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let rec fib_aux n a b = if n < 1 then 1 else if n = 2 then a + b else if a >= b then fib_aux (n-1) a (a+b) else fib_aux(n-1) (a+b) (b) let fib_tl n = let a = 1 in let b = 1 in fib_aux n a b;; |
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;; |
let rec fib_aux n a b = if n < 1 then 1 else if n = 2 then a + b else if a >= b then fib_aux (n-1) a (a+b) else fib_aux(n-1) (a+b) (b) let fib_tl n = let a = 1 in let b = 1 in fib_aux n a b;; |
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 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: int): bool = if n <= 1 then raise NotImplemented else let rec divider (x: int): bool = x * x > n || (n mod x != 0 && divider (x + 1)) in n >= 2 && divider 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 = if n = 0 then 1 else if n = 1 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 < 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 = let rec check x y = match y with | 1 -> true | _ -> match x mod y with | 0 -> false | _ -> check x (y-1) in match n with | 0 | 1 -> domain () | _ -> check n (n-1);; |
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 = match n with | 0 | 1 -> 1 | _ -> fib_aux n 1 1;; |
let fact (n: int): float = let rec fact_helper (n: int) (res: float): float = match n with | 0 -> res | 1 -> res | _ -> fact_helper (n-1) (float_of_int(n) *. res) in fact_helper n 1.0;; |
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 = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int ((dx * dx) + (dy * dy)));; |
let is_prime (n : int) : bool = let rec is_primer_helper (n : int) (counter_from_2 : int) : bool = if n <= 1 then domain () else if (counter_from_2 * counter_from_2) <= n then if n mod counter_from_2 == 0 then false else is_primer_helper (n) (counter_from_2 + 1) else true in is_primer_helper n 2;; |
let rec fib_aux (n : int) (a : int) (b : int) : int = match n with | 0 -> a | 1 -> b | _ -> 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 0. 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 = let rec helper n x = if n <= 1 then domain () else if (x * x <= n) && (n mod x == 0) then false else if (x * x <= n) && (n mod x != 0) then helper n (x + 1) else true 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 fact (n: int): float = let rec fact' n = if n = 0 then 1. else float_of_int n *. fact' (n - 1) in if n < 0 then domain() else fact' n ;; |
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 and dy = y1 - y2 in sqrt (float_of_int dx ** 2. +. float_of_int dy ** 2.) ;; |
let is_prime n = let rec is_prime' x = if x = 1 then true else if n mod x = 0 then false else is_prime' (x - 1) in if n <= 1 then domain() else ( let x = int_of_float (sqrt (float_of_int n)) in (x = 1) || (is_prime' x)) ;; |
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 = match n with 0 -> 1 | 1 -> 1 | _ -> fib_aux n 1 1;; |
let rec fact_tl (counter: float) (curFact: float) : float= if counter = 0. then curFact else fact_tl (counter -. 1.) (curFact *. counter) let fact (n: int): float = match n with | 0 -> 1. | _ -> let c = (float_of_int n) in (fact_tl c 1.);; |
let binomial (n: int) (k: int): float = if n < 0 || 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 = x1 - x2 in let dy = y1 - y2 in ((dx * dx) + (dy * dy)) |> float_of_int |> sqrt ;; let rec div_counter (number: int) (start: int) (count: int): int = if start >= number then count else div_counter number (start + 1) (if number mod start == 0 then (count + 1) else count) ;; |
let is_prime (n: int): bool = if n <= 1 then domain () else div_counter n 2 0 == 0 let rec approx_zeta (exp: float) (acc: float) (n: int) (sum_so_far: float): float = if acc > ((float_of_int n) ** exp) then sum_so_far else approx_zeta exp acc (n + 1) (sum_so_far +. ((float_of_int n) ** exp)) ;; |
let rec fib_aux (n: int) (count: int) (a: int) (b: int): int = if count = n then b else fib_aux n (count + 1) b (a + b) let fib_tl (n:int): int= match n with | 0 -> 1 | _ -> 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) = if n < 0 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 = y2 - y1 in sqrt (float_of_int((dx * dx) + (dy * dy))) ;; |
let is_prime (n: int): bool = let rec helper n i = if n = 2 then true else if n mod i = 0 then false else if i * i > n then true else helper (n) (i+1) in if n <= 1 then domain () else helper n 2;; |
let rec fib_aux n a b = if n = 1 then b else fib_aux (n-1) (b) (b+a) let fib_tl n = if n = 0 then 1 else if n = 1 then 1 else fib_aux (n) (1) (1);; |
let rec fact (n: int): float = if n < 0 then domain(); 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 < 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 helper n i = if n = 2 then true else if n mod i = 0 then false else if i * i > n then true else helper (n) (i+1) in if n <= 1 then domain () else helper n 2;; |
let rec fib_aux n a b = if n = 1 then b else fib_aux (n-1) (b) (b+a) let fib_tl n = if n = 0 then 1 else if n = 1 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): 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 = if n <= 1 then domain () else let x = n - 1 in let rec loopprime x n = if x <= 1 then true else (if ((n mod x) = 0) then false else loopprime (x-1) n) in loopprime x n;; |
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 = 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 is_prime (n: int): bool = if n <= 1 then domain () else (let rec check_div (m:int) : bool = (m*m > n) || (check_div (m + 1) && n mod m != 0) in check_div 2);; |
let rec fib_aux n a b = if n = 1 then b else (fib_aux (n-1) b (b+a));; 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 < 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 <= 1 then domain () else let rec check_dividor n x = if x = 1 then true else match (n mod x) with | 0 -> false | _ -> check_dividor n (x-1) in check_dividor n (int_of_float (sqrt (float_of_int (n))));; |
let rec fib_aux n a b = if n >= 2 then fib_aux (n-1) (b) (a+b) else if n=1 then b else a 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 || 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 = if n <= 1 then domain() else let rec helper x = if x * x > n then true else ( if n mod x = 0 then false else helper (x+1) ) in helper 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 = x2 - x1 in let dy = y2 - y1 in sqrt ((float_of_int dx *. float_of_int dx) +. (float_of_int dy *. float_of_int dy)) ;; |
let is_prime n = let rec helper_prime n x = if n = 2 then true else if (n mod x) = 0 then false else if (x*x) <= n then helper_prime n (x + 1) else true in helper_prime n 2 ;; |
let rec fib_aux n a b = if n = 0 then a else fib_aux (n - 1) (a + b) a ;; let fib_tl n = if n < 0 then domain () else 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) = 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) *. float_of_int(dx) +. float_of_int(dy) *. float_of_int(dy))) ;; |
let is_prime n = if n > 1 then let rec prime_for_real m = m * m > n || n mod m != 0 && prime_for_real (m+1) in n != 1 && prime_for_real 2 else domain ();; |
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 (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 = if n<=1 then domain() else let rec divisible a b = match b with | 1 -> true | _ -> (a mod b <> 0) && divisible a (b-1) in match n with | 0 | 1 -> false | _ -> divisible n (n-1) ;; |
let rec fib_aux (n: int) (a: int) (b: int) : int = if n<0 then domain() else if n==0 then 1 else if n==1 then (a+b) else let y =n-1 in fib_aux y 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 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 let rec helper n x = if n mod x > 0 && x * x > n then true else if n = 2 then true else if n mod x > 0 && x * x <= n then helper n (x+1) else false in helper n 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 domain () = raise NotImplemented;; |
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) +. float_of_int (dy * dy)) ;; |
let is_prime (n : int): bool = let rec helper_prime x = if n <= 1 then domain () else if x = n then true else if n mod x != 0 then helper_prime (x+1) else false in helper_prime 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 domain () = raise NotImplemented;; |
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) +. float_of_int (dy * dy)) ;; |
let is_prime (n : int): bool = let rec helper_prime x = if n <= 1 then domain () else if x = n then true else if n mod x != 0 then helper_prime (x+1) else false in helper_prime 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. | _ -> if n > 0 then float_of_int n *. fact (n - 1) else domain () ;; |
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_of_int (dx * dx + dy * dy)) ;; |
let is_prime n = if n <= 1 then domain () else let rec find_divisor n x = if n = 2 then true else if (n mod x) = 0 then false else if (x * x) <= n then find_divisor n (x + 1) else true in find_divisor n 2 ;; |
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