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65 lines
1.6 KiB
Dart
65 lines
1.6 KiB
Dart
/**
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* File: coin_change_ii.dart
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* Created Time: 2023-08-11
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* Author: liuyuxin (gvenusleo@gmail.com)
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*/
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/* 零钱兑换 II：动态规划 */
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int coinChangeIIDP(List<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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List<List<int>> dp = List.generate(n + 1, (index) => List.filled(amt + 1, 0));
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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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// 若超过目标金额，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：空间优化后的动态规划 */
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int coinChangeIIDPComp(List<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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List<int> dp = List.filled(amt + 1, 0);
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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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// 若超过目标金额，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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/* Driver Code */
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void main() {
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List<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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print("凑出目标金额的硬币组合数量为 $res");
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// 空间优化后的动态规划
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res = coinChangeIIDPComp(coins, amt);
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print("凑出目标金额的硬币组合数量为 $res");
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}
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