added dynamic algorithm for binomial coeffecients

Author: DanGarcia595

dynamic-programming/binomial-coeffecient.go

@@ -0,0 +1,47 @@
+package main
+
+import (
+	"fmt"
+	"time"
+)
+
+func main() {
+	myArrayOfK := [4]int{5, 6, 7, 8}
+	var x int
+
+	fmt.Println("\nBinomial Coefficient Using Dynamic Programming:", bin2(50, 5))
+	for _, element := range myArrayOfK {
+		start := time.Now()
+		x = bin2(50, element)
+		elapsed := time.Since(start)
+		fmt.Println("bin2 (50,", element, ") = ", x, "    took ", elapsed)
+
+	}
+
+}
+
+func bin2(n int, k int) int {
+	var i, j int
+	B := make([][]int, (n + 1))
+	for i := range B {
+		B[i] = make([]int, k+1)
+	}
+
+	for i = 0; i <= n; i++ {
+		for j = 0; j <= min(i, k); j++ {
+			if j == 0 || j == i {
+				B[i][j] = 1
+			} else {
+				B[i][j] = B[i-1][j-1] + B[i-1][j]
+			}
+		}
+	}
+	return B[n][k]
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}