You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
71 lines
2.0 KiB
71 lines
2.0 KiB
/**
|
|
* File: coin_change.cpp
|
|
* Created Time: 2023-07-11
|
|
* Author: krahets (krahets@163.com)
|
|
*/
|
|
|
|
#include "../utils/common.hpp"
|
|
|
|
/* 零钱兑换：动态规划 */
|
|
int coinChangeDP(vector<int> &coins, int amt) {
|
|
int n = coins.size();
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
vector<vector<int>> dp(n + 1, vector<int>(amt + 1, 0));
|
|
// 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] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[n][amt] != MAX ? dp[n][amt] : -1;
|
|
}
|
|
|
|
/* 零钱兑换：空间优化后的动态规划 */
|
|
int coinChangeDPComp(vector<int> &coins, int amt) {
|
|
int n = coins.size();
|
|
int MAX = amt + 1;
|
|
// 初始化 dp 表
|
|
vector<int> dp(amt + 1, MAX);
|
|
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] = min(dp[a], dp[a - coins[i - 1]] + 1);
|
|
}
|
|
}
|
|
}
|
|
return dp[amt] != MAX ? dp[amt] : -1;
|
|
}
|
|
|
|
/* Driver code */
|
|
int main() {
|
|
vector<int> coins = {1, 2, 5};
|
|
int amt = 4;
|
|
|
|
// 动态规划
|
|
int res = coinChangeDP(coins, amt);
|
|
cout << "凑到目标金额所需的最少硬币数量为 " << res << endl;
|
|
|
|
// 空间优化后的动态规划
|
|
res = coinChangeDPComp(coins, amt);
|
|
cout << "凑到目标金额所需的最少硬币数量为 " << res << endl;
|
|
|
|
return 0;
|
|
}
|