June 2018 Update

Task/Combinations-and-permutations/Common-Lisp/combinations-and-permutations.lisp

@@ -1,11 +1,16 @@
 (defun combinations (n k)
-  (let ((num 1)
-        (den 1) )
-    (dotimes (i k (/ num den))
-      (setq num (* num (- n i)) den (* den (- k i))) )))
-
+  (cond ((or (< n k) (< k 0) (< n 0)) 0)
+	((= k 0) 1)
+	(t (do* ((i 1 (1+ i))
+		 (m n (1- m))
+		 (a m (* a m))
+		 (b i (* b i)))
+	       ((= i k) (/ a b))))))
 
 (defun permutations (n k)
-  (let ((p 1))
-    (dotimes (i k p)
-      (setq p (* p (- n i))) )))
+  (cond ((or (< n k) (< k 0) (< n 0)) 0)
+	((= k 0) 1)
+	(t (do* ((i 1 (1+ i))
+		 (m n (1- m))
+		 (a m (* a m)))
+	       ((= i k) a)))))

Task/Combinations-and-permutations/Go/combinations-and-permutations.go

@@ -0,0 +1,64 @@
+package main
+
+import (
+	"fmt"
+	"math/big"
+)
+
+func main() {
+	var n, p int64
+	fmt.Printf("A sample of permutations from 1 to 12:\n")
+	for n = 1; n < 13; n++ {
+		p = n / 3
+		fmt.Printf("P(%d,%d) = %d\n", n, p, perm(big.NewInt(n), big.NewInt(p)))
+	}
+	fmt.Printf("\nA sample of combinations from 10 to 60:\n")
+	for n = 10; n < 61; n += 10 {
+		p = n / 3
+		fmt.Printf("C(%d,%d) = %d\n", n, p, comb(big.NewInt(n), big.NewInt(p)))
+	}
+	fmt.Printf("\nA sample of permutations from 5 to 15000:\n")
+	nArr := [...]int64{5, 50, 500, 1000, 5000, 15000}
+	for _, n = range nArr {
+		p = n / 3
+		fmt.Printf("P(%d,%d) = %d\n", n, p, perm(big.NewInt(n), big.NewInt(p)))
+	}
+	fmt.Printf("\nA sample of combinations from 100 to 1000:\n")
+	for n = 100; n < 1001; n += 100 {
+		p = n / 3
+		fmt.Printf("C(%d,%d) = %d\n", n, p, comb(big.NewInt(n), big.NewInt(p)))
+	}
+}
+
+func fact(n *big.Int) *big.Int {
+	if n.Sign() < 1 {
+		return big.NewInt(0)
+	}
+	r := big.NewInt(1)
+	i := big.NewInt(2)
+	for i.Cmp(n) < 1 {
+		r.Mul(r, i)
+		i.Add(i, big.NewInt(1))
+	}
+	return r
+}
+
+func perm(n, k *big.Int) *big.Int {
+	r := fact(n)
+	r.Div(r, fact(n.Sub(n, k)))
+	return r
+}
+
+func comb(n, r *big.Int) *big.Int {
+	if r.Cmp(n) == 1 {
+		return big.NewInt(0)
+	}
+	if r.Cmp(n) == 0 {
+		return big.NewInt(1)
+	}
+	c := fact(n)
+	den := fact(n.Sub(n, r))
+	den.Mul(den, fact(r))
+	c.Div(c, den)
+	return c
+}

Task/Combinations-and-permutations/Stata/combinations-and-permutations.stata

@@ -0,0 +1,7 @@
+real scalar comb1(n, k) {
+	return(exp(lnfactorial(n)-lnfactorial(k)-lnfactorial(n-k)))
+}
+
+real scalar perm(n, k) {
+	return(exp(lnfactorial(n)-lnfactorial(n-k)))
+}