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/coin_change.go

@@ -0,0 +1,66 @@
+// File: coin_change.go
+// Created Time: 2023-07-23
+// Author: Reanon (793584285@qq.com)
+
+package chapter_dynamic_programming
+
+import "math"
+
+/* 零钱兑换：动态规划 */
+func coinChangeDP(coins []int, amt int) int {
+	n := len(coins)
+	max := amt + 1
+	// 初始化 dp 表
+	dp := make([][]int, n+1)
+	for i := 0; i <= n; i++ {
+		dp[i] = make([]int, amt+1)
+	}
+	// 状态转移：首行首列
+	for a := 1; a <= amt; a++ {
+		dp[0][a] = max
+	}
+	// 状态转移：其余行列
+	for i := 1; i <= n; i++ {
+		for a := 1; a <= amt; a++ {
+			if coins[i-1] > a {
+				// 若超过背包容量，则不选硬币 i
+				dp[i][a] = dp[i-1][a]
+			} else {
+				// 不选和选硬币 i 这两种方案的较小值
+				dp[i][a] = int(math.Min(float64(dp[i-1][a]), float64(dp[i][a-coins[i-1]]+1)))
+			}
+		}
+	}
+	if dp[n][amt] != max {
+		return dp[n][amt]
+	}
+	return -1
+}
+
+/* 零钱兑换：动态规划 */
+func coinChangeDPComp(coins []int, amt int) int {
+	n := len(coins)
+	max := amt + 1
+	// 初始化 dp 表
+	dp := make([]int, amt+1)
+	for i := 1; i <= amt; i++ {
+		dp[i] = max
+	}
+	// 状态转移
+	for i := 1; i <= n; i++ {
+		// 倒序遍历
+		for a := 1; a <= amt; a++ {
+			if coins[i-1] > a {
+				// 若超过背包容量，则不选硬币 i
+				dp[a] = dp[a]
+			} else {
+				// 不选和选硬币 i 这两种方案的较小值
+				dp[a] = int(math.Min(float64(dp[a]), float64(dp[a-coins[i-1]]+1)))
+			}
+		}
+	}
+	if dp[amt] != max {
+		return dp[amt]
+	}
+	return -1
+}