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68 lines
2.1 KiB
C#
68 lines
2.1 KiB
C#
/**
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* File: coin_change_ii.cs
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* Created Time: 2023-07-12
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* Author: hpstory (hpstory1024@163.com)
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*/
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namespace hello_algo.chapter_dynamic_programming;
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public class coin_change_ii {
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/* 零钱兑换 II:动态规划 */
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public int coinChangeIIDP(int[] coins, int amt) {
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int n = coins.Length;
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// 初始化 dp 表
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int[,] dp = new int[n + 1, amt + 1];
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// 初始化首列
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for (int i = 0; i <= n; i++) {
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dp[i, 0] = 1;
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}
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// 状态转移
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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if (coins[i - 1] > a) {
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// 若超过背包容量,则不选硬币 i
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dp[i, a] = dp[i - 1, a];
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} else {
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// 不选和选硬币 i 这两种方案之和
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dp[i, a] = dp[i - 1, a] + dp[i, a - coins[i - 1]];
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}
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}
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}
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return dp[n, amt];
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}
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/* 零钱兑换 II:状态压缩后的动态规划 */
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public int coinChangeIIDPComp(int[] coins, int amt) {
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int n = coins.Length;
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// 初始化 dp 表
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int[] dp = new int[amt + 1];
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dp[0] = 1;
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// 状态转移
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for (int i = 1; i <= n; i++) {
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for (int a = 1; a <= amt; a++) {
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if (coins[i - 1] > a) {
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// 若超过背包容量,则不选硬币 i
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dp[a] = dp[a];
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} else {
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// 不选和选硬币 i 这两种方案之和
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dp[a] = dp[a] + dp[a - coins[i - 1]];
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}
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}
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}
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return dp[amt];
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}
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[Test]
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public void Test() {
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int[] coins = { 1, 2, 5 };
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int amt = 5;
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// 动态规划
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int res = coinChangeIIDP(coins, amt);
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Console.WriteLine("凑出目标金额的硬币组合数量为 " + res);
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// 状态压缩后的动态规划
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res = coinChangeIIDPComp(coins, amt);
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Console.WriteLine("凑出目标金额的硬币组合数量为 " + res);
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}
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}
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