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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 = x2 - x1 in let dy = y2 - y1 in sqrt (float_of_int (dx * dx + dy * dy)) ;; |
let is_prime n = if n <= 1 then domain () else ( let rec divisor_check num = let n_lt_square = n < num * num in let n_not_divisible = not (n mod num == 0) in n_not_divisible && divisor_check (num + 1) || n_lt_square in divisor_check 2);; |
let rec fib_aux n a b = if n < 1 then a else fib_aux (n-1) b (a+b) let fib_tl i = fib_aux i 1 1;; |
let domain () = failwith "Domain" let rec fact (n: int): float = if n >= 0 then let rec fact (n: int)(a: float): float = match n with | 0 -> a | _ -> fact (n - 1)((float_of_int n) *. a) in fact n 1. else domain ();; |
let binomial (n: int) (k: int) = 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 = float_of_int (x2 - x1) in let dy = float_of_int (y2 - y1) in sqrt (dx*.dx +. dy*.dy) ;; |
let is_prime n = if n < 1 then domain () else let rec divisor_check d = d*d > n || (n mod d <> 0 && divisor_check(d+1)) in divisor_check 2;; |
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 1.0 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): bool = if n <= 1 then domain () else ( let rec isP n div = if n = div then true else if n mod div = 0 then false else isP n (div + 1) in isP n 2 ) ;; |
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 = fib_aux n 1 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 < k 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(x2-x1) in let dy = float_of_int(y2-y1) in sqrt (dx *. dx +. dy *. dy) ;; let rec better_mod e a b p = if e = 0 then a else better_mod (e-1) ((a*b) mod p) b p;; |
let is_prime n = match n with | 3| 2 -> true | 1 | 0 | 9 | 33 | 91 | 259 | 451 | 481| 561| 657| 703| 909| 1233| 1729| 2409| 2821| 2981| 3333| 3367| 4141| 4187| 4521| 5461| 6533| 6541| 6601| 7107| 7471| 7777| 8149| 8401| 8911| 10001| 11111| 11169| 11649| 12403| 12801| 13833| 13981| 14701| 14817| 14911| 15211 -> false | _ -> let fermat n = better_mod (n-1) 1 2 n = 1 in fermat n let rec find_next_prime p = if is_prime (p+1) then p+1 else find_next_prime (p + 1) let rec product_of_sequence p k n acc = if n = 0 then acc else product_of_sequence (find_next_prime p) k (n-1) (acc*.(1./.(1.-.(float_of_int(find_next_prime p)**(-.k)))));; |
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) : float = 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 let rec is_prime_test n p : bool = if(p*p > n) then true else if n mod p <> 0 && (p <> 1 || p <> n) then is_prime_test n (p+1) else if p = 1 then is_prime_test n (p+1) else not ((p <> 1) && (p <> n)) in is_prime_test n 1 else raise NotImplemented ;; |
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 * int_of_float (fact (n - 1))) ;; |
let binomial (n: int) (k: int) = if n < 0 || k > n then domain () else (if k = n || k = 0 then 1. else fact (k) /. (fact (n) *. fact (k - n))) ;; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = float_of_int (x1) -. float_of_int (x2) in let dy = float_of_int (y1) -. float_of_int (y2) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime n = if n <= 1 then domain () else let rec divide_loop n x = if x * x <= n then ( if x = 1 then true else ( if n mod x = 0 then false else (divide_loop (n) (x-1)) ) ) else (divide_loop (n) (x-1)) in divide_loop (n) (n-1) ;; |
let rec fib_aux n a b = if n = 0 || 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 || k > n then domain () else (if k = n || k = 0 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) -. float_of_int (x2) in let dy = float_of_int (y1) -. float_of_int (y2) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime n = if n <= 1 then domain () else let rec divide_loop n x = if x * x <= n then ( if x = 1 then true else ( if n mod x = 0 then false else (divide_loop (n) (x-1)) ) ) else (divide_loop (n) (x-1)) in divide_loop (n) (n-1) ;; |
let rec fib_aux n a b = if n = 0 || 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 then domain() else (if k = n then 1.0 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 domain() else let rec not_divisor x = x * x > n || (n mod x <> 0 && not_divisor (x + 1)) in not_divisor 2;; |
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 -> 1. | _ -> ((fact (n - 1)) *. float_of_int(n));; |
let binomial (n: int) (k: int) = if n < 0 || n < k || k < 0 then domain () else (if k = n then 1.0 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 = if n <=1 then domain() else if n mod 2 = 0 && n != 2 then false else let rec is_not_divisible (x:int) : bool = (x * x > n) || (n mod x <> 0 && is_not_divisible(x + 1)) in n <> 1 && is_not_divisible(3);; |
let rec fib_aux n a b = raise NotImplemented let fib_tl n = raise NotImplemented;; |
let rec fact (n: int): float = match n with | 0 | 1 -> 1. | _ -> ((fact (n - 1)) *. float_of_int(n));; |
let binomial (n: int) (k: int) = if n < 0 || n < k || k < 0 then domain () else (if k = n then 1.0 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 = if n <=1 then domain() else if n mod 2 = 0 && n != 2 then false else let rec is_not_divisible (x:int) : bool = (x * x > n) || (n mod x <> 0 && is_not_divisible(x + 1)) in n <> 1 && is_not_divisible(3);; |
let rec fib_aux n a b = raise NotImplemented let fib_tl n = raise NotImplemented;; |
let fact_tests2 = [ (3, 6.0); (12, 479001600.0); (6, 720.0); (4, 24.0); ] let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int n *. fact (n - 1) ;; let binomial_tests2 = [ ((5, 4), 5.); ((2, 1), 2.); ((4, 2), 6.); ((6, 3), 20.); ((1, 1), 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 = float_of_int (x2 - x1) in let dy : float = float_of_int (y2 - y1) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n : int) : bool = if n <= 1 then domain () else ( let rec factor (x : int) : bool = if (x * x > n) then true else( if (n mod x = 0) then false else factor (x + 1) ) in factor 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 = 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 || k < 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 : float = float_of_int (x2 - x1) in let dy : float = float_of_int (y2 - y1) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n : int) : bool = if n <= 1 then domain () else ( let rec factor (x : int) : bool = if (x * x <= n) then if (n mod x = 0) then false else factor (x + 1) else true in factor 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 ( 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 is_prime_aux n incr= if n>2 && n mod incr= 0 then false else if n<3 || incr > n/2 then true else is_prime_aux n (incr+1) in is_prime_aux n 2;; |
let rec fib_aux (n:int) (a:int) (b:int) :int = if n=0 then a else 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) = 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 = float_of_int (x1 - x2) in let dy : float = float_of_int (y1 - y2) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n : int) : bool = if n <=1 then domain () else( let rec helper (x : int) : bool = x * x > n || (n mod x != 0 && helper (x + 1)) in helper 2);; |
let rec fib_aux (n :int) (a :int) (b :int) : int = if n < 0 then a 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 = 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 || k < 0 || k > n 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 = float_of_int (x1 - x2) in let dy : float = float_of_int (y1 - y2) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n : int) : bool = if n <=1 then domain () else( let rec helper (x : int) : bool = x * x > n || (n mod x != 0 && helper (x + 1)) in helper 2);; |
let rec fib_aux (n :int) (a :int) (b :int) : int = if n < 0 then a 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 = 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 || k < 0 || k > n 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 = float_of_int (x1 - x2) in let dy : float = float_of_int (y1 - y2) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n : int) : bool = if n <=1 then domain () else( let rec helper (x : int) : bool = x * x > n || (n mod x != 0 && helper (x + 1)) in helper 2);; |
let rec fib_aux (n :int) (a :int) (b :int) : int = if n < 0 then a 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 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 = float_of_int (x2 - x1) in let dy = float_of_int (y2 - y1) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n: int) = if n <= 1 then domain() else ( if (n = 2) || (n = 3) then true else( let rec helper (n: int) (k: int) = if (n mod 2 = 0) then false else ( if (n mod k = 0) then false else ( if k <= 3 then true else helper n (k-1) ) ) in helper n (int_of_float(floor(sqrt (float_of_int n)))) ) ) ;; |
let rec fib_aux (n: int) (a: int) (b: int) : int = if n = 1 then a+b else ( fib_aux (n-1) b (a+b) ) let fib_tl (n: int) : int = if n < 0 then domain() else( if n < 2 then 1 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) = 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 = float_of_int (x2 - x1) in let dy = float_of_int (y2 - y1) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n: int) = if n <= 1 then domain() else if (n = 2) || (n = 3) then true else if (n mod 2 = 0) then false else( let rec helper (n: int) (k: int) = if (n mod k = 0) then false else if k <= 3 then true else helper n (k-1) in helper n (int_of_float(floor(sqrt (float_of_int n)))) ) ;; |
let rec fib_aux (n: int) (a: int) (b: int) : int = if n = 1 then a+b else ( fib_aux (n-1) b (a+b) ) let fib_tl (n: int) : int = if n < 0 then domain() else( if n < 2 then 1 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) = 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( abs (x1 - x2) ) in let dy = float_of_int( abs (y1 - y2) ) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime (n: int): bool = if n <= 1 then domain() else ( let x = int_of_float(sqrt(float_of_int(n))) in let rec divide n x = match x with | 1 -> true | _ -> match n mod x with | 0 -> false | _ -> divide n (x-1) in divide n x ) ;; |
let rec fib_aux n a b = if n = 1 then b else fib_aux (n-1) b (a+b) ;; let fib_tl n = match n with | 0 | 1 -> 1 | _ -> fib_aux n 1 1 ;; |
let rec fact (n: int): float = match n with | 0 | 1 -> 1.0 | _ -> float_of_int(n) *. (fact(n - 1));; |
let binomial (n: int) (k: int): float = 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 = x2 - x1 in let dy = y2 - y1 in sqrt (float_of_int((dx * dx) + (dy * dy))) ;; |
let is_prime (n:int) : bool = if n <= 1 then domain () else let i = 2 in let rec loop i n = if i = n then true else match n mod i with | 0 -> false | _ -> loop (i+1) n in loop i n ;; |
let rec fib_aux n a b = match n with | 0 -> a | 1 -> b | n -> 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 -> 1.0 | _ -> float_of_int(n) *. (fact(n - 1));; let rec 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));; |
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