feat(go/dp): support dynamic programming (#622)

* feat(go/dp): support climbing stairs

* feat(go/dp): support knapsack

* feat(go/dp): coin_change & edit_distance

codes/go/chapter_dynamic_programming/knapsack_test.go

@@ -0,0 +1,54 @@
+// File: knapsack_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestKnapsack(t *testing.T) {
+	wgt := []int{10, 20, 30, 40, 50}
+	val := []int{50, 120, 150, 210, 240}
+	c := 50
+	n := len(wgt)
+
+	// 暴力搜索
+	res := knapsackDFS(wgt, val, n, c)
+	fmt.Printf("不超过背包容量的最大物品价值为 %d\n", res)
+
+	// 记忆化搜索
+	mem := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		mem[i] = make([]int, c+1)
+		for j := 0; j <= c; j++ {
+			mem[i][j] = -1
+		}
+	}
+	res = knapsackDFSMem(wgt, val, mem, n, c)
+	fmt.Printf("不超过背包容量的最大物品价值为 %d\n", res)
+
+	// 动态规划
+	res = knapsackDP(wgt, val, c)
+	fmt.Printf("不超过背包容量的最大物品价值为 %d\n", res)
+
+	// 状态压缩后的动态规划
+	res = knapsackDPComp(wgt, val, c)
+	fmt.Printf("不超过背包容量的最大物品价值为 %d\n", res)
+}
+
+func TestUnboundedKnapsack(t *testing.T) {
+	wgt := []int{1, 2, 3}
+	val := []int{5, 11, 15}
+	c := 4
+
+	// 动态规划
+	res := unboundedKnapsackDP(wgt, val, c)
+	fmt.Printf("不超过背包容量的最大物品价值为 %d\n", res)
+
+	// 状态压缩后的动态规划
+	res = unboundedKnapsackDPComp(wgt, val, c)
+	fmt.Printf("不超过背包容量的最大物品价值为 %d\n", res)
+}