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79 lines
2.1 KiB
79 lines
2.1 KiB
/**
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* File: coin_change.c
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* Created Time: 2023-10-02
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* Author: Zuoxun (845242523@qq.com)
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*/
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#include "../utils/common.h"
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/* 求最小值 */
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int min(int a, int b) {
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return a < b ? a : b;
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}
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/* 零钱兑换：动态规划 */
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int coinChangeDP(int coins[], int amt, int coinsSize) {
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int n = coinsSize;
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int MAX = amt + 1;
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// 初始化 dp 表
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int dp[n + 1][amt + 1];
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memset(dp, 0, sizeof(dp));
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// 状态转移：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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// 状态转移：其余行列
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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 这两种方案的较小值
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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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/* 零钱兑换：空间优化后的动态规划 */
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int coinChangeDPComp(int coins[], int amt, int coinsSize) {
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int n = coinsSize;
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int MAX = amt + 1;
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// 初始化 dp 表
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int dp[amt + 1];
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memset(dp, MAX, sizeof(dp));
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dp[0] = 0;
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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 这两种方案的较小值
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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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int coins[] = {1, 2, 5};
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int coinsSize = sizeof(coins) / sizeof(coins[0]);
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int amt = 4;
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// 动态规划
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int res = coinChangeDP(coins, amt, coinsSize);
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printf("凑到目标金额所需的最少硬币数量为 %d\n", res);
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// 空间优化后的动态规划
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res = coinChangeDPComp(coins, amt, coinsSize);
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printf("凑到目标金额所需的最少硬币数量为 %d\n", res);
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return 0;
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}
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