Just another update
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Ingy döt Net
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6591 changed files with 94363 additions and 23227 deletions
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@ -0,0 +1,43 @@
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#include <stdio.h>
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#include <limits.h>
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/* We go to some effort to handle overflow situations */
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static unsigned long gcd_ui(unsigned long x, unsigned long y) {
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unsigned long t;
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if (y < x) { t = x; x = y; y = t; }
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while (y > 0) {
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t = y; y = x % y; x = t; /* y1 <- x0 % y0 ; x1 <- y0 */
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}
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return x;
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}
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unsigned long binomial(unsigned long n, unsigned long k) {
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unsigned long d, g, r = 1;
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if (k == 0) return 1;
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if (k == 1) return n;
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if (k >= n) return (k == n);
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if (k > n/2) k = n-k;
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for (d = 1; d <= k; d++) {
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if (r >= ULONG_MAX/n) { /* Possible overflow */
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unsigned long nr, dr; /* reduced numerator / denominator */
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g = gcd_ui(n, d); nr = n/g; dr = d/g;
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g = gcd_ui(r, dr); r = r/g; dr = dr/g;
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if (r >= ULONG_MAX/nr) return 0; /* Unavoidable overflow */
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r *= nr;
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r /= dr;
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n--;
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} else {
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r *= n--;
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r /= d;
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}
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}
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return r;
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}
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int main() {
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printf("%lu\n", binomial(5, 3));
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printf("%lu\n", binomial(40, 19));
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printf("%lu\n", binomial(67, 31));
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return 0;
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}
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@ -0,0 +1,9 @@
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binomial_coefficient = (n, k) ->
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result = 1
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for i in [0...k]
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result *= (n - i) / (i + 1)
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result
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n = 5
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for k in [0..n]
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console.log "binomial_coefficient(#{n}, #{k}) = #{binomial_coefficient(n,k)}"
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@ -1,8 +1,8 @@
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T binomial(T)(in T n, T k) pure /*nothrow*/ {
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T binomial(T)(in T n, T k) pure nothrow {
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if (k > (n / 2))
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k = n - k;
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T bc = 1;
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foreach (T i; cast(T)2 .. k + 1)
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foreach (T i; T(2) .. k + 1)
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bc = (bc * (n - k + i)) / i;
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return bc;
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}
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@ -10,7 +10,7 @@ T binomial(T)(in T n, T k) pure /*nothrow*/ {
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void main() {
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import std.stdio, std.bigint;
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foreach (d; [[5, 3], [100, 2], [100, 98]])
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foreach (const d; [[5, 3], [100, 2], [100, 98]])
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writefln("(%3d %3d) = %s", d[0], d[1], binomial(d[0], d[1]));
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writeln("(100 50) = ", binomial(100.BigInt, 50.BigInt));
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}
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@ -0,0 +1,31 @@
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program test_choose
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implicit none
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write (*, '(i0)') choose (5, 3)
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contains
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function factorial (n) result (res)
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implicit none
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integer, intent (in) :: n
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integer :: res
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integer :: i
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res = product ((/(i, i = 1, n)/))
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end function factorial
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function choose (n, k) result (res)
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implicit none
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integer, intent (in) :: n
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integer, intent (in) :: k
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integer :: res
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res = factorial (n) / (factorial (k) * factorial (n - k))
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end function choose
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end program test_choose
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@ -0,0 +1,5 @@
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coeffs = iterate next [1]
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where
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next ns = zipWith (+) (0:ns) $ ns ++ [0]
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main = print $ coeffs !! 5 !! 3
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@ -1,17 +1,18 @@
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public class Binom {
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public class Binomial
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{
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private static long binomial(int n, int k)
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{
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if (k>n-k)
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k=n-k;
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static long combinations(int n, int k) {
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long coeff = 1;
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for (int i = n - k + 1; i <= n; i++) {
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coeff *= i;
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}
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for (int i = 1; i <= k; i++) {
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coeff /= i;
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}
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return coeff;
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}
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long b=1;
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for (int i=1, m=n; i<=k; i++, m--)
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b=b*m/i;
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return b;
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}
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public static void main(String[] args){
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System.out.println(combinations(5, 3));
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public static void main(String[] args)
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{
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System.out.println(binomial(5, 3));
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}
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}
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@ -0,0 +1,17 @@
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public class Binomial
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{
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private static long binom(int n, int k)
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{
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if (k==0)
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return 1;
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else if (k>n-k)
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return binom(n, n-k);
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else
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return binom(n-1, k-1)*n/k;
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}
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public static void main(String[] args)
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{
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System.out.println(binom(5, 3));
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}
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}
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@ -0,0 +1,22 @@
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binomial_coefficients:
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procedure options (main);
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declare (n, k) fixed;
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get (n, k);
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put (coefficient(n, k));
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coefficient: procedure (n, k) returns (fixed decimal (15));
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declare (n, k) fixed;
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return (fact(n)/ (fact(n-k) * fact(k)) );
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end coefficient;
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fact: procedure (n) returns (fixed decimal (15));
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declare n fixed;
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declare i fixed, f fixed decimal (15);
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f = 1;
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do i = 1 to n;
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f = f * i;
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end;
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return (f);
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end fact;
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end binomial_coefficients;
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@ -1,3 +1,2 @@
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sub infix:<choose>($n, $k) { ([*] $n-$k+1 .. $n) / [*] 2 .. $k }
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sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. $^p }
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say 5 choose 3;
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@ -0,0 +1,8 @@
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sub binomial {
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use bigint;
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my ($r, $n, $k) = (1, @_);
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for (1 .. $k) { $r *= $n--; $r /= $_ }
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$r;
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}
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print binomial(5, 3);
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sub binomial {
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use bigint;
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my($n,$k) = @_;
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(0+$n)->bnok($k);
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}
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use ntheory qw/binomial/;
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print length(binomial(100000,50000)), "\n";
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@ -1,8 +0,0 @@
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sub binomial {
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use bigint;
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my ($r, $n, $k) = (1, @_);
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for (1 .. $k) { $r *= $n + 1 - $_; $r /= $_ }
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$r;
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}
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print binomial(30, 13);
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@ -1,3 +1,7 @@
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(de binomial (N K)
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(let f '((N) (apply * (range 1 N)))
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(/ (f N) (* (f (- N K)) (f K))) ) )
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(let f
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'((N)
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(if (=0 N) 1 (apply * (range 1 N))) )
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(/
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(f N)
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(* (f (- N K)) (f K)) ) ) )
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@ -0,0 +1 @@
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choose(5,3)
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@ -1,12 +1,9 @@
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/*REXX program calculates binomial coefficients (aka, combinations). */
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numeric digits 100000
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parse arg n k .
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say 'combinations('n","k') =' comb(n,k)
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numeric digits 100000 /*allow some gihugeic numbers. */
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parse arg n k . /*get N and K from the C.L.*/
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say 'combinations('n","k')=' comb(n,k) /*display the result to terminal.*/
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────COMB subroutine─────────────────────*/
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comb: procedure; parse arg x,y; return fact(x) / (fact(x-y) * fact(y))
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comb: procedure; parse arg x,y; return fact(x) % (fact(x-y) * fact(y))
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/*──────────────────────────────────FACT subroutine─────────────────────*/
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fact: procedure; parse arg z; !=1; do j=2 to z; !=!*j; end; return !
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fact: procedure; !=1; do j=2 to arg(1); !=!*j; end; return !
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/*REXX program calculates binomial coefficients (aka, combinations). */
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numeric digits 100000 /*allow some gihugeic numbers. */
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parse arg n k . /*get N and K from the C.L.*/
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say 'combinations('n","k')=' comb(n,k) /*display the result to terminal.*/
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exit /*stick a fork in it, we're done.*/
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/*──────────────────────────────────COMB subroutine─────────────────────*/
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comb: procedure; parse arg x,y; return pfact(x-y+1,x) % pfact(2,y)
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/*──────────────────────────────────PFACT subroutine────────────────────*/
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pfact: procedure; !=1; do j=arg(1) to arg(2); !=!*j; end; return !
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@ -1 +1,8 @@
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The Binomial Coefficient of 5 and 3 equals 10.
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object Binomial extends App {
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def binomialCoefficient(n: Int, k: Int) =
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(BigInt(n - k + 1) to n).product /
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(BigInt(1) to k).product
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val Array(n, k) = args.map(_.toInt)
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println("The Binomial Coefficient of %d and %d equals %,3d.".format(n, k, binomialCoefficient(n, k)))
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}
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@ -1,8 +1,6 @@
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object Binomial extends App {
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def binomialCoefficient(n: Int, k: Int) =
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(BigInt(n - k + 1) to n).product /
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(BigInt(1) to k).product
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val Array(n, k) = args.map(_.toInt)
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println("The Binomial Coefficient of %d and %d equals %,3d.".format(n, k, binomialCoefficient(n, k)))
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}
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def bico(n: Long, k: Long): Long = (n, k) match {
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case (n, 0) => 1
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case (0, k) => 0
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case (n, k) => bico(n - 1, k - 1) + bico(n - 1, k)
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}
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println("bico(5,3) = " + bico(5, 3))
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@ -0,0 +1,12 @@
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(define (factorial n)
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(define (*factorial n acc)
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(if (zero? n)
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acc
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(*factorial (- n 1) (* acc n))))
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(*factorial n 1))
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(define (choose n k)
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(/ (factorial n) (* (factorial k) (factorial (- n k)))))
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(display (choose 5 3))
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(newline)
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@ -0,0 +1,14 @@
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$ include "seed7_05.s7i";
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const proc: main is func
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local
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var integer: n is 0;
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var integer: k is 0;
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begin
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for n range 0 to 66 do
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for k range 0 to n do
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write(n ! k <& " ");
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end for;
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writeln;
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end for;
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end func;
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@ -0,0 +1,26 @@
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const func bigInteger: (in bigInteger: n) ! (in var bigInteger: k) is func
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result
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var bigInteger: binom is 0_;
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local
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var bigInteger: numerator is 0_;
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var bigInteger: denominator is 0_;
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begin
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if n >= 0_ and k > n >> 1 then
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k := n - k;
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end if;
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if k < 0_ then
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binom := 0_;
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elsif k = 0_ then
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binom := 1_;
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else
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binom := n;
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numerator := pred(n);
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denominator := 2_;
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while denominator <= k do
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binom *:= numerator;
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binom := binom div denominator;
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decr(numerator);
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incr(denominator);
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end while;
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end if;
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end func;
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@ -1,26 +0,0 @@
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$ include "seed7_05.s7i";
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const func integer: binomial (in integer: n, in var integer: k) is func
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result
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var integer: binomial is 0;
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local
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var integer: l is 0;
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begin
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if n >= k then
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if k > n - k then
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k := n - k; # Optimization
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end if;
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binomial := 1;
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l := 0;
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while l < k do
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binomial *:= n - l;
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incr(l);
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binomial := binomial div l;
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end while;
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end if;
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end func;
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const proc: main is func
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begin
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writeln("binomial coefficient of (5, 3) is " <& binomial(5, 3));
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end func;
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