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71 lines
2.0 KiB
71 lines
2.0 KiB
/**
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* File: coin_change.cpp
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* Created Time: 2023-07-11
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* 零錢兌換：動態規劃 */
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int coinChangeDP(vector<int> &coins, int amt) {
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int n = coins.size();
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int MAX = amt + 1;
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// 初始化 dp 表
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vector<vector<int>> dp(n + 1, vector<int>(amt + 1, 0));
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// 狀態轉移：首行首列
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for (int a = 1; a <= amt; a++) {
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dp[0][a] = MAX;
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}
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// 狀態轉移：其餘行和列
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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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// 若超過目標金額，則不選硬幣 i
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dp[i][a] = dp[i - 1][a];
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} else {
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// 不選和選硬幣 i 這兩種方案的較小值
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dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
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}
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}
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}
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return dp[n][amt] != MAX ? dp[n][amt] : -1;
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}
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/* 零錢兌換：空間最佳化後的動態規劃 */
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int coinChangeDPComp(vector<int> &coins, int amt) {
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int n = coins.size();
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int MAX = amt + 1;
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// 初始化 dp 表
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vector<int> dp(amt + 1, MAX);
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dp[0] = 0;
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// 狀態轉移
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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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// 若超過目標金額，則不選硬幣 i
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dp[a] = dp[a];
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} else {
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// 不選和選硬幣 i 這兩種方案的較小值
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dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);
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}
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}
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}
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return dp[amt] != MAX ? dp[amt] : -1;
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}
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/* Driver code */
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int main() {
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vector<int> coins = {1, 2, 5};
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int amt = 4;
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// 動態規劃
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int res = coinChangeDP(coins, amt);
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cout << "湊到目標金額所需的最少硬幣數量為 " << res << endl;
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// 空間最佳化後的動態規劃
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res = coinChangeDPComp(coins, amt);
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cout << "湊到目標金額所需的最少硬幣數量為 " << res << endl;
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return 0;
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}
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