codes/cpp/chapter_dynamic_programming/coin_change.cpp - main - githubmirror/hello-algo

codes/cpp/chapter_dynamic_programming/coin_change.cpp

70 строк2 KB

Yudong Jin

Some improvements (#1073)

07 фев 2024, 17:21

07 фев 2024, 17:21a005c6e

/**
 * 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;
}