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let rec fib_aux (n : int) (a : int) (b : int) : int = match n with 0 -> a | _ -> fib_aux (n-1) b (a+b) ;; let fib_tl (n : int) : int = fib_aux n 1 1 ;; fib_tl 27;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> ((float_of_int n) *. (fact (n - 1)));; |
let binomial (n: int) (k: int) : float = if n < 0 then domain () else (if k > n then domain () else fact n /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int (dx) *. float_of_int (dx) +. float_of_int (dy) *. float_of_int (dy)) ;; |
let is_prime (n : int) : bool = if n <= 1 then domain () else let rec check m = (m * m > n) || (n mod m != 0 && check (m + 1)) in n >= 2 && check 2 ;; |
let rec fib_aux (n : int) (a : int) (b : int) : int = match n with 0 -> a | _ -> fib_aux (n-1) b (a+b) ;; let fib_tl (n : int) : int = fib_aux n 1 1 ;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int n *. fact (n - 1);; |
let binomial (n: int) (k: int): float = if n < 0 then domain () else (if k > n then domain () else fact n /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int (dx * dx + dy * dy));; |
let is_prime (n:int): bool = let rec divides (i:int) (n:int): bool= if (i = 1) then true else if ((n mod i) = 0) then false else divides (i-1) n in if n <= 1 then domain () else divides (n-1) n;; let pi = 2.0 *. asin 1.0;; |
let rec fib_aux n a b = if (n = 1) then b else (fib_aux (n-1) b (a+b));; let fib_tl n = if (n=0) then 1 else fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> (float_of_int n) *. fact (n - 1);; |
let binomial (n: int) (k: int) = if n>=k && k>=0 then fact n /. (fact k *. fact (n - k)) else domain();; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = abs(x1 - x2) in let dy = abs(y1 - y2) in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime (n:int) :bool = if n<=1 then domain() else if n = 2 || n = 3 then true else let rec check (n:int) (a:int) :bool = match (n mod a) with |0 -> false |_ -> if a>2 then check n (a-1) else true in check n (int_of_float(sqrt(float_of_int n)));; |
let rec fib_aux n a b = if n<2 then 1 else if n<3 then a+b else fib_aux (n-1) b (a+b) let fib_tl n = fib_aux n 1 1;; |
let rec fact (n: int): float = match n with 0 -> 1. | _ -> float_of_int n *. fact(n - 1);; |
let binomial (n: int) (k: int) : float = if n < 0 then domain () else (if k = n then 1. else fact n /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = float_of_int (x1 - x2) in let dy = float_of_int (y1 - y2) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n: int) = let rec prime_helper x n = if x = 1 then true else if n mod x = 0 then false else prime_helper (x - 1) n in if n <= 1 then domain() else prime_helper (int_of_float (sqrt(float_of_int n))) n ;; |
let rec fib_aux n a b = if n = 0 then a else fib_aux (n - 1) b (a + b) let fib_tl n = if n < 0 then domain() else fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int n *. fact (n - 1);; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (if k = n then 1. else fact n /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int (dx * dx + dy * dy)) ;; let rec is_prime_helper n x = if x*x <= n then if (n mod x) = 0 then false else is_prime_helper n (x+1) else true;; |
let is_prime n = if n <= 1 then domain () else is_prime_helper n 2;; |
let rec fib_aux n a b = if n=0 then a else if n=1 then b else fib_aux (n-1) b (a+b) let fib_tl n = if n < 0 then domain() else fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int(n) *. fact (n - 1);; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (if k > n then domain () else fact n /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime n = let rec helper n d = if d > (int_of_float(sqrt (float_of_int n))+1) then true else if (n mod d) == 0 then false else helper n (d+1) in if n <= 1 then domain() else (n==2) || (helper n 2) ;; |
let rec fib_aux n a b = if n = 2 then a+b else fib_aux (n-1) b (a+b) let fib_tl n = if n = 0 || n = 1 then 1 else if n < 0 then domain() else fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int(n) *. fact (n - 1);; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (if k > n then domain () else fact n /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime n = let rec helper n d = if d > (int_of_float(sqrt (float_of_int n))+1) then true else if (n mod d) == 0 then false else helper n (d+1) in if n <= 1 then domain() else (n==2) || (helper n 2) ;; |
let rec fib_aux n a b = if n = 2 then a+b else fib_aux (n-1) b (a+b) let fib_tl n = if n = 0 || n = 1 then 1 else if n < 0 then domain() else fib_aux n 1 1;; |
let rec fact (n: int): float = match n with 0 -> 1. | _ -> (float_of_int n) *. fact (n - 1);; |
let binomial (n: int) (k: int): float = if n < 0 then domain () else if k > n then domain () else fact n /. (fact k *. fact (n - k));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int (dx * dx + dy * dy)) ;; let rec checker (x: float) (n: int): bool = if x**2. > (float_of_int n) then true else if x**2. <= (float_of_int n) && n mod (int_of_float x) = 0 then false else checker (x +. 1.) n;; |
let is_prime (n: int): bool = if n <= 1 then domain () else checker 2. n;; |
let rec fib_aux n a b = if n < 1 then b else fib_aux (n - 1) b (a + b) let fib_tl n = fib_aux n 0 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int n *. fact (n - 1);; |
let binomial (n: int) (k: int) = if k > n then domain () else fact n /. (fact k *. fact (n-k));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime (n : int) : bool = let rec not_div ( m : int) : bool = if m*m > n then true else if n mod m != 0 then not_div (m + 1) else false in (n >= 2) && (not_div 2) ;; |
let rec fib_aux (n : int) (m: int) ( a: int) ( b: int) : int = if m = n then a else fib_aux (n) (m+1) (b) (a+b) ;; let fib_tl (n: int): int = fib_aux (n+1) 0 0 1;; |
let fact (n: int): float = let rec helper n acc = if n=0 then acc else helper(n-1) (acc*.float_of_int(n)) in helper n 1.;; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (if k = n then 1. else if n<k then domain() else fact n /. (fact (n-k) *. fact (k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x2 - x1 in let dy = y2 - y1 in if (dx * dx + dy * dy) < 0 then domain () else sqrt(float_of_int(dx * dx + dy * dy));; |
let is_prime n: bool = let rec helper n x : bool = if n <= 1 then domain () else( if x*x <= n then if (n mod x == 0) then false else helper n (x+1) else true ) in helper n 2;; |
let rec fib_aux n a b = if n = 0 then b else fib_aux (n-1) (b) (a+b) let fib_tl n = fib_aux n 0 1;; |
let fact (n: int): float = let rec helper n acc = if n=0 then acc else helper(n-1) (acc*.float_of_int(n)) in helper n 1.;; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (if k = n then 1. else if n<k then domain() else fact n /. (fact (n-k) *. fact (k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x2 - x1 in let dy = y2 - y1 in if (dx * dx + dy * dy) < 0 then domain () else sqrt(float_of_int(dx * dx + dy * dy));; |
let is_prime n: bool = let rec helper n x : bool = if n <= 1 then domain () else( if x*x <= n then if (n mod x == 0) then false else helper n (x+1) else true ) in helper n 2;; |
let rec fib_aux n a b = if n = 0 then b else fib_aux (n-1) (b) (a+b) let fib_tl n = fib_aux n 0 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> (float_of_int n) *. (fact (n - 1)) ;; |
let binomial (n: int) (k: int) = if k < 0 then domain () else (if k > n then domain () else fact n /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int (dx * dx) +. float_of_int (dy * dy)) ;; |
let is_prime (n:int) = if n<=1 then domain() else let rec helper (curr:int)= if float_of_int curr>sqrt(float_of_int n) then true else if (n mod curr) =0 then false else helper (curr+1) in helper 2;; |
let rec fib_aux n a b = if n=0 then b else if n=1 then b else if n>1 then fib_aux (n-1) (b) (a+b) else domain() ;; let fib_tl n =fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int(n) *. (fact (n-1));; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (if k = n then 1. else (fact n) /. (fact k) /. (fact (n-k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = (x1 - x2)*(x1 - x2) in let dy = (y1 - y2)*(y1 - y2) in sqrt (float_of_int((dx+ dy))) ;; |
let is_prime n = let rec helper n x = if (n<=1) then domain () else if (x*x > n) then true else if (n mod x)=0 then false else helper (n) (x+1) in helper n 2;; |
let rec fib_aux n a b = if (n=0) then a else if (n=1) then b else fib_aux (n-1) (b) (a+b) let fib_tl n = fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int(n) *. (fact (n - 1));; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (if k > n || k < 0 then domain () else fact (n) /. (fact k *. fact (n - k)));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x2 - x1 in let dy = y2 - y1 in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime (n: int): bool = let rec check_mod_zero (x:int) (m : int): bool= match m with | 1 -> true | _ -> check_mod_zero x (m-1) && (x mod m <> 0) in match n with 0 -> domain() | 1 -> domain() | _ -> check_mod_zero n (n-1) ;; |
let rec fib_aux n a b = match n with | 0 -> a + b | _ -> fib_aux (n-1) b (a+b) let fib_tl (n: int) : int = match n with | 0 -> 1 | 1 -> 1 | _ -> fib_aux (n-2) 1 1;; |
let mode (l: 'a list) : 'a = let rec aux lst ( (max_el, max_num) : 'a * int) = match lst with | [] -> max_el | h::_ ->( let nL = List.filter (fun x -> x <> h) lst in let count = List.length (List.filter (fun x -> x = h) lst) in if count > max_num then aux nL (h, count) else aux nL (max_el, max_num) ) in let sortedL = List.sort compare l in match sortedL with | [] -> failwith "Invalid Input" | minE::_ -> let count = List.length (List.filter (fun x -> x = minE) sortedL) in aux (List.filter (fun x -> x <> minE) sortedL) (minE,count) ;; |
let pair_mode (l: 'a list) : 'a * 'a = match l with | [] -> failwith "Invalid Input" | _::t -> match t with | [] -> failwith "Invalid Input" | _::_ -> let l2 = List.rev l in match l2 with | [] -> failwith "Cannot occur" | _::t2 -> let combined = List.combine (List.rev t2) t in mode (combined) ;; |
let convert_time ( (from_unit, val_) : time_unit value) (to_unit : time_unit) : time_unit value = match to_unit with | Second -> ( match from_unit with | Second -> (from_unit, val_) | Hour -> (to_unit, val_ *. 3600.0) ) | Hour -> ( match from_unit with | Hour -> (from_unit, val_) | Second -> (to_unit, val_ /. 3600.0) ) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) (to_unit : dist_unit) : dist_unit value = match to_unit with | Foot -> ( match from_unit with | Foot -> (from_unit, val_) | Meter -> (to_unit, val_ /. 0.3048) | Mile -> (to_unit, val_ *. 5280.0) ) | Meter -> ( match from_unit with | Meter -> (from_unit, val_) | Foot -> (to_unit, val_ *. 0.3048) | Mile -> (to_unit, val_ *. 0.3048 *. 5280.0) ) | Mile -> ( match from_unit with | Mile -> (from_unit, val_) | Foot -> (to_unit, val_ /. 5280.0) | Meter -> (to_unit, val_ /. 0.3048 /. 5280.0) ) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) (to_unit: speed_unit) : speed_unit value = let (d_unit,t_unit) = from_unit in let (d_unit',t_unit') = to_unit in let c = convert_dist (d_unit, val_) d_unit' in let (_,cVal) = c in let c2 = convert_time (t_unit', cVal) t_unit in let (_,c2Val) = c2 in (to_unit, c2Val) ;; |
let add_speed (a : speed_unit value) ((b_unit, b_val) : speed_unit value) : speed_unit value = let a_conv = convert_speed a b_unit in let (_,a_conVal) = a_conv in (b_unit, (a_conVal +. b_val)) ;; |
let passes_da_vinci t = let rec sumTlist l acc = match l with | [] -> acc | Leaf :: tl -> sumTlist tl acc | Branch (width, _) :: tl -> sumTlist tl (acc +. (width *. width)) in let rec check l = match l with | [] -> true | Leaf :: tl -> check tl | Branch (width, subtree) :: tl -> let childSum = sumTlist subtree 0. in let wSq = width *. width in if ( (not (check subtree)) || childSum > wSq ) then false else check tl in check [t] ;; |
let invalidInput () = failwith "Invalid Input, dad";; |
let mode (l : 'a list) : 'a = let rec aux (l : 'a list) ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with | [] -> max_el | h::t -> if (h = cur_el) then if (cur_num = max_num) then aux t (h, cur_num + 1) (h, cur_num + 1) else aux t (h, cur_num + 1) (max_el, max_num) else aux t (h, 0) (max_el, max_num) in aux (List.sort compare l) ((List.nth (List.sort compare l) 0), -1) ((List.nth (List.sort compare l) 0), -1) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if (List.length l < 2) then invalidInput() else let tupleize (l1 : 'a list) (l2 : 'a list) : 'a * 'a = let call_mode (l : 'b list) : 'b = mode l in call_mode (List.combine l1 l2) in tupleize (List.rev (List.tl (List.rev l))) (List.tl l) ;; |
let convert_time ((from_unit, val_) : time_unit value) (to_unit : time_unit) : time_unit value = match (from_unit, val_) with | (Second, _) -> (match to_unit with | (Second) -> (from_unit, val_) | (Hour) -> (Hour, val_ /. 3600.)) | (Hour, _) -> (match to_unit with | (Second) -> (Hour, val_ *. 3600.) | (Hour) -> (from_unit, val_)) ;; |
let convert_dist ((from_unit, val_) : dist_unit value) (to_unit : dist_unit) : dist_unit value = match to_unit with | (Foot) -> (match (from_unit, val_) with | (Foot, v) -> (Foot, val_) | (Meter, v) -> (Foot, v /. 0.3048) | (Mile, v) -> (Foot, v *. 5280.)) | (Meter) -> (match (from_unit, val_) with | (Foot, v) -> (Meter, v *. 0.3048) | (Meter, v) -> (Meter, v) | (Mile, v) -> (Meter, v *. 1609.344)) | (Mile) -> (match (from_unit, val_) with | (Foot, v) -> (Mile, v /. 5280.) | (Meter, v) -> (Mile, v /. 1609.344) | (Mile, v) -> (Mile, v)) ;; |
let convert_speed ((from_unit, val_) : speed_unit value) to_unit : speed_unit value = match to_unit with | (Foot, Second) -> (let (a,b) = from_unit in ((Foot, Second), (let (_, v) = (convert_dist (a, val_)(Foot)) in v /. (let(_,v) = (convert_time (b, 1.)(Second)) in v)))) | (Foot, Hour) -> (let (a,b) = from_unit in ((Foot, Hour), (let (_, v) = (convert_dist (a, val_) (Foot)) in v /. (let (_, v) = (convert_time (b, 1.) (Hour)) in v)))) | (Meter, Second) -> (let (a,b) = from_unit in ((Meter, Second), (let (_, v) = (convert_dist (a, val_) (Meter)) in v/. (let (_, v) = (convert_time (b, 1.) (Second)) in v)))) | (Meter, Hour) -> (let (a,b) = from_unit in ((Meter, Hour), (let (_, v) = (convert_dist (a, val_) (Meter)) in v /. (let (_, v) = (convert_time (b, 1.) (Hour)) in v)))) | (Mile, Second) -> (let (a,b) = from_unit in ((Mile, Second), (let (_, v) = (convert_dist (a, val_) (Mile)) in v/. (let (_, v) = (convert_time (b, 1.) (Second)) in v)))) | (Mile, Hour) -> (let (a,b) = from_unit in ((Mile, Hour),(let (_, v) = (convert_dist (a, val_) (Mile)) in v /. (let (_, v) = (convert_time (b, 1.) (Hour)) in v)))) ;; |
let dist_traveled time ((speed_unit, speed_val) : speed_unit value) : dist_unit value = let (a,b) = time in let (c,_) = speed_unit in let ((dist, _), v) = convert_speed (speed_unit, speed_val) (c, a) in (dist, b *. v) ;; let rec fetch_subtrees t = match t with | hd::tl -> (match hd with | Branch (v, _) -> v *. v +. fetch_subtrees tl | _ -> 0. +. fetch_subtrees tl) | [] -> 0. ;; let rec passes_da_vinci t = match t with | Leaf -> true | Branch (v, tl) -> if (v *. v < fetch_subtrees tl) then false else match tl with | hd::_ -> passes_da_vinci hd | [] -> true ;; |
let mode (l: 'a list) : 'a = if l = [] then failwith "empty list received." else let lst = List.sort compare l in let rec get_mode my_list ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) : 'a = match my_list with | [] -> max_el | head::tail -> if head = cur_el then if cur_num + 1 > max_num then get_mode tail (cur_el, cur_num + 1) (cur_el, cur_num + 1) else get_mode tail (cur_el, cur_num + 1) (max_el, max_num) else get_mode tail (head, 1) (max_el, max_num) in get_mode lst (List.hd lst, 0) (List.hd lst, 0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if l = [] || List.length l = 1 then failwith "input list is too short." else let rec to_bigrams (my_list : 'a list) (cur_bigrams :('a * 'a) list) : (('a * 'a) list) = match my_list with | e1::e2::tail -> to_bigrams (e2::tail) ((e1,e2)::cur_bigrams) | _ -> cur_bigrams in mode (to_bigrams l []) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = if from_unit = to_unit then (from_unit, val_) else match (from_unit, to_unit) with | (Second, Hour) -> (Hour, val_ /. 3600.) | (Hour, Second) -> (Second, val_ *. 3600.) | _ -> failwith "Error in checking units" ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = if from_unit = to_unit then (from_unit, val_) else match (from_unit, to_unit) with | (Foot, Meter) -> (Meter, val_ *. 0.3048) | (Meter, Foot) -> (Meter, val_ /. 0.3048) | (Foot, Mile) -> (Mile, val_ /. 5280.) | (Mile, Foot) -> (Foot, val_ *. 5280.) | (Meter, Mile) -> (Mile, val_ /. 1609.344) | (Mile, Meter) -> (Meter, val_ *. 1609.344) | _ -> failwith "Error in checking units" ;; |
let convert_speed (((from_unit_dist, from_unit_time), val_) : speed_unit value) (to_unit_dist, to_unit_time) : speed_unit value = let (_, val_dist) = convert_dist (from_unit_dist, val_) to_unit_dist in let (_, val_time) = convert_time (from_unit_time, 1.) to_unit_time in ((to_unit_dist, to_unit_time), val_dist /. val_time) ;; |
let dist_traveled time (((dist_unit, time_unit), speed_val) : speed_unit value) : dist_unit value = let (_, duration) = convert_time time time_unit in (dist_unit, speed_val *. duration) ;; let compare_widths ((par_width, children) : (float * tree list)) : bool = let fold_squares (acc : float) (t : tree) : float = match t with | Leaf -> acc | Branch (width, _) -> acc +. width *. width in List.fold_left fold_squares 0. children <= par_width *. par_width ;; let rec passes_da_vinci (t : tree) = match t with | Leaf -> true | Branch (width, children) -> if width <= 0. then failwith "invalid width value" else compare_widths (width, children) && List.fold_left (&&) true (List.map passes_da_vinci children) ;; |
let mode (l: 'a list) : 'a = if l = [] then failwith "empty list received." else let lst = List.sort compare l in let rec get_mode my_list ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) : 'a = match my_list with | [] -> max_el | head::tail -> if head = cur_el then if cur_num + 1 > max_num then get_mode tail (cur_el, cur_num + 1) (cur_el, cur_num + 1) else get_mode tail (cur_el, cur_num + 1) (max_el, max_num) else get_mode tail (head, 1) (max_el, max_num) in get_mode lst (List.hd lst, 0) (List.hd lst, 0) ;; |
let pair_mode (l: 'a list) : 'a * 'a = if l = [] || List.length l = 1 then failwith "input list is too short." else let rec to_bigrams (my_list : 'a list) (cur_bigrams :('a * 'a) list) : (('a * 'a) list) = match my_list with | e1::e2::tail -> to_bigrams (e2::tail) ((e1,e2)::cur_bigrams) | _ -> cur_bigrams in mode (to_bigrams l []) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = if from_unit = to_unit then (from_unit, val_) else match (from_unit, to_unit) with | (Second, Hour) -> (Hour, val_ /. 3600.) | (Hour, Second) -> (Second, val_ *. 3600.) | _ -> failwith "error in checking units." ;; |
let convert_dist ((from_unit, val_) : dist_unit value) to_unit : dist_unit value = if from_unit = to_unit then (from_unit, val_) else match (from_unit, to_unit) with | (Foot, Meter) -> (Meter, val_ *. 0.3048) | (Meter, Foot) -> (Meter, val_ /. 0.3048) | (Foot, Mile) -> (Mile, val_ /. 5280.) | (Mile, Foot) -> (Foot, val_ *. 5280.) | (Meter, Mile) -> (Mile, val_ /. 1609.344) | (Mile, Meter) -> (Meter, val_ *. 1609.344) | _ -> failwith "error in checking units." ;; |
let convert_speed (((from_unit_dist, from_unit_time), val_) : speed_unit value) (to_unit : speed_unit) : speed_unit value = let (_, val_dist) = convert_dist (from_unit_dist, val_) (fst to_unit) in let (_, val_time) = convert_time (from_unit_time, 1.) (snd to_unit) in (to_unit, val_dist /. val_time) ;; |
let dist_traveled time ((speed_unit, speed_val) : speed_unit value) : dist_unit value = let (_, duration) = convert_time time (snd speed_unit) in ((fst speed_unit), speed_val *. duration) ;; let compare_widths ((par_width, children) : (float * tree list)) : bool = let fold_squares (acc : float) (t : tree) : float = match t with | Leaf -> acc | Branch (width, _) -> acc +. width *. width in List.fold_left fold_squares 0. children <= par_width *. par_width ;; let rec passes_da_vinci (t : tree) : bool = match t with | Leaf -> true | Branch (width, children) -> if width <= 0. then failwith "invalid width value." else compare_widths (width, children) && List.fold_left (&&) true (List.map passes_da_vinci children) ;; |
let mode (l: 'a list) : 'a = let rec aux l ((cur_el, cur_num) : 'a * int) ((max_el, max_num) : 'a * int) = match l with [] -> max_el | a :: l' when a = max_el -> aux l' (cur_el, cur_num + 1) (max_el, max_num + 1) | a :: l' when a = cur_el && cur_num = max_num -> aux l' (cur_el, cur_num + 1) (cur_el, cur_num + 1) | a :: l' when a = cur_el -> aux l' (cur_el, cur_num +1) (max_el, max_num) | a :: l' -> aux l' (a, 1) (max_el, max_num) in match List.sort compare l with [] -> failwith "Error : Empty list." | a :: l' -> aux l' (a, 1) (a, 1) ;; |
let pair_mode (l: 'a list) : 'a * 'a = let rec get_bigrams l bigrams = match l with [] -> bigrams | [a] -> bigrams | a :: l' -> get_bigrams l' ((a, List.hd l') :: bigrams) in match l with [] -> failwith "Error : Empty list -> No bi-gram." | [a] -> failwith "Error : List has one element -> No bi-gram." | _ -> mode (get_bigrams l []) ;; |
let convert_time ((from_unit, val_) : time_unit value) to_unit : time_unit value = match (from_unit, to_unit) with (Hour, Second) -> (Second, val_ *. 3600.) | (Second, Hour) -> (Hour, val_ /. 3600.) | _ -> (from_unit, val_) ;; |
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