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_dfs_mem.go

@@ -0,0 +1,32 @@
+// File: climbing_stairs_dfs_mem.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* 记忆化搜索 */
+func dfsMem(i int, mem []int) int {
+	// 已知 dp[1] 和 dp[2] ，返回之
+	if i == 1 || i == 2 {
+		return i
+	}
+	// 若存在记录 dp[i] ，则直接返回之
+	if mem[i] != -1 {
+		return mem[i]
+	}
+	// dp[i] = dp[i-1] + dp[i-2]
+	count := dfsMem(i-1, mem) + dfsMem(i-2, mem)
+	// 记录 dp[i]
+	mem[i] = count
+	return count
+}
+
+/* 爬楼梯：记忆化搜索 */
+func climbingStairsDFSMem(n int) int {
+	// mem[i] 记录爬到第 i 阶的方案总数，-1 代表无记录
+	mem := make([]int, n+1)
+	for i := range mem {
+		mem[i] = -1
+	}
+	return dfsMem(n, mem)
+}