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let is_prime (n: int): bool = if n <= 1 then domain() else let rec factors (i : int) : bool = i * i > n || (n mod i != 0 && factors (i + 1)) in n >= 2 && factors 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 = fib_aux n 1 1;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float(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 = float(x2 - x1) and dy = float(y2 - y1) in sqrt( dx *. dx +. dy *. dy );; |
let is_prime (n: int): bool = if n <= 1 then domain() else let rec check x = if x*x>n then true else match n mod x with |0 -> false |_ -> check (x+1) in check 2 ;; |
let rec fib_aux (n: int) (a:int) (b:int): int = 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 match n with |0 -> 1 |1 -> 1 |_ -> fib_aux n 1 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 sqrt ( input : float) : float = let rec sqroot (x: float): float = let tmp = (( x +. input/.x) /. 2.0) in if abs_float(tmp -. x) < 0.0000001 then tmp else sqroot tmp in if input >= 0.0 then sqroot 1.0 else domain();; |
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) *. (float_of_int dx) +. (float_of_int dy) *. (float_of_int dy)) ;; |
let is_prime n = if n <= 1 then domain() else if n = 2 then true else let rec check_primality x range = match range with | 1 -> true | _ -> (x mod range <> 0) && check_primality x (range-1) in check_primality n (n-1) ;; |
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) = if n < 0 then domain () else match n with | 0 -> 1. | _ -> (fact (n-1)) *. (float_of_int 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 = (x2 - x1) and dy = (y2 - y1) in sqrt (((float_of_int dx) *. (float_of_int dx)) +. ((float_of_int dy) *. (float_of_int dy))) ;; |
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 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 n x = match x with | 1 -> true | _ -> match n mod x with | 0 -> false | _ -> helper n (x-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 = if n <= 1 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 (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 n x = match x with | 1 -> true | _ -> match n mod x with | 0 -> false | _ -> helper n (x-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 = if n <= 1 then 1 else fib_aux n 0 1;; |
exception NotImplemented let domain () = failwith "REMINDER: You should not be writing tests for undefined values." let rec factorial (m: float): float = match m with | 0. -> 1. | _ -> m *. factorial (m -. 1.) let rec fact (n: int): float = if n < 0 then domain () else match n with | 0 -> 1. | _ -> float_of_int n *. factorial (float_of_int n -. 1.);; |
let binomial (n: int) (k: int): float = 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 = y2 - y1 in sqrt (float_of_int(dx * dx + dy * dy)) let rec is_divisible (n: int) (c: int): bool = if n = 0 then true else ( if n < c then false else is_divisible (n - c) c) let rec naive_test (n: int) (c: int): bool = if c * c > n then true else ( if is_divisible n c then false else naive_test n (c + 1));; |
let is_prime (n: int): bool = if n <= 1 then domain () else naive_test n 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 = 0 then 1 else (if n < 0 then domain() else (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 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 = if n <= 1 then domain() else let rec helper a b = if a == b then true else match (a mod b) with | 0 -> false | _ -> helper (a) (b+1) in helper n 2;; |
let rec fib_aux n a b = match n with | 0 -> b | _ -> 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 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) * (x2 - x1) in let dy = (y2 - y1) * (y2 - y1) in sqrt (float_of_int(dx + dy)) ;; |
let is_prime (n: int): bool = let rec test_primality (x: int) (n: int) = if x = n then true else ( if n mod x = 0 then false else test_primality (x+1) n ) in if n <=1 then domain () else test_primality 2 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 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) * (x2 - x1) in let dy = (y2 - y1) * (y2 - y1) in sqrt (float_of_int(dx + dy)) ;; |
let is_prime (n: int): bool = let rec test_primality (x: int) (n: int) = if x = n then true else ( if n mod x = 0 then false else test_primality (x+1) n ) in if n <=1 then domain () else test_primality 2 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 = if n <= 1 then 1. else (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 (if n < k then domain () else (fact (n) /. ((fact k) *. ( fact (n - k))))));; |
let distance ((x1, y1): (int * int)) ((x2, y2): (int * int)) : float = if (x1 = x2) && (y1 = y2) then 0. else (sqrt( float_of_int((x2-x1) * (x2-x1)) +. float_of_int((y2-y1) * (y2-y1)) )) ;; |
let is_prime n = if n <= 1 then domain() else (let rec div (m : int) : bool = m * m > n || (n mod m != 0 && div (m + 1)) in n >= 2 && div 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 (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 n = abs n in let rec divider (m: int) = m * m > n || (n mod m != 0 && divider (m+1)) in n >= 1 && divider 2 ;; |
let rec fib_aux n a b : int = if (n<0) then domain() else 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( 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 -> 1.0 | _ -> let rec tail (n: int) (res: float) = if n <= 1 then res else tail (n - 1) (float_of_int n *. res) in tail n 1.0;; |
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 = x2 - x1 in let dy = y2 - y1 in sqrt (float_of_int (dx * dx + dy * dy)) ;; |
let is_prime (n: int) = if n <= 1 then domain() else (let rec tail (n: int) (res: int) = if res = 1 then true else if n mod res = 0 then false else tail n (res - 1) in tail n (int_of_float(sqrt(float_of_int n))));; |
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 1.0 else (float_of_int n) *. (fact (n - 1));; |
let binomial (n: int) (k: int) = 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 = 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 (); if n = 2 then true else if n mod x = 0 then false else if x * x > n then true else helper n (x+1) in helper n 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 = if n = 0 then 1.0 else (float_of_int n) *. (fact (n - 1));; |
let binomial (n: int) (k: int) = 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 = 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 (); if n = 2 then true else if n mod x = 0 then false else if x * x > n then true else helper n (x+1) in helper n 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 = 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 = let rec prime_detector n x = if x * x > n then true else (n mod x != 0 && prime_detector n (x + 1)) in if n <= 1 then domain () else prime_detector 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 = 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 = let rec prime_detector n m = if m * m > n then true else (n mod m != 0 && prime_detector n (m + 1)) in if n <= 1 then domain () else prime_detector n 2;; |
let rec fib_aux n x y = if n = 0 then x else fib_aux (n-1) y (x+y) 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 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 let rec aux n x = if x * x <= n then let n_divisable_by_x = let n = float_of_int n in let x = float_of_int x in floor (n /. x) = ceil (n /. x) in if n_divisable_by_x then false else aux n (x+1) else true in match n with | 2 -> true | n -> aux n 2 else domain ();; |
let rec fib_aux n a b = if n > 0 then if a > b then fib_aux (n-1) a (a+b) else fib_aux (n-1) (a+b) b else max 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 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 let rec aux n x = if x * x <= n then if (n mod x) = 0 then false else aux n (x+1) else true in (n = 2) || (aux n 2) else domain ();; |
let rec fib_aux n a b = if n > 0 then if a > b then fib_aux (n-1) a (a+b) else fib_aux (n-1) (a+b) b else max 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 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 let rec aux n x = if x * x <= n then if (n mod x) = 0 then false else aux n (x+1) else true in (n = 2) || (aux n 2) else domain ();; |
let rec fib_aux n (a: int64) (b: int64) : int64 = if n > 0 then if a > b then fib_aux (n-1) a (Int64.add a b) else fib_aux (n-1) (Int64.add a b) b else max a b let fib_tl n = Int64.to_int (fib_aux n Int64.zero Int64.one);; |
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 = if n > 1 then let rec aux n x = if x * x <= n then if (n mod x) = 0 then false else aux n (x+1) else true in (n = 2) || (aux n 2) else domain ();; |
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