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_dp.go

@@ -0,0 +1,35 @@
+// File: climbing_stairs_dp.go
+// Created Time: 2023-07-18
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+/* 爬楼梯：动态规划 */
+func climbingStairsDP(n int) int {
+	if n == 1 || n == 2 {
+		return n
+	}
+	// 初始化 dp 表，用于存储子问题的解
+	dp := make([]int, n+1)
+	// 初始状态：预设最小子问题的解
+	dp[1] = 1
+	dp[2] = 2
+	// 状态转移：从较小子问题逐步求解较大子问题
+	for i := 3; i <= n; i++ {
+		dp[i] = dp[i-1] + dp[i-2]
+	}
+	return dp[n]
+}
+
+/* 爬楼梯：状态压缩后的动态规划 */
+func climbingStairsDPComp(n int) int {
+	if n == 1 || n == 2 {
+		return n
+	}
+	a, b := 1, 2
+	// 状态转移：从较小子问题逐步求解较大子问题
+	for i := 3; i <= n; i++ {
+		a, b = b, a+b
+	}
+	return b
+}