September 2017 Update
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Ingy döt Net
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14570 changed files with 153136 additions and 63871 deletions
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# syntax: GAWK -f EVALUATE_BINOMIAL_COEFFICIENTS.AWK
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BEGIN {
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main(5,3)
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main(100,2)
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main(33,17)
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exit(0)
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}
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function main(n,k, i,r) {
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r = 1
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for (i=1; i<k+1; i++) {
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r *= (n - i + 1) / i
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}
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printf("%d %d = %d\n",n,k,r)
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}
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@ -1,27 +0,0 @@
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#include <stdio.h>
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#include <limits.h>
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typedef unsigned long ULONG;
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ULONG binomial(ULONG n, ULONG k)
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{
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ULONG r = 1, d = n - k;
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/* choose the smaller of k and n - k */
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if (d > k) { k = d; d = n - k; }
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while (n > k) {
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if (r >= UINT_MAX / n) return 0; /* overflown */
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r *= n--;
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/* divide (n - k)! as soon as we can to delay overflows */
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while (d > 1 && !(r % d)) r /= d--;
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}
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return r;
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}
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int main()
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{
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printf("%lu\n", binomial(5, 3));
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return 0;
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}
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@ -1 +0,0 @@
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10
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@ -1,9 +0,0 @@
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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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@ -1,7 +0,0 @@
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> coffee binomial.coffee
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binomial_coefficient(5, 0) = 1
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binomial_coefficient(5, 1) = 5
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binomial_coefficient(5, 2) = 10
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binomial_coefficient(5, 3) = 10
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binomial_coefficient(5, 4) = 5
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binomial_coefficient(5, 5) = 1
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@ -0,0 +1 @@
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[sx1q]sz[d0=zd1-lfx*]sf[skdlfxrlk-lfxlklfx*/]sb
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@ -0,0 +1 @@
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5 3lbxp
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@ -0,0 +1,31 @@
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[ macro z: factorial base case when n is (z)ero ]sx
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[sx [ x is our dump register; get rid of extraneous copy of n we no longer need]sx
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1 [ return value is 1 ]sx
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q] [ abort processing of calling macro ]sx
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sz
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[ macro f: factorial ]sx [
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d [ duplicate the input (n) ]sx
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0 =z [ if n is zero, call z, which stops here and returns 1 ]sx
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d [ otherwise, duplicate n again ]sx
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1 - [ subtract 1 ]sx
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lfx [ take the factorial ]sx
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* [ we have (n-1)!; multiply it by the copy of n to get n! ]sx
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] sf
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[ macro b(n,k): binomial function (n choose k).
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straightforward RPN version of formula.]sx [
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sk [ remember k. stack: n ]sx
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d [ duplicate: n n ]sx
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lfx [ call factorial: n n! ]sx
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r [ swap: n! n ]sx
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lk [ load k: n! n k ]sx
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- [ subtract: n! n-k ]sx
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lfx [ call factorial: n! (n-k)! ]sx
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lk [ load k: n! (n-k)! k ]sx
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lfx [ call factorial; n! (n-k)! k! ]sx
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* [ multiply: n! (n-k)!k! ]sx
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/ [ divide: n!/(n-k)!k! ]sx
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] sb
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5 3 lb x p [print(5 choose 3)]sx
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@ -1,31 +0,0 @@
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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 +1,28 @@
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// version 1.0.5-2
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fun factorial(n: Int) = when {
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n < 0 -> throw IllegalArgumentException("negative numbers not allowed")
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else -> {
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var ans = 1L
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for (i in 2..n) ans *= i
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ans
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}
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}
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fun binomial(n: Int, k: Int) = when {
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n < 0 || k < 0 -> throw IllegalArgumentException("negative numbers not allowed")
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n == k -> 1L
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else -> {
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var ans = 1L
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for (i in n - k + 1..n) ans *= i
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ans / factorial(k)
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}
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}
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fun main(args: Array<String>) {
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for (n in 0..14) {
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for (k in 0..n)
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print("%4d ".format(binomial(n, k)))
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println()
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}
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}
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local Binomial = setmetatable({},{
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__call = function(self,n,k)
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local hash = (n<<32) | (k & 0xffffffff)
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local ans = self[hash]
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if not ans then
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if n<0 or k>n then
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return 0 -- not save
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elseif n<=1 or k==0 or k==n then
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ans = 1
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else
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if 2*k > n then
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ans = self(n, n - k)
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else
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local lhs = self(n-1,k)
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local rhs = self(n-1,k-1)
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local sum = lhs + rhs
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if sum<0 or not math.tointeger(sum)then
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-- switch to double
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ans = lhs/1.0 + rhs/1.0 -- approximate
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else
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ans = sum
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end
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end
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end
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rawset(self,hash,ans)
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end
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return ans
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end
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})
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print( Binomial(100,50)) -- 1.0089134454556e+029
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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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function binom(integer n, k)
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return factorial(n)/(factorial(k)*factorial(n-k))
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end function
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?binom(5,3)
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include builtins\bigatom.e
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function ba_binom(integer n, k)
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bigatom r = ba_new(1)
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for i=1 to k do
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r = ba_divide(ba_multiply(r,n-i+1),i)
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end for
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return r
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end function
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?ba_sprintf("%B",ba_binom(5,3))
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?ba_sprintf("%B",ba_binom(100,50))
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?ba_sprintf("%B",ba_binom(60,30))
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?ba_sprintf("%B",ba_binom(1200,120))
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choose(5,3)
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[1] 10
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java Binomial 100 30
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The Binomial Coefficient of 100 and 30 equals 29,372,339,821,610,944,823,963,760.
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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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bico(5,3) = 10
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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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choose(n, k) := product(k + 1 ... n) / product(1 ... n - k);
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choose(n,k) := binomial(n, k, 1, 1);
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binomial(n, k, i, result) :=
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result when i > k else
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binomial(n, k, i + 1, (result * (n - i + 1)) / i);
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. display comb(5,3)
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10
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fcn binomial(n,k){ (1).reduce(k,fcn(p,i,n){ p*(n-i+1)/i },1,n) }
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