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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. | _ -> (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 if 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) -. (float_of_int x1) in let dy = (float_of_int y2) -. (float_of_int y1) in sqrt ((dx *. dx) +. (dy *. dy)) ;; |
let is_prime n = let a = int_of_float (sqrt (float_of_int n)) in if n <= 1 then domain() else if n = 2 then true else if n = 4 then false else let rec recp n m = if m = 1 then true else if (n mod m) = 0 then false else recp n (m-1) in recp n a;; |
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+1) 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) = 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 = if n > 1 then let rec is_divisible (k : int) : bool = k * k > n || (n mod k != 0 && is_divisible (k + 1)) in (n >= 2 && is_divisible 2) else domain ();; |
let rec fib_aux n a b = if n == 0 then a else if n == 1 then b else let new_a = b in let new_b = a + b in let new_n = n - 1 in fib_aux new_n new_a new_b let fib_tl n = if n < 0 then domain () else if n == 1 then 1 else let new_n = n + 1 in fib_aux new_n 0 1;; |
let fact (n: int): float = let rec help n result = if n = 0 then result else help (n - 1) ((float_of_int n) *. result) in if n < 0 then domain() else help 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 = x2 - x1 in let dy = y2 - y1 in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime (n:int) : bool = let rec helper n x = if x*x > n then true else(if n mod x = 0 && x != n then false else helper n (x+1)) in if n > 1 then helper n 2 else domain();; |
let rec fib_aux n a b = if n = 0 || n = 1 then b + a else fib_aux (n-1) b (a+b) let fib_tl (n:int) : int = if n < 0 then domain() else fib_aux n 0 1;; |
let fact (n: int): float = let rec fact_helper n result = if n = 0 then result else fact_helper (n - 1) ((float_of_int n) *. result) in if n < 0 then domain() else fact_helper 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 = x2 - x1 in let dy = y2 - y1 in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime (n:int) : bool = let rec is_prime_helper n x = if x*x > n then true else(if n mod x = 0 && x != n then false else is_prime_helper n (x+1)) in if n > 1 then is_prime_helper n 2 else domain();; |
let rec fib_aux n a b = if n = 0 || n = 1 then b + a else fib_aux (n-1) b (a+b) let fib_tl (n:int) : int = if n < 0 then domain() else fib_aux n 0 1;; |
let rec fact (n: int): float = match n with | 0 -> 1.0 | 1 -> 1.0 | _ -> 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(x2 - x1) in let dy = float_of_int(y2 - y1) in sqrt (dx *. dx +. dy *. dy) ;; |
let is_prime n = let rec not_divisor y = y * y > n || n mod y != 0 && not_divisor (y + 1) in n >= 2 && not_divisor 2;; |
let rec fib_aux n a b = if n = 0 then 1 else if n = 1 then b else fib_aux (n-1) b (a+b) let fib_tl n = fib_aux (n+1) 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 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)(dx * dx + dy * dy)) ;; |
let is_prime n = if n<=1 then domain() else if n =2 then true else let rec helper x n = if x*x<=n then helper (x+1) n else x-1 in let rec isprime a n= if n mod a =0 && a!=1 then false else if a= 1 then true else isprime (a-1) n in isprime (helper 1 n) n;; |
let rec fib_aux n a b = if n >0 then fib_aux (n-1) b (a+b) else 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 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)(dx * dx + dy * dy)) ;; |
let is_prime n = if n<=1 then domain() else if n =2 then true else let rec helper x n = if x*x<=n then helper (x+1) n else x-1 in let rec isprime a n= if n mod a =0 && a!=1 then false else if a= 1 then true else isprime (a-1) n in isprime (helper 1 n) n;; |
let rec fib_aux n a b = if n >0 then fib_aux (n-1) b (a+b) else 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 domain () else if 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 = (y1 - y2) in sqrt(float_of_int((dx) * (dx) + (dy) * (dy))) ;; |
let is_prime (n: int): bool = if n <= 1 then domain() else( let x = n in let rec helper x n = match x with | 2 -> true | _ -> (if n mod (x-1) = 0 then false else helper (x-1) n) in helper x n) ;; |
let rec fib_aux n a b = match n with | 0 -> a | _ -> fib_aux (n-1) b (a + b) ;; let fib_tl n = if n = 0 then 1 else if n = 1 then 1 else fib_aux n 1 1 ;; |
let fact_tests = [ (0, 1.); (1, 1.); (2, 2.); (5, 120.) ] 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 = 0 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) +. float_of_int(dy * dy)) ;; let rec helper x n = if x * x > n then true else ( if n mod x = 0 then false else helper (x+1) n ) ;; |
let is_prime n = if n <= 1 then domain() else helper 2 n ;; |
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 -> 1.0 | _ -> (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 = 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 divideTillZero (x : int) : bool = (x * x) > n || (n mod x != 0 && divideTillZero (x + 1) ) in divideTillZero 2;; |
let rec fib_aux n a b = if n = 0 then 1 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 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:int) = if n <= 1 then domain () else let rec factor (x:int) = if n mod x = 0 && n != x then false else ( if x * x > n then true else factor (x + 1) ) in factor 2;; |
let rec fib_aux n a b = if n-2 = 0 then a+b else fib_aux (n-1) b (a+b) let fib_tl n = if n <= 1 then 1 else fib_aux n 1 1;;; |
let fact (n : int) = let rec f (n : int) (acc : float) = match n with | 0 | 1 -> acc | _ -> f (n-1) ((float_of_int n) *. acc) in f 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 = 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 mod0 x = x * x > n || ((n mod x <> 0) && mod0 (x+1)) in mod0 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 = match n with | 0 | 1 -> 1 | _ -> fib_aux n 0 1 ;; |
let rec fact (n: int): float = if n=0 then 1. else 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 = 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 rec nonDivisible (x: int) : bool = if ( n < x * x ) then true else (( nonDivisible(x + 1) && (n mod x != 0) ) ) in nonDivisible(2) );; |
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 + 1) 0 1;; |
let rec fact (n: int): float = if n=0 then 1. else 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 = 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 rec nonDivisible (x: int) : bool = ( n < x * x ) || ( nonDivisible(x + 1) && (n mod x != 0) ) in nonDivisible(2) );; |
let rec fib_aux n a b = if n >= 0 then fib_aux n-1 a b else fib_aux n-1 a b let fib_tl n = fib_aux 2 0 0;; |
let rec fact (n: int): float = if n=0 then 1. else 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 = 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 rec nonDivisible (x: int) : bool = ( n < x * x ) || ( nonDivisible(x + 1) && (n mod x != 0) ) in nonDivisible(2) );; |
let rec fib_aux n a b = if n = 0 then b else if n = 1 then b else fib_aux (n - 1) (b) (a + b) let fib_tl n = 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) = 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 is_primeRec (a: int) (b: int) = if (a <= 1) then false else if b = 1 then true else if (a mod b) = 0 then false else is_primeRec (a) (b - 1);; |
let is_prime n = is_primeRec n (int_of_float(sqrt(float_of_int(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 = if n < 0 then domain() else match n with | 0 -> 1. | _ -> (float n) *. (fact (int_of_float (float(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 = x2 - x1 in let dy = y2 - y1 in sqrt (float ((dx * dx) + (dy * dy))) ;; let rec is_prime_rc n a = if (a*a <= n) then ( if (n mod a <> 0) then is_prime_rc n (a+1) else false) else (true);; |
let is_prime n = if n > 1 then ( if n > 2 then (is_prime_rc n 2) else true) else domain();; |
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 fib_aux n 1 1 else domain();; |
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): 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 : bool = if n <= 1 then domain () else if n == 2 then true else if n == 3 then true else let rec iterate (k:int) : bool = (n mod k != 0 && iterate (k+1)) || k*k > n in iterate 2;; |
let rec fib_aux n a b = let rec iterate k a b = if k == n then b else iterate (k+1) b (a+b) in iterate 0 0 1 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 = 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 helper n x = if x*x <= n && n mod x = 0 then false else (if (x+1) * (x+1) > n then true else helper n (x+1)) in helper n 2 ) ;; |
let rec fib_aux n a b = if n < 0 then domain() else if n = 0 then b else fib_aux (n-1) b (b+a);; 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 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(dx) *. float(dx)) +. (float(dy)*.float(dy))) ;; |
let is_prime n = if n<= 1 then domain() else let rec check_factor i = if float i > sqrt (float n) then true else ( if float(n) /. float(i) = float(n/i) then false else ( check_factor(i + 1) ) ) in check_factor 2;; |
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