53: combinatoric selections

53_combinatoric_selections/main.go

@@ -0,0 +1,46 @@
+package main
+
+import (
+	"fmt"
+	"math/big"
+	"strconv"
+)
+
+func main() {
+	result := 0
+	limit, _ := (&big.Int{}).SetString("1000000", 0)
+	nLimit := 100
+	for i := 1; i <= nLimit; i++ {
+		for j := 0; j <= i; j++ {
+			bi, _ := (&big.Int{}).SetString(strconv.Itoa(i), 0)
+			fi := factorialOf(bi)
+			bj, _ := (&big.Int{}).SetString(strconv.Itoa(j), 0)
+			fj := factorialOf(bj)
+			bk, _ := (&big.Int{}).SetString(strconv.Itoa(i-j), 0)
+			fk := factorialOf(bk)
+			mik := fj.Mul(fj, fk)
+			dvk := mik.Div(fi, mik)
+			if x := dvk.Add(dvk, limit.Neg(limit)); x.Int64() >= 0 {
+				result++
+			}
+		}
+	}
+	fmt.Println(result)
+}
+
+func factorialOf(n *big.Int) *big.Int {
+	one, _ := (&big.Int{}).SetString("1", 0)
+	if n.Int64() <= 2 {
+		return one
+	}
+	p, _ := (&big.Int{}).SetString("1", 0)
+	i, _ := (&big.Int{}).SetString("2", 0)
+	for {
+		p = p.Mul(p, i)
+		if i.String() == n.String() {
+			break
+		}
+		i = i.Add(i, one)
+	}
+	return p
+}