hello-algo/codes/cpp/chapter_dynamic_programming/coin_change_ii.cpp
2023-11-03 22:48:43 +08:00

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/**
* File: coin_change_ii.cpp
* Created Time: 2023-07-11
* Author: Krahets (krahets@163.com)
*/
#include "../utils/common.hpp"
/* 零钱兑换 II动态规划 */
int coinChangeIIDP(vector<int> &coins, int amt) {
int n = coins.size();
// 初始化 dp 表
vector<vector<int>> dp(n + 1, vector<int>(amt + 1, 0));
// 初始化首列
for (int i = 0; i <= n; i++) {
dp[i][0] = 1;
}
// 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[i][a] = dp[i - 1][a];
} else {
// 不选和选硬币 i 这两种方案之和
dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];
}
}
}
return dp[n][amt];
}
/* 零钱兑换 II空间优化后的动态规划 */
int coinChangeIIDPComp(vector<int> &coins, int amt) {
int n = coins.size();
// 初始化 dp 表
vector<int> dp(amt + 1, 0);
dp[0] = 1;
// 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 这两种方案之和
dp[a] = dp[a] + dp[a - coins[i - 1]];
}
}
}
return dp[amt];
}
/* Driver code */
int main() {
vector<int> coins = {1, 2, 5};
int amt = 5;
// 动态规划
int res = coinChangeIIDP(coins, amt);
cout << "凑出目标金额的硬币组合数量为 " << res << endl;
// 空间优化后的动态规划
res = coinChangeIIDPComp(coins, amt);
cout << "凑出目标金额的硬币组合数量为 " << res << endl;
return 0;
}