mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-28 23:36:28 +08:00
e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
88 lines
2.4 KiB
C
88 lines
2.4 KiB
C
/**
|
|
* File: coin_change.c
|
|
* Created Time: 2023-10-02
|
|
* Author: Zuoxun (845242523@qq.com)
|
|
*/
|
|
|
|
#include "../utils/common.h"
|
|
|
|
/* 求最小值 */
|
|
int myMin(int a, int b) {
|
|
return a < b ? a : b;
|
|
}
|
|
|
|
/* 零钱兑换：动态规划 */
|
|
int coinChangeDP(int coins[], int amt, int coinsSize) {
|
|
int n = coinsSize;
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
int **dp = malloc((n + 1) * sizeof(int *));
|
|
for (int i = 0; i <= n; i++) {
|
|
dp[i] = calloc(amt + 1, sizeof(int));
|
|
}
|
|
// 状态转移：首行首列
|
|
for (int a = 1; a <= amt; a++) {
|
|
dp[0][a] = MAX;
|
|
}
|
|
// 状态转移：其余行和列
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// 若超过目标金额，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] = myMin(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
int res = dp[n][amt] != MAX ? dp[n][amt] : -1;
|
|
// 释放内存
|
|
for (int i = 0; i <= n; i++) {
|
|
free(dp[i]);
|
|
}
|
|
free(dp);
|
|
return res;
|
|
}
|
|
|
|
/* 零钱兑换：空间优化后的动态规划 */
|
|
int coinChangeDPComp(int coins[], int amt, int coinsSize) {
|
|
int n = coinsSize;
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
int *dp = calloc(amt + 1, sizeof(int));
|
|
dp[0] = 0;
|
|
// 状态转移
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// 若超过目标金额，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] = myMin(dp[a], dp[a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
int res = dp[amt] != MAX ? dp[amt] : -1;
|
|
// 释放内存
|
|
free(dp);
|
|
return res;
|
|
}
|
|
|
|
/* Driver code */
|
|
int main() {
|
|
int coins[] = {1, 2, 5};
|
|
int coinsSize = sizeof(coins) / sizeof(coins[0]);
|
|
int amt = 4;
|
|
|
|
// 动态规划
|
|
int res = coinChangeDP(coins, amt, coinsSize);
|
|
printf("凑到目标金额所需的最少硬币数量为 %d\n", res);
|
|
|
|
// 空间优化后的动态规划
|
|
res = coinChangeDPComp(coins, amt, coinsSize);
|
|
printf("凑到目标金额所需的最少硬币数量为 %d\n", res);
|
|
|
|
return 0;
|
|
}
|