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let rec fib_aux a b n = if n=0 then b else fib_aux b (a+b) (n-1) let fib_tl n = if n=0 then 1 else fib_aux 1 1 (n-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 > 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 if n = 2 then true else( let rec helper_prime x = if (n mod x = 0) then false else if x * x <= n then helper_prime (x+1) else true in helper_prime 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 = let rec helper (n:float) : float = match n with | 0. -> 1. | _ -> n *. helper (n -. 1.) in helper (float_of_int n);; |
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 = if n<= 1 then domain () else if n=2 then true else let rec checker i n = if n mod i = 0 then false else if (i*i) < n then checker (i+1) n else true in checker 2 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 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 divides (n: int) (k: int) = if float_of_int k > sqrt(float_of_int n) then true else if n mod k = 0 then false else divides n (k+1) in divides n 2;; |
let rec fib_aux n a b = if n = 1 || n = 0 then (a+b) 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 if n = 0 then 1. else float_of_int n *. fact (n - 1);; |
let binomial (n : int) (k : int) : float = if n < 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 (x2 - x1) in let dy = 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 helper n acc = if acc * acc > n then true else if n / acc * acc = n then false else helper n (acc + 1) in helper n 2 ;; |
let rec fib_aux n a b = if n < 0 then domain () else if n = 0 || n = 1 then (a + 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) : float = if (n < 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 = 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 = if n <= 1 then domain () else (let x = int_of_float(sqrt(float_of_int(n))) in let rec check (x: int) : bool = if (x = 1) then true else if (n mod x) = 0 then false else check(x-1) in check x) ;; |
let rec fib_aux n a b = let x = n - 1 in ( if (x < -1) then domain () else if (x = -1 || x = 0) then a + b 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 > 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 = 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 = if n <= 1 then domain () else (let x = int_of_float(sqrt(float_of_int(n))) in let rec check (x: int) : bool = if (x = 1) then true else if (n mod x) = 0 then false else check(x-1) in check x) ;; |
let rec fib_aux n a b = let x = n - 1 in ( if (x < -1) then domain () else if (x = -1 || x = 0) then a + b 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 -> 1.0 | _ -> float_of_int n *. fact (n - 1) ;; |
let binomial (n: int) (k: int) = if n < 0 then domain () else let z = n - k in fact n /. (fact k *. fact z);; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = x1 - x2 in let dy = y1 - y2 in let dx_f = float_of_int dx in let dy_f = float_of_int dy in sqrt ((dx_f ** 2.) +. (dy_f ** 2.)) ;; |
let is_prime n = if n <= 1 then domain() else if n = 2 then true else let rec counter num x = if x * x > num then true else match num mod x with |0 -> false |_ -> counter num (x + 1) in counter n 2;; |
let rec fib_aux n a b = if n > 1 then let n = n - 1 in let c = a + b in fib_aux n b c else 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: int) = if (n <= 1) then domain () else let rec min_divisor n k = if (k * k > n) then 0 else if ((n / k) * k == n) then k else min_divisor n (k+1) in min_divisor n 2 == 0 ;; |
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<=1 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 let a= fact n in let b= fact k in let c= fact(n-k) in a /. (b *. c) ;; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float= let dx= x2 - x1 in let dy= y2 - y1 in let dx_2= dx * dx in let dy_2= dy * dy in sqrt(float_of_int(dx_2 + dy_2));; |
let is_prime n = if n<=1 then domain() else if n=2 then true else let rec helper (n:int) (x:int)= 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 = 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 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 = let rec helper x = if x <= 1 then true else (n mod x != 0 && helper (x-1)) in if n <= 1 then domain () else helper (n-1);; |
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 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 = 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 helper x = if x <= 1 then true else (n mod x != 0 && helper (x-1)) in if n <= 1 then domain () else helper (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) 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) = 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 = 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 helper x = if x <= 1 then true else (n mod x != 0 && helper (x-1)) in if n <= 1 then domain () else helper (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) 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 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 = let rec helper x = if x <= 1 then true else (n mod x != 0 && helper (x-1)) in if n <= 1 then domain () else helper (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) 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 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 = let rec helper x = if x <= 1 then true else (n mod x != 0 && helper (x-1)) in if n <= 1 then domain () else helper (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) 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 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 = let rec helper x = if x <= 1 then true else (n mod x != 0 && helper (x-1)) in if n <= 1 then domain () else helper (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) 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 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 = let rec helper x = if x <= 1 then true else (n mod x != 0 && helper (x-1)) in if n <= 1 then domain () else helper (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) 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 x = sqrt(45.) in (((4,8), (7,2)), x); (((0,0), (0,0)), 0.) ] ;; |
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 factors (acc: int) (n:int) (z:int) = if float_of_int(z) > (float_of_int(n) ** 0.5) then acc else let x = (n mod z) in if x == 0 then factors (acc+z) n (z+1) else factors acc n (z+1) in if n<2 then domain () else let acc = factors 0 n 1 in acc == 1;; |
let rec fib_aux n a b = match n with | 0 -> b | _ -> fib_aux (n-1) (a+b) a 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 < 0 then domain () else (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 = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int(dx * dx) +. float_of_int(dy * dy)) ;; |
let is_prime n = if n<=1 then domain() else let rec helper n (div:int) = if float_of_int(div) > sqrt(float_of_int(n)) then true else if (n mod div) == 0 then false else helper n (div+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. | n -> 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 domain() else let rec not_divisor d = d*d > n || (n mod d <> 0 && not_divisor (d+1)) in n >= 2 && not_divisor 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 1. else (float n) *. (fact (n-1));; |
let binomial (n: int) (k: int): float = if k>n then domain() else fact(n) /. (fact(k) *. fact(n-k));; let absolute (x: int) (y: int): float = if x>y then (float (x-y)) else (float (y-x));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = let dx = absolute x1 x2 in let dy = absolute y1 y2 in sqrt ((dx *. dx) +. (dy *. dy));; let rec prime_helper (n: int) (x: int): bool = if x = 1 then true else if n mod x = 0 then false else prime_helper (n) (x-1) ;; |
let is_prime (n: int): bool = if n<=1 then domain() else let x = floor(sqrt (float n)) in prime_helper n (truncate x) ;; |
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