2016 Update
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Tina Müller
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7965 changed files with 139854 additions and 31002 deletions
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This programming task, is to calculate ANY binomial coefficient.
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However, it has to be able to output <math>\binom{5}{3}</math>, which is 10.
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However, it has to be able to output <big><big><math>\binom{5}{3}</math></big></big>, which is '''10'''.
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This formula is recommended:
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: <math>\binom{n}{k} = \frac{n!}{(n-k)!k!} = \frac{n(n-1)(n-2)\ldots(n-k+1)}{k(k-1)(k-2)\ldots 1}</math>
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<big><big>
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:: <math>\binom{n}{k} = \frac{n!}{(n-k)!k!} = \frac{n(n-1)(n-2)\ldots(n-k+1)}{k(k-1)(k-2)\ldots 1}</math>
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</big></big>
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'''See Also:'''
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* [[Combinations and permutations]]
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* [[Pascal's triangle]]
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{{Template:Combinations and permutations}}
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<br>
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@ -0,0 +1,15 @@
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: fact ( n -- n-factorial )
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dup 0 = [ drop 1 ] [ dup 1 - fact * ] if ;
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: choose ( n k -- n-choose-k )
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2dup - fact swap fact * swap fact swap / ;
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! outputs 10
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5 3 choose .
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! alternative using folds
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USE: math.ranges
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! (product [n..k+1] / product [n-k..1])
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: choose-fold ( n k -- n-choose-k )
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2dup 1 + [a,b] product -rot - 1 [a,b] product / ;
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@ -3,7 +3,7 @@ function binom(n,k)
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n == 1 && return 1
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k == 0 && return 1
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binom(n-1,k-1) + binom (n-1,k) #recursive call
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(n * binom(n - 1, k - 1)) ÷ k #recursive call
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end
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julia> binom(5,2)
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@ -1,2 +1 @@
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sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. $^p }
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say 5 choose 3;
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say combinations(5, 3).elems;
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@ -1 +1,2 @@
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sub infix:<choose> { ([*] ($^n ... 0) Z/ 1 .. $^p).Int }
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sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. $^p }
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say 5 choose 3;
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@ -0,0 +1 @@
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sub infix:<choose> { [*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p) }
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@ -0,0 +1 @@
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sub infix:<choose> { ([*] ($^n ... 0) Z/ 1 .. min($n - $^p, $p)).Int }
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/*REXX program calculates binomial coefficients (aka, combinations). */
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numeric digits 100000 /*be able to handle gihugeic numbers. */
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parse arg n k . /*obtain N and K from the C.L. */
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say 'combinations('n","k')=' comb(n,k) /*display the number of combinations. */
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exit /*stick a fork in it, we're all done. */
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/*────────────────────────────────────────────────────────────────────────────*/
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/*REXX program calculates binomial coefficients (also known as combinations). */
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numeric digits 100000 /*be able to handle gihugeic numbers. */
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parse arg n k . /*obtain N and K from the C.L. */
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say 'combinations('n","k')=' comb(n,k) /*display the number of combinations. */
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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comb: procedure; parse arg x,y; return !(x) % (!(x-y) * !(y))
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/*────────────────────────────────────────────────────────────────────────────*/
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!: procedure; !=1; do j=2 to arg(1); !=!*j; end; return !
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!: procedure; !=1; do j=2 to arg(1); !=!*j; end /*j*/; return !
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@ -1,9 +1,9 @@
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/*REXX program calculates binomial coefficients (aka, combinations). */
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numeric digits 100000 /*be able to handle gihugeic numbers. */
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parse arg n k . /*obtain N and K from the C.L. */
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say 'combinations('n","k')=' comb(n,k) /*display the number of combinations. */
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exit /*stick a fork in it, we're all done. */
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/*────────────────────────────────────────────────────────────────────────────*/
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comb: procedure; parse arg x,y; return pfact(x-y+1,x) % pfact(2,y)
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/*────────────────────────────────────────────────────────────────────────────*/
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pfact: procedure; !=1; do j=arg(1) to arg(2); !=!*j; end; return !
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/*REXX program calculates binomial coefficients (also known as combinations). */
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numeric digits 100000 /*be able to handle gihugeic numbers. */
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parse arg n k . /*obtain N and K from the C.L. */
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say 'combinations('n","k')=' comb(n,k) /*display the number of combinations. */
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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comb: procedure; parse arg x,y; return pfact(x-y+1, x) % pfact(2, y)
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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pfact: procedure; !=1; do j=arg(1) to arg(2); !=!*j; end /*j*/; return !
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@ -0,0 +1 @@
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(1..60).to_a.combination(30).size #=> 118264581564861424
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@ -0,0 +1,19 @@
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fn fact(n:u32) -> u64 {
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let mut f:u64 = n as u64;
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for i in 2..n {
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f *= i as u64;
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}
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return f;
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}
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fn choose(n: u32, k: u32) -> u64 {
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let mut num:u64 = n as u64;
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for i in 1..k {
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num *= (n-i) as u64;
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}
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return num / fact(k);
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}
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fn main() {
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println!("{}", choose(5,3));
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}
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@ -0,0 +1,10 @@
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10 LET n=33: LET k=17: PRINT "Binomial ";n;",";k;" = ";
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20 LET r=1: LET d=n-k
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30 IF d>k THEN LET k=d: LET d=n-k
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40 IF n<=k THEN GO TO 90
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50 LET r=r*n
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60 LET n=n-1
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70 IF (d>1) AND (FN m(r,d)=0) THEN LET r=r/d: LET d=d-1: GO TO 70
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80 GO TO 40
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90 PRINT r
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100 DEF FN m(a,b)=a-INT (a/b)*b
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