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/climbing_stairs_backtrack.go

@@ -0,0 +1,36 @@
+// File: climbing_stairs_backtrack.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* 回溯 */
+func backtrack(choices []int, state, n int, res []int) {
+	// 当爬到第 n 阶时，方案数量加 1
+	if state == n {
+		res[0] = res[0] + 1
+	}
+	// 遍历所有选择
+	for _, choice := range choices {
+		// 剪枝：不允许越过第 n 阶
+		if state+choice > n {
+			break
+		}
+		// 尝试：做出选择，更新状态
+		backtrack(choices, state+choice, n, res)
+		// 回退
+	}
+}
+
+/* 爬楼梯：回溯 */
+func climbingStairsBacktrack(n int) int {
+	// 可选择向上爬 1 或 2 阶
+	choices := []int{1, 2}
+	// 从第 0 阶开始爬
+	state := 0
+	res := make([]int, 1)
+	// 使用 res[0] 记录方案数量
+	res[0] = 0
+	backtrack(choices, state, n, res)
+	return res[0]
+}