93 lines
2.6 KiB
C
93 lines
2.6 KiB
C
/**
|
|
* File: coin_change.c
|
|
* Created Time: 2023-10-02
|
|
* Author: Zuoxun (845242523@qq.com)
|
|
*/
|
|
|
|
#include "../utils/common.h"
|
|
|
|
/* Find minimum value */
|
|
int myMin(int a, int b) {
|
|
return a < b ? a : b;
|
|
}
|
|
|
|
/* Coin change: Dynamic programming */
|
|
int coinChangeDP(int coins[], int amt, int coinsSize) {
|
|
int n = coinsSize;
|
|
int MAX = amt + 1;
|
|
// Initialize dp table
|
|
int **dp = malloc((n + 1) * sizeof(int *));
|
|
for (int i = 0; i <= n; i++) {
|
|
dp[i] = calloc(amt + 1, sizeof(int));
|
|
}
|
|
// State transition: first row and first column
|
|
for (int a = 1; a <= amt; a++) {
|
|
dp[0][a] = MAX;
|
|
}
|
|
// State transition: the rest of the rows and columns
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[i][a] = dp[i - 1][a];
|
|
} else {
|
|
// The smaller value between not choosing and choosing coin i
|
|
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;
|
|
// Free memory
|
|
for (int i = 0; i <= n; i++) {
|
|
free(dp[i]);
|
|
}
|
|
free(dp);
|
|
return res;
|
|
}
|
|
|
|
/* Coin change: Space-optimized dynamic programming */
|
|
int coinChangeDPComp(int coins[], int amt, int coinsSize) {
|
|
int n = coinsSize;
|
|
int MAX = amt + 1;
|
|
// Initialize dp table
|
|
int *dp = malloc((amt + 1) * sizeof(int));
|
|
for (int j = 1; j <= amt; j++) {
|
|
dp[j] = MAX;
|
|
}
|
|
dp[0] = 0;
|
|
|
|
// State transition
|
|
for (int i = 1; i <= n; i++) {
|
|
for (int a = 1; a <= amt; a++) {
|
|
if (coins[i - 1] > a) {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[a] = dp[a];
|
|
} else {
|
|
// The smaller value between not choosing and choosing coin i
|
|
dp[a] = myMin(dp[a], dp[a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
int res = dp[amt] != MAX ? dp[amt] : -1;
|
|
// Free memory
|
|
free(dp);
|
|
return res;
|
|
}
|
|
|
|
/* Driver code */
|
|
int main() {
|
|
int coins[] = {1, 2, 5};
|
|
int coinsSize = sizeof(coins) / sizeof(coins[0]);
|
|
int amt = 4;
|
|
|
|
// Dynamic programming
|
|
int res = coinChangeDP(coins, amt, coinsSize);
|
|
printf("Minimum number of coins required to reach the target amount = %d\n", res);
|
|
|
|
// Space-optimized dynamic programming
|
|
res = coinChangeDPComp(coins, amt, coinsSize);
|
|
printf("Minimum number of coins required to reach the target amount = %d\n", res);
|
|
|
|
return 0;
|
|
}
|