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/unbounded_knapsack.go

@@ -0,0 +1,50 @@
+// File: unbounded_knapsack.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import "math"
+
+/* 完全背包：动态规划 */
+func unboundedKnapsackDP(wgt, val []int, cap int) int {
+	n := len(wgt)
+	// 初始化 dp 表
+	dp := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		dp[i] = make([]int, cap+1)
+	}
+	// 状态转移
+	for i := 1; i <= n; i++ {
+		for c := 1; c <= cap; c++ {
+			if wgt[i-1] > c {
+				// 若超过背包容量，则不选物品 i
+				dp[i][c] = dp[i-1][c]
+			} else {
+				// 不选和选物品 i 这两种方案的较大值
+				dp[i][c] = int(math.Max(float64(dp[i-1][c]), float64(dp[i][c-wgt[i-1]]+val[i-1])))
+			}
+		}
+	}
+	return dp[n][cap]
+}
+
+/* 完全背包：状态压缩后的动态规划 */
+func unboundedKnapsackDPComp(wgt, val []int, cap int) int {
+	n := len(wgt)
+	// 初始化 dp 表
+	dp := make([]int, cap+1)
+	// 状态转移
+	for i := 1; i <= n; i++ {
+		for c := 1; c <= cap; c++ {
+			if wgt[i-1] > c {
+				// 若超过背包容量，则不选物品 i
+				dp[c] = dp[c]
+			} else {
+				// 不选和选物品 i 这两种方案的较大值
+				dp[c] = int(math.Max(float64(dp[c]), float64(dp[c-wgt[i-1]]+val[i-1])))
+			}
+		}
+	}
+	return dp[cap]
+}