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let rec fib_aux n a b = match n with | 0 -> 1 | 1 -> b | _ -> fib_aux (n-1) b (a + b) let fib_tl n = match n < 0 with | true -> domain () | _ -> 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 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 < 0 then domain () else match n with | 0 -> domain () | 1 -> domain () | 2 -> true | _ -> let rec primeRec n i : bool = match (n mod i = 0),((i * i) > n) with | _,true -> true | true,_ -> false |_ -> primeRec n (i + 1) in primeRec n 2;; |
let rec fib_aux n a b = match n with | 0 -> 1 | 1 -> b | _ -> fib_aux (n-1) b (a + b) let fib_tl n = match n < 0 with | true -> domain () | _ -> 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 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 < 0 then domain () else match n with | 0 -> domain () | 1 -> domain () | 2 -> true | _ -> let rec primeRec n i : bool = match (n mod i = 0),((i * i) > n) with | _,true -> true | true,_ -> false |_ -> primeRec n (i + 1) in primeRec n 2;; |
let rec fib_aux n a b = match n with | 0 -> 1 | 1 -> b | _ -> fib_aux (n-1) b (a + b) let fib_tl n = match n < 0 with | true -> domain () | _ -> 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 = if n <= 1 then domain () else let rec helper (f: int) : bool = if f*f > n then true else if (n mod f) == 0 then false else helper(f+1) in helper(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 <=1 then 1 else if n == 2 then 2 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 (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 match n with 2 -> true | 3 -> true | n -> let rec check_divisible x n = if x * x > n then false else if n mod x = 0 then true else check_divisible (succ x) n in check_divisible 2 n |> not;; |
let rec fib_aux n a b = if n = 0 then a + b else fib_aux (n - 1) b (a + b) let fib_tl n = if n < 0 then domain () else match n with 0 -> 1 | 1 -> 1 | 2 -> 2 | n -> fib_aux (n - 2) 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1.0 | _ -> float(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 = 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 (x: int) (n: int) (res: bool): bool = if n < 4 then true else( if x * x > n then res else (if n mod x = 0 then false else helper (x+1) n true)) in helper 2 n true) ;; |
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 = fib_aux (n+1) 0 1 ;; |
let rec fact (n: int) : float = if n < 0 then domain () else if n = 0 then 1.0 else float_of_int (n) *. (fact (n - 1)) ;; |
let binomial (n: int) (k: int) = if ( (n < 0 || k < 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 = x2 - x1 in let dy = y2 - y1 in sqrt ( (float_of_int dx ** 2.) +. (float_of_int dy ** 2.) ) ;; |
let is_prime n = let rec primer n d = if (n <= 1) then domain () else if (d <= 1) then true else if (n mod d = 0 && n != d) then false else primer (n) (d - 1) in primer n n ;; |
let zeta (k: float) : float = let rec approx_zeta k acc n sum_so_far = if k <= 2. then domain () else if (acc > 1. /. (float_of_int (n) ** k)) then sum_so_far else approx_zeta (k) (acc) (n+1) (sum_so_far +. 1. /. (float_of_int (n) ** k)) in approx_zeta k epsilon_float 1 0. ;; let;; |
let rec fib_aux n a b = if ( n = 0 ) then a else fib_aux (n-1) (b) (a+b) in fib_aux n 1 1 ;; |
let rec fact (n: int) : float = if n < 0 then domain () else if n = 0 then 1.0 else float_of_int (n) *. (fact (n - 1)) ;; |
let binomial (n: int) (k: int) = if ( (n < 0 || k < 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 = x2 - x1 in let dy = y2 - y1 in sqrt ( (float_of_int dx ** 2.) +. (float_of_int dy ** 2.) ) ;; |
let is_prime n = let rec primer d = if (n <= 1) then domain () else if (d * d > n) then true else if (n mod d = 0) then false else primer (d + 1) in primer (2) ;; |
let zeta (k: float) : float = let rec approx_zeta k acc n sum_so_far = if k <= 2. then domain () else if (acc > 1. /. (float_of_int (n) ** k)) then sum_so_far else approx_zeta (k) (acc) (n+1) (sum_so_far +. 1. /. (float_of_int (n) ** k)) in approx_zeta k epsilon_float 1 0. ;; let;; |
let rec fib_aux n a b = if ( n = 0 ) then a else fib_aux (n-1) (b) (a+b) in fib_aux n 1 1 ;; |
let fact (n: int): float = let rec helper n res = if n<=0 then res else helper (n-1) (float_of_int n *. res) in helper n 1.;; |
let binomial (n: int) (k: int): float= if n < 0 then domain () ; if k < 0 then domain () ; if k > n then domain () ; fact n /. (fact k *. fact (n - k));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = sqrt(float_of_int ((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1))) ;; |
let is_prime n = let rec divisible a b = match b with | 1->true | _->(a mod b <> 0) && divisible a (b-1) in if (n<=1) then domain() else divisible n (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 = 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 = 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: int) : bool = let rec divisor (n:int) (x:int) : bool= if x*x<=n then if n mod (n/x) ==0 then false else divisor n (x+1) else true in if n = 2 || n = 3 then true else if n <=1 then domain() else divisor n 2;; |
let rec fib_aux n a b = if n=0 || n = 1 then 1 else if n = 2 then (a+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 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 is_prime n = if n <= 1 then domain() else(let rec divide num = if num <= 2 then true else(if n mod (num - 1) = 0 then false else divide (num - 1)) in divide n );; |
let rec fib_aux n a b = 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): float= if n < 0 then domain () else if n = 0 then 1. 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 domain() else let rec prime_tail n x = if x*x <=n then if n mod x = 0 && x!=n then false else prime_tail n (x+1) else true in prime_tail 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 (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): float= if n < 0 then domain () else if n = 0 then 1. 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 domain() else let rec prime_tail n x = if x*x <=n then if n mod x = 0 && x!=n then false else prime_tail n (x+1) else true in prime_tail 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 (b+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 -> 1. | _ -> float_of_int n *. fact (n - 1);; |
let binomial (n: int) (k: int) = if n < 0 then domain() else if 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 = if n <= 1 then domain() else let x = (n-1) in let rec divides x n : bool = match x with 1 -> true | _ -> match n mod x with 0 -> false | _ -> divides (x - 1) n in divides x n ;; |
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 = if n < 0 then domain() else 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 < 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 = let rec is_prime_rec n x = if x = n then true else if n mod x = 0 then false else is_prime_rec n (x+1) in if n <= 1 then domain() else is_prime_rec n 2 ;; |
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 -> 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 = x2 - x1 in let dy = y2 - y1 in sqrt (float_of_int (dx * dx + dy * dy)) ;; |
let is_prime n = let rec is_prime_rec n x = if x = n then true else if n mod x = 0 then false else is_prime_rec n (x+1) in if n <= 1 then domain() else is_prime_rec n 2 ;; |
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 = 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 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 check_div (x: int) : bool = if x = 1 then true else if (n mod x = 0) then false else check_div (x - 1) in check_div ( int_of_float (floor (sqrt (float_of_int n) )));; |
let rec fib_aux n a b = if n = 1 then b else fib_aux (n - 1) b (a + b) 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 || 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 = let rec helper n result = if result <= 1 then true else( if n mod result = 0 then false else helper n (result - 1) ) in helper n (int_of_float(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 = 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 = x1 - x2 in let dy = y1 - y2 in sqrt (float_of_int(dx*dx + dy*dy)) ;; |
let is_prime n = let rec no_divs x = if x * x >= n then x * x != n else if n mod x = 0 then n < x else no_divs (x+1) in if n > 1 then no_divs 2 else domain () ;; |
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 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,dy) = (x1-x2,y1-y2) in sqrt (float_of_int(dx*dx + dy*dy)) ;; |
let is_prime n = let rec no_divs x = if x * x >= n then x * x != n else if n mod x = 0 then n < x else no_divs (x+1) in if n > 1 then no_divs 2 else domain () ;; |
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 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 fact (n) /. (fact (k) *. fact (n - k));; |
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