain_length <= 0 or number_limit <= 0:
raise ValueError(
"Parameters chain_length and number_limit must be greater than 0"
)
# the counter for the chains with the exact desired length
chains_counter = 0
# the cached sizes of the previous chains
chain_sets_lengths: dict[int, int] = {}
for start_chain_element in range(1, number_limit):
# The temporary set will contain the elements of the chain
chain_set = set()
chain_set_length = 0
# Stop computing the chain when you find a cached size, a repeating item or the
# length is greater then the desired one.
chain_element = start_chain_element
while (
chain_element not in chain_sets_lengths
and chain_element not in chain_set
and chain_set_length <= chain_length
):
chain_set.add(chain_element)
chain_set_length += 1
chain_element = digit_factorial_sum(chain_element)
if chain_element in chain_sets_lengths:
chain_set_length += chain_sets_lengths[chain_element]
chain_sets_lengths[start_chain_element] = chain_set_length
# If chain contains the exact amount of elements increase the counter
if chain_set_length == chain_length:
chains_counter += 1
return chains_counter | project_euler |
def sum_digit_factorials(n: int) -> int:
if n in CACHE_SUM_DIGIT_FACTORIALS:
return CACHE_SUM_DIGIT_FACTORIALS[n]
ret = sum(DIGIT_FACTORIALS[let] for let in str(n))
CACHE_SUM_DIGIT_FACTORIALS[n] = ret
return ret | project_euler |
def chain_length(n: int, previous: set | None = None) -> int:
previous = previous or set()
if n in CHAIN_LENGTH_CACHE:
return CHAIN_LENGTH_CACHE[n]
next_number = sum_digit_factorials(n)
if next_number in previous:
CHAIN_LENGTH_CACHE[n] = 0
return 0
else:
previous.add(n)
ret = 1 + chain_length(next_number, previous)
CHAIN_LENGTH_CACHE[n] = ret
return ret | project_euler |
def solution(num_terms: int = 60, max_start: int = 1000000) -> int:
return sum(1 for i in range(1, max_start) if chain_length(i) == num_terms) | project_euler |
def solution(max_d: int = 12_000) -> int:
fractions_number = 0
for d in range(max_d + 1):
for n in range(d // 3 + 1, (d + 1) // 2):
if gcd(n, d) == 1:
fractions_number += 1
return fractions_number | project_euler |
def solution(limit: int = 50000000) -> int:
ret = set()
prime_square_limit = int((limit - 24) ** (1 / 2))
primes = set(range(3, prime_square_limit + 1, 2))
primes.add(2)
for p in range(3, prime_square_limit + 1, 2):
if p not in primes:
continue
primes.difference_update(set(range(p * p, prime_square_limit + 1, p)))
for prime1 in primes:
square = prime1 * prime1
for prime2 in primes:
cube = prime2 * prime2 * prime2
if square + cube >= limit - 16:
break
for prime3 in primes:
tetr = prime3 * prime3 * prime3 * prime3
total = square + cube + tetr
if total >= limit:
break
ret.add(total)
return len(ret) | project_euler |
def solution(n: int = 2000000) -> int:
primality_list = [0 for i in range(n + 1)]
primality_list[0] = 1
primality_list[1] = 1
for i in range(2, int(n**0.5) + 1):
if primality_list[i] == 0:
for j in range(i * i, n + 1, i):
primality_list[j] = 1
sum_of_primes = 0
for i in range(n):
if primality_list[i] == 0:
sum_of_primes += i
return sum_of_primes | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def prime_generator() -> Iterator[int]:
num = 2
while True:
if is_prime(num):
yield num
num += 1 | project_euler |
def solution(n: int = 2000000) -> int:
return sum(takewhile(lambda x: x < n, prime_generator())) | project_euler |
def is_prime(number: int) -> bool:
if 1 < number < 4:
# 2 and 3 are primes
return True
elif number < 2 or number % 2 == 0 or number % 3 == 0:
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
return False
# All primes number are in format of 6k +/- 1
for i in range(5, int(math.sqrt(number) + 1), 6):
if number % i == 0 or number % (i + 2) == 0:
return False
return True | project_euler |
def solution(n: int = 2000000) -> int:
return sum(num for num in range(3, n, 2) if is_prime(num)) + 2 if n > 2 else 0 | project_euler |
def solution(n: int = 1000) -> int:
# number of letters in zero, one, two, ..., nineteen (0 for zero since it's
# never said aloud)
ones_counts = [0, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, 8]
# number of letters in twenty, thirty, ..., ninety (0 for numbers less than
# 20 due to inconsistency in teens)
tens_counts = [0, 0, 6, 6, 5, 5, 5, 7, 6, 6]
count = 0
for i in range(1, n + 1):
if i < 1000:
if i >= 100:
# add number of letters for "n hundred"
count += ones_counts[i // 100] + 7
if i % 100 != 0:
# add number of letters for "and" if number is not multiple
# of 100
count += 3
if 0 < i % 100 < 20:
# add number of letters for one, two, three, ..., nineteen
# (could be combined with below if not for inconsistency in
# teens)
count += ones_counts[i % 100]
else:
# add number of letters for twenty, twenty one, ..., ninety
# nine
count += ones_counts[i % 10]
count += tens_counts[(i % 100 - i % 10) // 10]
else:
count += ones_counts[i // 1000] + 8
return count | project_euler |
def solution(n: int = 1001) -> int:
total = 1
for i in range(1, int(ceil(n / 2.0))):
odd = 2 * i + 1
even = 2 * i
total = total + 4 * odd**2 - 6 * even
return total | project_euler |
def sum_of_divisors(n: int) -> int:
total = 0
for i in range(1, int(sqrt(n) + 1)):
if n % i == 0 and i != sqrt(n):
total += i + n // i
elif i == sqrt(n):
total += i
return total - n | project_euler |
def solution(n: int = 10000) -> int:
total = sum(
i
for i in range(1, n)
if sum_of_divisors(sum_of_divisors(i)) == i and sum_of_divisors(i) != i
)
return total | project_euler |
def solution(numerator: int = 1, digit: int = 1000) -> int:
the_digit = 1
longest_list_length = 0
for divide_by_number in range(numerator, digit + 1):
has_been_divided: list[int] = []
now_divide = numerator
for _ in range(1, digit + 1):
if now_divide in has_been_divided:
if longest_list_length < len(has_been_divided):
longest_list_length = len(has_been_divided)
the_digit = divide_by_number
else:
has_been_divided.append(now_divide)
now_divide = now_divide * 10 % divide_by_number
return the_digit | project_euler |
def solution():
days_per_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
day = 6
month = 1
year = 1901
sundays = 0
while year < 2001:
day += 7
if (year % 4 == 0 and year % 100 != 0) or (year % 400 == 0):
if day > days_per_month[month - 1] and month != 2:
month += 1
day = day - days_per_month[month - 2]
elif day > 29 and month == 2:
month += 1
day = day - 29
else:
if day > days_per_month[month - 1]:
month += 1
day = day - days_per_month[month - 2]
if month > 12:
year += 1
month = 1
if year < 2001 and day == 1:
sundays += 1
return sundays | project_euler |
def solution(limit: int = 1000000) -> int:
num_cuboids: int = 0
max_cuboid_size: int = 0
sum_shortest_sides: int
while num_cuboids <= limit:
max_cuboid_size += 1
for sum_shortest_sides in range(2, 2 * max_cuboid_size + 1):
if sqrt(sum_shortest_sides**2 + max_cuboid_size**2).is_integer():
num_cuboids += (
min(max_cuboid_size, sum_shortest_sides // 2)
- max(1, sum_shortest_sides - max_cuboid_size)
+ 1
)
return max_cuboid_size | project_euler |
def solution(limit: int = 1000000) -> int:
primes = set(range(3, limit, 2))
primes.add(2)
for p in range(3, limit, 2):
if p not in primes:
continue
primes.difference_update(set(range(p * p, limit, p)))
phi = [float(n) for n in range(limit + 1)]
for p in primes:
for n in range(p, limit + 1, p):
phi[n] *= 1 - 1 / p
return int(sum(phi[2:])) | project_euler |
def solution(limit: int = 1_000_000) -> int:
phi = [i - 1 for i in range(limit + 1)]
for i in range(2, limit + 1):
if phi[i] == i - 1:
for j in range(2 * i, limit + 1, i):
phi[j] -= phi[j] // i
return sum(phi[2 : limit + 1]) | project_euler |
def solution(limit: int = 1500000) -> int:
frequencies: DefaultDict = defaultdict(int)
euclid_m = 2
while 2 * euclid_m * (euclid_m + 1) <= limit:
for euclid_n in range((euclid_m % 2) + 1, euclid_m, 2):
if gcd(euclid_m, euclid_n) > 1:
continue
primitive_perimeter = 2 * euclid_m * (euclid_m + euclid_n)
for perimeter in range(primitive_perimeter, limit + 1, primitive_perimeter):
frequencies[perimeter] += 1
euclid_m += 1
return sum(1 for frequency in frequencies.values() if frequency == 1) | project_euler |
def solution(filename: str = "matrix.txt") -> int:
with open(os.path.join(os.path.dirname(__file__), filename)) as in_file:
data = in_file.read()
grid = [[int(cell) for cell in row.split(",")] for row in data.strip().splitlines()]
dp = [[0 for cell in row] for row in grid]
n = len(grid[0])
dp = [[0 for i in range(n)] for j in range(n)]
dp[0][0] = grid[0][0]
for i in range(1, n):
dp[0][i] = grid[0][i] + dp[0][i - 1]
for i in range(1, n):
dp[i][0] = grid[i][0] + dp[i - 1][0]
for i in range(1, n):
for j in range(1, n):
dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])
return dp[-1][-1] | project_euler |
def is_substring_divisible(num: tuple) -> bool:
if num[3] % 2 != 0:
return False
if (num[2] + num[3] + num[4]) % 3 != 0:
return False
if num[5] % 5 != 0:
return False
tests = [7, 11, 13, 17]
for i, test in enumerate(tests):
if (num[i + 4] * 100 + num[i + 5] * 10 + num[i + 6]) % test != 0:
return False
return True | project_euler |
def solution(n: int = 10) -> int:
return sum(
int("".join(map(str, num)))
for num in permutations(range(n))
if is_substring_divisible(num)
) | project_euler |
def is_pentagonal(n: int) -> bool:
root = (1 + 24 * n) ** 0.5
return ((1 + root) / 6) % 1 == 0 | project_euler |
def solution(limit: int = 5000) -> int:
pentagonal_nums = [(i * (3 * i - 1)) // 2 for i in range(1, limit)]
for i, pentagonal_i in enumerate(pentagonal_nums):
for j in range(i, len(pentagonal_nums)):
pentagonal_j = pentagonal_nums[j]
a = pentagonal_i + pentagonal_j
b = pentagonal_j - pentagonal_i
if is_pentagonal(a) and is_pentagonal(b):
return b
return -1 | project_euler |
def maxpooling(arr: np.ndarray, size: int, stride: int) -> np.ndarray:
arr = np.array(arr)
if arr.shape[0] != arr.shape[1]:
raise ValueError("The input array is not a square matrix")
i = 0
j = 0
mat_i = 0
mat_j = 0
# compute the shape of the output matrix
maxpool_shape = (arr.shape[0] - size) // stride + 1
# initialize the output matrix with zeros of shape maxpool_shape
updated_arr = np.zeros((maxpool_shape, maxpool_shape))
while i < arr.shape[0]:
if i + size > arr.shape[0]:
# if the end of the matrix is reached, break
break
while j < arr.shape[1]:
# if the end of the matrix is reached, break
if j + size > arr.shape[1]:
break
# compute the maximum of the pooling matrix
updated_arr[mat_i][mat_j] = np.max(arr[i : i + size, j : j + size])
# shift the pooling matrix by stride of column pixels
j += stride
mat_j += 1
# shift the pooling matrix by stride of row pixels
i += stride
mat_i += 1
# reset the column index to 0
j = 0
mat_j = 0
return updated_arr | computer_vision |
def avgpooling(arr: np.ndarray, size: int, stride: int) -> np.ndarray:
arr = np.array(arr)
if arr.shape[0] != arr.shape[1]:
raise ValueError("The input array is not a square matrix")
i = 0
j = 0
mat_i = 0
mat_j = 0
# compute the shape of the output matrix
avgpool_shape = (arr.shape[0] - size) // stride + 1
# initialize the output matrix with zeros of shape avgpool_shape
updated_arr = np.zeros((avgpool_shape, avgpool_shape))
while i < arr.shape[0]:
# if the end of the matrix is reached, break
if i + size > arr.shape[0]:
break
while j < arr.shape[1]:
# if the end of the matrix is reached, break
if j + size > arr.shape[1]:
break
# compute the average of the pooling matrix
updated_arr[mat_i][mat_j] = int(np.average(arr[i : i + size, j : j + size]))
# shift the pooling matrix by stride of column pixels
j += stride
mat_j += 1
# shift the pooling matrix by stride of row pixels
i += stride
mat_i += 1
# reset the column index to 0
j = 0
mat_j = 0
return updated_arr | computer_vision |
def __init__(self, k: float, window_size: int):
if k in (0.04, 0.06):
self.k = k
self.window_size = window_size
else:
raise ValueError("invalid k value") | computer_vision |
def __str__(self) -> str:
return str(self.k) | computer_vision |
def detect(self, img_path: str) -> tuple[cv2.Mat, list[list[int]]]:
img = cv2.imread(img_path, 0)
h, w = img.shape
corner_list: list[list[int]] = []
color_img = img.copy()
color_img = cv2.cvtColor(color_img, cv2.COLOR_GRAY2RGB)
dy, dx = np.gradient(img)
ixx = dx**2
iyy = dy**2
ixy = dx * dy
k = 0.04
offset = self.window_size // 2
for y in range(offset, h - offset):
for x in range(offset, w - offset):
wxx = ixx[
y - offset : y + offset + 1, x - offset : x + offset + 1
].sum()
wyy = iyy[
y - offset : y + offset + 1, x - offset : x + offset + 1
].sum()
wxy = ixy[
y - offset : y + offset + 1, x - offset : x + offset + 1
].sum()
det = (wxx * wyy) - (wxy**2)
trace = wxx + wyy
r = det - k * (trace**2)
# Can change the value
if r > 0.5:
corner_list.append([x, y, r])
color_img.itemset((y, x, 0), 0)
color_img.itemset((y, x, 1), 0)
color_img.itemset((y, x, 2), 255)
return color_img, corner_list | computer_vision |
def mean_threshold(image: Image) -> Image:
height, width = image.size
mean = 0
pixels = image.load()
for i in range(width):
for j in range(height):
pixel = pixels[j, i]
mean += pixel
mean //= width * height
for j in range(width):
for i in range(height):
pixels[i, j] = 255 if pixels[i, j] > mean else 0
return image | computer_vision |
def main() -> None:
img_paths, annos = get_dataset(LABEL_DIR, IMAGE_DIR)
print("Processing...")
new_images, new_annos, paths = update_image_and_anno(img_paths, annos, FLIP_TYPE)
for index, image in enumerate(new_images):
# Get random string code: '7b7ad245cdff75241935e4dd860f3bad'
letter_code = random_chars(32)
file_name = paths[index].split(os.sep)[-1].rsplit(".", 1)[0]
file_root = f"{OUTPUT_DIR}/{file_name}_FLIP_{letter_code}"
cv2.imwrite(f"/{file_root}.jpg", image, [cv2.IMWRITE_JPEG_QUALITY, 85])
print(f"Success {index+1}/{len(new_images)} with {file_name}")
annos_list = []
for anno in new_annos[index]:
obj = f"{anno[0]} {anno[1]} {anno[2]} {anno[3]} {anno[4]}"
annos_list.append(obj)
with open(f"/{file_root}.txt", "w") as outfile:
outfile.write("\n".join(line for line in annos_list)) | computer_vision |
def get_dataset(label_dir: str, img_dir: str) -> tuple[list, list]:
img_paths = []
labels = []
for label_file in glob.glob(os.path.join(label_dir, "*.txt")):
label_name = label_file.split(os.sep)[-1].rsplit(".", 1)[0]
with open(label_file) as in_file:
obj_lists = in_file.readlines()
img_path = os.path.join(img_dir, f"{label_name}.jpg")
boxes = []
for obj_list in obj_lists:
obj = obj_list.rstrip("\n").split(" ")
boxes.append(
[
int(obj[0]),
float(obj[1]),
float(obj[2]),
float(obj[3]),
float(obj[4]),
]
)
if not boxes:
continue
img_paths.append(img_path)
labels.append(boxes)
return img_paths, labels | computer_vision |
def update_image_and_anno(
img_list: list, anno_list: list, flip_type: int = 1
) -> tuple[list, list, list]:
new_annos_lists = []
path_list = []
new_imgs_list = []
for idx in range(len(img_list)):
new_annos = []
path = img_list[idx]
path_list.append(path)
img_annos = anno_list[idx]
img = cv2.imread(path)
if flip_type == 1:
new_img = cv2.flip(img, flip_type)
for bbox in img_annos:
x_center_new = 1 - bbox[1]
new_annos.append([bbox[0], x_center_new, bbox[2], bbox[3], bbox[4]])
elif flip_type == 0:
new_img = cv2.flip(img, flip_type)
for bbox in img_annos:
y_center_new = 1 - bbox[2]
new_annos.append([bbox[0], bbox[1], y_center_new, bbox[3], bbox[4]])
new_annos_lists.append(new_annos)
new_imgs_list.append(new_img)
return new_imgs_list, new_annos_lists, path_list | computer_vision |
def random_chars(number_char: int = 32) -> str:
assert number_char > 1, "The number of character should greater than 1"
letter_code = ascii_lowercase + digits
return "".join(random.choice(letter_code) for _ in range(number_char)) | computer_vision |
def warp(
image: np.ndarray, horizontal_flow: np.ndarray, vertical_flow: np.ndarray
) -> np.ndarray:
flow = np.stack((horizontal_flow, vertical_flow), 2)
# Create a grid of all pixel coordinates and subtract the flow to get the
# target pixels coordinates
grid = np.stack(
np.meshgrid(np.arange(0, image.shape[1]), np.arange(0, image.shape[0])), 2
)
grid = np.round(grid - flow).astype(np.int32)
# Find the locations outside of the original image
invalid = (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]))
grid[invalid] = 0
warped = image[grid[:, :, 1], grid[:, :, 0]]
# Set pixels at invalid locations to 0
warped[invalid[:, :, 0] | invalid[:, :, 1]] = 0
return warped | computer_vision |
def horn_schunck(
image0: np.ndarray,
image1: np.ndarray,
num_iter: SupportsIndex,
alpha: float | None = None,
) -> tuple[np.ndarray, np.ndarray]:
if alpha is None:
alpha = 0.1
# Initialize flow
horizontal_flow = np.zeros_like(image0)
vertical_flow = np.zeros_like(image0)
# Prepare kernels for the calculation of the derivatives and the average velocity
kernel_x = np.array([[-1, 1], [-1, 1]]) * 0.25
kernel_y = np.array([[-1, -1], [1, 1]]) * 0.25
kernel_t = np.array([[1, 1], [1, 1]]) * 0.25
kernel_laplacian = np.array(
[[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]
)
# Iteratively refine the flow
for _ in range(num_iter):
warped_image = warp(image0, horizontal_flow, vertical_flow)
derivative_x = convolve(warped_image, kernel_x) + convolve(image1, kernel_x)
derivative_y = convolve(warped_image, kernel_y) + convolve(image1, kernel_y)
derivative_t = convolve(warped_image, kernel_t) + convolve(image1, -kernel_t)
avg_horizontal_velocity = convolve(horizontal_flow, kernel_laplacian)
avg_vertical_velocity = convolve(vertical_flow, kernel_laplacian)
# This updates the flow as proposed in the paper (Step 12)
update = (
derivative_x * avg_horizontal_velocity
+ derivative_y * avg_vertical_velocity
+ derivative_t
)
update = update / (alpha**2 + derivative_x**2 + derivative_y**2)
horizontal_flow = avg_horizontal_velocity - derivative_x * update
vertical_flow = avg_vertical_velocity - derivative_y * update
return horizontal_flow, vertical_flow | computer_vision |
def price_plus_tax(price: float, tax_rate: float) -> float:
return price * (1 + tax_rate) | financial |
Subsets and Splits