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/min_path_sum_test.go

@@ -0,0 +1,43 @@
+// File: min_path_sum_test.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestMinPathSum(t *testing.T) {
+	grid := [][]int{
+		{1, 3, 1, 5},
+		{2, 2, 4, 2},
+		{5, 3, 2, 1},
+		{4, 3, 5, 2},
+	}
+	n, m := len(grid), len(grid[0])
+
+	// 暴力搜索
+	res := minPathSumDFS(grid, n-1, m-1)
+	fmt.Printf("从左上角到右下角的做小路径和为  %d\n", res)
+
+	// 记忆化搜索
+	mem := make([][]int, n)
+	for i := 0; i < n; i++ {
+		mem[i] = make([]int, m)
+		for j := 0; j < m; j++ {
+			mem[i][j] = -1
+		}
+	}
+	res = minPathSumDFSMem(grid, mem, n-1, m-1)
+	fmt.Printf("从左上角到右下角的做小路径和为  %d\n", res)
+
+	// 动态规划
+	res = minPathSumDP(grid)
+	fmt.Printf("从左上角到右下角的做小路径和为  %d\n", res)
+
+	// 状态压缩后的动态规划
+	res = minPathSumDPComp(grid)
+	fmt.Printf("从左上角到右下角的做小路径和为  %d\n", res)
+}