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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 rec is_prime_rec (n:int) (x:int) : bool = if (x*x)>n then true else if (n mod x) = 0 then false else let x = x + 1 in is_prime_rec n x;; |
let is_prime (n: int): bool = if n <= 1 then domain () else let x = 2 in is_prime_rec n x;; |
let rec fib_aux (n:int) (a:int) (b:int):int = if n = 0 then b else (fib_aux (n-1) (b) (a+b)) let fib_tl (n:int):int = 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 n < 0 then domain () else if n < k then domain () else (if k = n then 1. else fact n /. (fact k) /. fact (n - k)) let max (a:int) (b:int) = if a >= b then a else b;; let min (a:int) (b:int) = if a <= b then a else b;; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = float_of_int(max x1 x2 - min x1 x2) in let dy = float_of_int(max y1 y2 - min y1 y2) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime n = if n <= 1 then domain() else ( let div = (n - 1) in let rec remainderCheck div n = match div with 1 -> true | _ -> match n mod div with 0 -> false | _ -> remainderCheck (div - 1) n in remainderCheck div n) ;; let pi = 2.0 *. asin 1.0;; let currentterm (n:float) (k:float) : float = 1. /. (n ** k);; |
let rec fib_aux n a b = if n = 0 then a 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 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 = if n <= 1 then raise Domain else let rec x_divides n x = if x*x > n then true else if n mod x = 0 then false else x_divides n (x+1) in x_divides 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: int): int = if n < 0 then raise Domain else (if (n=1 || n = 0) then 1 else fib_aux (n+1) 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) :float = if (n < 0 || n < k) 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 = x2 - x1 in let dy = y2 - y1 in let dx_squared = dx * dx in let dy_squared = dy * dy in sqrt((float_of_int dx_squared) +. (float_of_int dy_squared));; |
let is_prime (n: int): bool = if n <= 1 then domain() else let rec helper n x = if n = 2 then true else if n mod x = 0 then false else if x*x > n then true else helper (n) (x+1) in helper n 2;; |
let rec fib_aux (n: int) (a: int) (b: int): int = 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) :float = if (n < 0 || n < k) 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 = x2 - x1 in let dy = y2 - y1 in let dx_squared = dx * dx in let dy_squared = dy * dy in sqrt((float_of_int dx_squared) +. (float_of_int dy_squared));; |
let is_prime (n: int): bool = if n <= 1 then domain() else let rec helper n x = if n = 2 then true else if n mod x = 0 then false else if x*x > n then true else helper (n) (x+1) in helper n 2;; |
let rec fib_aux (n: int) (a: int) (b: int): int = 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 then domain () 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 = let rec helper n c = if c = 1 then true else if (n mod c) = 0 then false else helper n (c - 1) in if n <= 1 then domain () else helper n (truncate (sqrt (float_of_int n))) ;; |
let rec fib_aux n a b = if n = 0 then b else fib_aux (n-1) b (a+b) let fib_tl n = if n <= 1 then 1 else fib_aux (n-1) 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 rec p_helper (n: int) (d: int) : bool = if d * d > n then true else (if n mod d = 0 then false else p_helper n (d+1));; |
let is_prime (n : int) : bool = if n < 1 then domain () else p_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 = if n < 0 then domain () else fib_aux n 0 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> fact (n - 1) *. (float) n;; |
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 = (float) (x1 - x2) in let dy = (float) (y1 - y2) in sqrt (dx *. dx +. dy *. dy) ;; let rec prime (n:int) (i:int) : bool = if n = i then true else if (i * i) > n then true else if n mod i = 0 then false else prime n (i+1);; |
let is_prime (n: int) : bool = if n <= 1 then domain() else prime n 2 ;; |
let rec fib_aux (n:int) (a:int) (b:int) : int = if n = 0 then a else if n = 1 then b else fib_aux (n-1) b (a+b) let fib_tl (n:int) : int = if n < 0 then domain() else fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> fact (n - 1) *. (float) n;; |
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 = (float) (x1 - x2) in let dy = (float) (y1 - y2) in sqrt (dx *. dx +. dy *. dy) ;; let rec prime (n:int) (i:int) : bool = if n = i then true else if (i * i) > n then true else if n mod i = 0 then false else prime n (i+1);; |
let is_prime (n: int) : bool = if n <= 1 then domain() else prime n 2 ;; |
let rec fib_aux (n:int) (a:int) (b:int) : int = if n = 0 then a else if n = 1 then b else fib_aux (n-1) b (a+b) let fib_tl (n:int) : int = 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 || 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 = x1 - x2 in let dy = y1 - y2 in (sqrt (float_of_int((dx * dx) + (dy * dy)))) ;; |
let is_prime (n: int) : bool = if n <= 1 then domain () else let rec has_divisors (m: int) : bool = (m * m) > n || ((n mod m) != 0 && has_divisors (m+1)) in has_divisors (2) ;; |
let rec fib_aux n a b : int = if n = 0 then a else if n = 1 then b else fib_aux (n - 1) (b) (a + b) ;; let fib_tl n : 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) = 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 = 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 < 2 then domain () else ( let rec find_x (n : int) (x : int) = if (x * x) > n then true else ( if (n mod x) = 0 then false else find_x n (x+1) ) in find_x 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 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 = 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 < 2 then domain () else ( let rec find_x (n : int) (x : int) = if (x * x) > n then true else ( if (n mod x) = 0 then false else find_x n (x+1) ) in find_x 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 = if n < 0 then domain () else ( match n with 0 -> 1. | _ -> (float_of_int n) *. ( fact (n-1) ) ) ;; |
let binomial (n: int) (k: int) = if n < 0 or k > n or k < 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 = 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 < 2 then domain () else ( let rec find_x (n : int) (x : int) = if (x * x) > n then true else ( if (n mod x) = 0 then false else find_x n (x+1) ) in find_x 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 = if n < 0 then domain () else fib_aux n 0 1 ;; |
let rec fact (n: int) : float = if n < 0 then domain () else ( match n with 0 -> 1. | _ -> (float_of_int n) *. ( fact (n-1) ) ) ;; |
let binomial (n: int) (k: int) = if n < 0 or k > n or k < 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 is_prime (n: int) : bool = if n < 2 then domain () else ( let rec find_x (n : int) (x : int) = if (x * x) > n then true else ( if (n mod x) = 0 then false else find_x n (x+1) ) in find_x 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 = if n < 0 then domain () else 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): 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 = match n with | 0 | 1 -> domain() | _ -> let i = (n - 1) in let rec check i n = if ( i > 1) then if (n mod i = 0) then false else check (i - 1) n else true in check i n ;; |
let rec fib_aux n a b = if (n = 0) then a else fib_aux (n-1) (a+b) a let fib_tl n = fib_aux n 1 0;; |
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 || k < 0 || 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 = if n <= 1 then domain() else let z = true in (let r = n in (let k = n-1 in (let rec is_prime2 ((r, k): (int * int)) : bool = match k with | 0 | 1 -> z | _ -> if r mod k = 0 then false else is_prime2 (r, (k-1)) in is_prime2 (r, k-1))));; |
let rec fib_aux n a b = match n with | 0 -> a | 1 -> b | _ -> fib_aux (n-1) b (a+b) let fib_tl n = match n with | 0 -> 1 | 1 -> 1 | _ -> 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 || k < 0 || 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 = if n <= 1 then domain() else let z = true in (let r = n in (let k = n-1 in (let rec is_prime2 ((r, k): (int * int)) : bool = match k with | 0 | 1 -> z | _ -> if r mod k = 0 then false else is_prime2 (r, (k-1)) in is_prime2 (r, k-1))));; |
let rec fib_aux n a b = match n with | 0 | 1 -> b | _ -> fib_aux (n-1) b (a+b) let fib_tl n = match n with | 0 -> 1 | 1 -> 1 | _ -> fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1.0 | _ -> float_of_int(n) *. (fact (n - 1));; |
let binomial (n: int) (k: int) = if n < 0 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 = if n <= 1 then domain () else let rec divisible a n = if a * a > n then true else match n mod a with 0 -> false | _ -> divisible (a + 1) n in divisible 2 n ;; |
let rec fib_aux n a b = if n == 0 then 1 else if n == 1 then a+b else let w = n-1 in let v = a+b in fib_aux w b v let fib_tl n = fib_aux n 0 1;; |
let rec fact (n: int): float = match n with 0 | 1 -> 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 = float_of_int (x1 - x2) in let dy = float_of_int (y1 - y2) in sqrt (dx *. dx +. dy *. dy) ;; let rec is_div (n: int) (x: int) : bool = if n mod x = 0 then false else if x * x > n then true else is_div n (x + 1) ;; |
let is_prime n = if n <= 1 then domain () else match n with 2 | 3 -> true | _ -> is_div 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 n *. fact (n - 1);; |
let binomial (n: int) (k: int) = if n < 0 || 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 (dx * dx + dy * dy)) ;; |
let is_prime (n:int) : bool = if n <= 1 then domain () else if n = 2 then true else let rec f x sqrtn : bool = if n mod x = 0 then false else if x > int_of_float sqrtn then true else f (x + 1) sqrtn in f 2 (sqrt (float n)) ;; |
let rec fib_aux n a b = if n <= 0 then a else fib_aux (n - 1) (a + b) a ;; let fib_tl n = match n with | 0 -> 1 | 1 -> 1 | _ -> fib_aux (n - 1) 1 1 ;; |
let rec fact (n: int): float = if n < 0 then domain () else match n with | 0 -> 1. | _ -> (float_of_int n) *. fact (n-1) ;; |
let binomial (n: int) (k: int) : float = if n < 0 || k < 0 || n < k then domain () else fact n /. ((fact k) *. (fact (n - k))) ;; |
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