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let rec fib_aux n a b = if(n <= 1) then 1 else let rec fib_count n a b x = if(x = n) then b else fib_count n b (a+b) (x+1) in fib_count n 1 2 2 let fib_tl n = fib_aux n 0 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 = 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) : bool = if n <= 1 then domain() else let rec not_divide (d:int):bool = d * d > n || (n mod d <> 0) && not_divide(d+1) in not_divide 2 ;; |
let rec fib_aux (n:int) (a:int) (b:int) :int = match n with | 0 -> a | _ -> fib_aux (n - 1) (a + b) (a) ;; let fib_tl (n:int):int = 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 = 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) : bool = if n <= 1 then domain() else let rec not_divide (d:int):bool = d * d > n || (n mod d <> 0) && not_divide(d+1) in not_divide 2;; ;; |
let rec fib_aux (m:int) (a:int) (b:int) :int = if m = n then a else fib_aux (m+1) (b) (a+b) in fib_aux 0 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 -. 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) : bool = if n <= 1 then domain() else let rec not_divide (d:int):bool = d * d > n || (n mod d <> 0) && not_divide(d+1) in not_divide 2 ;; |
let rec fib_aux (n:int) (a:int) (b:int) :int = match n with | 0 -> a | _ -> 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) = 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 -. 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) : bool = if n <= 1 then domain() else let rec not_divide (d:int):bool = d * d > n || (n mod d <> 0) && not_divide(d+1) in not_divide 2 ;; |
let rec fib_aux (n:int) (a:int) (b:int) :int = match n with | 0 -> a | _ -> 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) = 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 = let rec divides n k = if k * k > 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 = 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) = 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(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 helper d = if (d <= 1) then true else (if (n mod d = 0) then false else helper (d-1)) in helper (n-1);; |
let rec fib_aux n a b = if n = 0 then b else fib_aux (n-1) (a+b) a 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 = x2 - x1 in let dy = y2 - y1 in (sqrt (float_of_int (dx * dx + dy * dy))) ;; let rec is_prime_helper n x = if x * x <= n && n mod x != 0 then is_prime_helper n (x+1) else (if n mod x != 0 then true else n=2 ) ;; |
let is_prime (n: int) = if n <= 1 then domain () else (is_prime_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 = if n >=0 then fib_aux n 1 1 else domain () ;; |
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 = x2 - x1 in let dy = y2 - y1 in (sqrt (float_of_int (dx * dx + dy * dy))) ;; let rec is_prime_helper n x = if x * x <= n && n mod x != 0 then is_prime_helper n (x + 1) else (if n mod x != 0 then true else n = 2 ) ;; |
let is_prime (n: int) = if n <= 1 then domain () else (is_prime_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 = if n >= 0 then fib_aux n 1 1 else domain () ;; |
let fact (n: int): float = let rec f (n: float): float = match n with | 0. when n<=0. -> 1. | _ -> n *. (f (n -. 1.)) in f (float_of_int(n)) ;; |
let binomial (n: int) (k: int) = let helper (fn: float) (fk: float) (fnk: float) = fn /. (fk *. fnk) in if n<0 then domain () else if k>n then domain () else helper (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 (i: int) (n: int) : bool = if i * i <= n then (if n mod i = 0 then false else helper (i+1) n) else true in if n<= 1 then domain () else helper 2 n ;; |
let rec fib_aux n a b = if n=2 then a+b else fib_aux (n-1) b (b+a) ;; let fib_tl n = if n<0 then domain() else if n=0 then 1 else if n=1 then 1 else 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): float = if n < 0 then domain () else (if k > n || k < 0 then domain () else if k = n || 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 = 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 helper (n: int) (k: int): bool = if k = 1 then true else (n mod k <> 0) && (helper n (k-1)) in helper n (int_of_float(sqrt(float_of_int(n)))));; |
let rec fib_aux n a b = match n with | 0 -> a | 1 -> a | _ -> 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) : float = if n < 0 then domain () else (if k < 0 then domain () else (if n < k then domain () else fact n /. (fact k *. fact (n - k)))) ;; let rec generateBinomialTests startval endval = for i = startval to endval do for j = startval to endval do if j < i then generateBinomialTests (succ startval) endval; print_string "(("; print_int j; print_string ", "; print_int i; print_string "), "; print_float (binomial j i); print_string "); "; done; done;; *) let rec sqrt (x : float) (niters : int) (acc : float) : float = if x = 0. then 0. else if niters >= 0 then sqrt x (niters-1) ((acc +. (x /. acc)) /. 2.) else acc;; |
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))) 100 (float_of_int ((dx * dx) + (dy * dy))) ;; let generateDistanceTests startval endval = for i = startval to endval do print_string "((("; print_int (i*i); print_string ", "; print_int (i+1); print_string "), ("; print_int (i*i*i); print_string ", "; print_int (i+3); print_string ")), ("; print_float (distance ((i*i), (i+1)) ((i*i*i), (i+3))); print_string ")); "; done;; *);; |
let is_prime (n:int) : bool = if n <= 1 then domain () else let rec helper (x:int) = if x < 1 then domain () else match x with | 1 -> true | y when y * y <= n -> if n mod x = 0 then false else helper (x-1) | _ -> helper (x-1) in helper (int_of_float (sqrt (float_of_int n) 100 (float_of_int n))) ;; let rec generatePrimeTests maxn = if maxn > 1 then ( print_string "("; print_int maxn; print_string ", "; print_string (string_of_bool (is_prime maxn)); print_string "); "; generatePrimeTests (maxn-1) ) ;; |
let rec fib_aux n a b = if n < 0 then a else (fib_aux (n-1) (b) (b+a)) let fib_tl n = if n >= 0 then fib_aux n 0 1 else domain () ;; let rec generateFibTests (maxn : int) = if maxn >= 0 then ( print_string "("; print_int maxn; print_string ", "; print_int (fib_tl maxn); print_string "); "; generateFibTests (maxn-1) ) ;; |
let rec fact (n: int): float = match n with | 0 -> 1. | _ -> float_of_int(n * int_of_float(fact(n - 1)));; |
let binomial (n: int) (k: int) = if n < 0 then domain () else (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 = x2 - x1 in let dy = y2 - y1 in sqrt(float_of_int(dx * dx + dy * dy)) ;; |
let is_prime n : bool = if n <= 1 then domain () else (let rec check a n = match a with | 1 -> true | _ -> match n mod a with | 0 -> false | _ -> check (a-1) n in check (n-1) 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 = 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 = (if x1 > x2 then x1 - x2 else x2 - x1) in let dy = (if y1 > y2 then y1 - y2 else y2 - y1) in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime n = let rec helper (n: int) (c: int): bool = if c > (n / 2) then true else (if (n - ((n / c) * c)) = 0 then false else helper n (c + 1)) in if n <= 1 then domain() else helper n 2 ;; |
let rec fib_aux n a b = if n < 2 then b else fib_aux (n - 1) (b) (a + b) ;; let fib_tl n = if n < 0 then domain() else (if n = 0 || n = 1 then 1 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 || k < 0 || n < k 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 = (if x1 > x2 then x1 - x2 else x2 - x1) in let dy = (if y1 > y2 then y1 - y2 else y2 - y1) in sqrt (float_of_int(dx * dx + dy * dy)) ;; |
let is_prime n = let rec helper (n: int) (c: int): bool = if c > (n / 2) then true else (if (n - ((n / c) * c)) = 0 then false else helper n (c + 1)) in if n <= 1 then domain() else helper n 2 ;; |
let rec fib_aux n a b = if n < 2 then b else fib_aux (n - 1) (b) (a + b) ;; let fib_tl n = if n < 0 then domain() else (if n = 0 || n = 1 then 1 else fib_aux n 1 1) ;; |
let rec fact (n: int): float = 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 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 is_divisible x n = if (x > 1) then match n mod x with |0 -> false |_ -> is_divisible (x - 1) n else true in is_divisible x 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 = match n with |0 |1 -> 1 |_ -> 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 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 = let rec prime_check (n:int) (x : int) : bool = if x * x > n then true else (if x = 1 then prime_check n (x+1) else (if (n mod x) = 0 then false else prime_check n (x+1))) in prime_check n 1;; |
let rec fib_aux (n: int) (a: int) (b: int) : int = if n < 0 then domain () else(if n <= 1 then b else fib_aux (n-1) b (a+b)) ;; let fib_tl (n: int) : int = let fib (k: int) = fib_aux k 1 1 in fib n ;; |
let rec fact (n: int): float = match n with | 0 -> 1. | 1 -> 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 = 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 if n = 2 then true else if (n mod 2) = 0 then false else (let rec prm n i = if (float_of_int i) > (sqrt (float_of_int n)) then true else if (n mod i) = 0 then false else prm n (i+2) in prm n 3) ;; |
let rec fib_aux n a b = if n = 2 then a + b else fib_aux (n-1) b (a+b) ;; let fib_tl n = if n < 0 then domain () else if n < 2 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 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) = let rec helper x = if (n == (n / x) * x) then x else helper (x-1) in if (n <= 1) then domain () else helper(int_of_float(sqrt(float_of_int(n)))) == 1 ;; |
let rec fib_aux n a b = if (n == 1) then 1 else if (n == 2) then a + b else fib_aux (n-1) (b+a) a let fib_tl n = if n < 0 then domain () else if n < 2 then 1 else 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) = if n = 0 then 1. 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 + dy*dy)) ;; let rec is_divisible_by n rest rest_of_rest = if rest_of_rest = 1 then false else if rest_of_rest * rest = n then true else is_divisible_by n rest (rest_of_rest-1);; |
let is_prime n = if n > 1 then let rec is_prime_rec n rest = if rest = 1 then false else let result = is_divisible_by n rest rest in (if result then true else is_prime_rec n (rest-1)) in not (is_prime_rec n (n-1)) else domain ();; |
let rec fib_aux n a b = if n = 1 then a else fib_aux (n-1) (a+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) : 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) *. float_of_int (dx) +. float_of_int (dy) *. float_of_int (dy)) ;; |
let is_prime (n : int) : bool = if n <= 1 then domain () else let rec check m = (m * m > n) || (n mod m != 0 && check (m + 1)) in n >= 2 && check 2 ;; |
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