硬币找零问题 - 动态规划

最新推荐文章于 2024-06-04 16:05:29 发布

win1611

最新推荐文章于 2024-06-04 16:05:29 发布

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分类专栏：算法设计与分析文章标签：动态规划硬币找零

本文链接：https://blog.youkuaiyun.com/win1611/article/details/14224197

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本文详细阐述了如何使用动态规划方法解决硬币找零问题，通过实例演示了从不同面额硬币中找出特定金额所需最少硬币数量的过程。包括核心算法步骤、代码实现以及实际应用案例。

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硬币找零问题：要找开money元钱，需要的最小硬币数

question: 硬币面额：CoinValues[], coinNum, 需要找零钱：money
output: 从1 -- money对应需要的硬币数目coinsUsed[]
动态规划思想：
    coinsUsed[0] = 0;
    coinsUsed[i] = Min { coinsUsed[i-CoinValues[j]] +１ } [j: 1 to coinNum],if i >= CoinValues[j]
    //保存要找开 i 元钱，需要的最小硬币数量

例如：硬币：2, 5, 6, 8, 1 找钱money：10
    i = 1时，对j从1 to coinNum遍历，if i>=CoinValues[j],则求Min{coinsUsed[i-CoinValues[j]] +１}
      即coinsUsed[1] = coinsUsed[i-CoinValues[4]] + 1 = coinsUsed[0] + 1 = 1

    i = 2时，coinsUsed[2] = Min {coinsUsed[2-CoinValues[0]]+1, coinsUsed[2-CoinValues[4]]+1}

                      = Min {coinsUsed[0]+1, coinsUsed[1]+1} = 1
   ...
    i = 8时，coinsUsed[8] = Min {coinsUsed[8-CoinValues[j]]+1} [j From 0 To coinNum(4)] = 1

int main()
{
    int coinValue[] = {2, 5, 6, 8, 1};
    int coinNum = sizeof(coinValue)/sizeof(int);
    int money = 20;
    int coinsUsed[money];
    makeChange(coinValue, coinNum, money, coinsUsed);
    return 0;
}

void makeChange(int coinValues[], int coinNum, int money, int coinsUsed[])
{
    coinsUsed[0] = 0;
    for (int cents = 1; cents <= money; cents ++)
    {
        int minCoins = INF;
        for (int kind = 0; kind < coinNum; kind ++)
        {
            if (coinValues[kind] <= cents)
            {
                int temp = coinsUsed[cents - coinValues[kind]] + 1;
                if (temp < minCoins)
                {
                    minCoins = temp;
                }
            }
        }
        coinsUsed[cents] = minCoins;
        cout << "面值为 " << cents << " 的最小硬币数 : " << coinsUsed[cents] << endl;
    }
}

Reference Url：

http://blog.youkuaiyun.com/JarvisChu/article/details/6056963#

http://blog.163.com/huang_zhong_yuan/blog/static/174975283201110604819214/

http://58.20.53.45/files/files_upload/content/material_177/content/002001/file_2.htm