HDU---1114 Piggy-Bank【完全背包】

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本文探讨了一个经典的计算机科学问题——如何使用不同类型的硬币填充存钱罐以达到特定重量的同时使硬币总价值最小。通过动态规划算法求解，并提供了解决方案的C++实现。

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Before ACM can do anything, a budget must be prepared and the necessary financial support obtained. The main income for this action comes from Irreversibly Bound Money (IBM). The idea behind is simple. Whenever some ACM member has any small money, he takes all the coins and throws them into a piggy-bank. You know that this process is irreversible, the coins cannot be removed without breaking the pig. After a sufficiently long time, there should be enough cash in the piggy-bank to pay everything that needs to be paid.

But there is a big problem with piggy-banks. It is not possible to determine how much money is inside. So we might break the pig into pieces only to find out that there is not enough money. Clearly, we want to avoid this unpleasant situation. The only possibility is to weigh the piggy-bank and try to guess how many coins are inside. Assume that we are able to determine the weight of the pig exactly and that we know the weights of all coins of a given currency. Then there is some minimum amount of money in the piggy-bank that we can guarantee. Your task is to find out this worst case and determine the minimum amount of cash inside the piggy-bank. We need your help. No more prematurely broken pigs!

Input

The input consists of T test cases. The number of them (T) is given on the first line of the input file. Each test case begins with a line containing two integers E and F. They indicate the weight of an empty pig and of the pig filled with coins. Both weights are given in grams. No pig will weigh more than 10 kg, that means 1 <= E <= F <= 10000. On the second line of each test case, there is an integer number N (1 <= N <= 500) that gives the number of various coins used in the given currency. Following this are exactly N lines, each specifying one coin type. These lines contain two integers each, Pand W (1 <= P <= 50000, 1 <= W <=10000). P is the value of the coin in monetary units, W is it's weight in grams.

Output

Print exactly one line of output for each test case. The line must contain the sentence "The minimum amount of money in the piggy-bank is X." where X is the minimum amount of money that can be achieved using coins with the given total weight. If the weight cannot be reached exactly, print a line "This is impossible.".

Sample Input

Sample Output

The minimum amount of money in the piggy-bank is 60.
The minimum amount of money in the piggy-bank is 100.
This is impossible.

大意：

　　已知存钱罐前后的重量和硬币的种类，每种硬币都有其重量与价值，问将存钱罐装满后使得价值最少。

输入：

　　第一行T，表示T组测试案例，第二行存钱罐前后的重量，第三行N,表示有N种硬币，后面N行表示每种硬币的价值以及重量。


解析：
　　dp[i]表示当存钱罐的容量为i时所能装的硬币的最小价值。

SOURCE:点击打开链接

代码：#include <iostream>
#include <algorithm>
using namespace std;
#define INF 1<<30
int main()
{
    int dp[10006];
    int p[505];
    int w[505];
    int t,e,f,n;
    cin>>t;
    while(t--)
    {
        cin>>e>>f;
        cin>>n;
        for(int i=0;i<n;i++)
            cin>>p[i]>>w[i];
        for(int i=1;i<=f-e;i++)
            dp[i]=INF;
        dp[0]=0;
        for(int i=0;i<n;i++)
            for(int j=w[i];j<=f-e;j++)
                dp[j]=min(dp[j],dp[j-w[i]]+p[i]);
        if(dp[f-e]==INF)
            cout<<"This is impossible."<<endl;
        else
            cout<<"The minimum amount of money in the piggy-bank is "<<dp[f-e]<<"."<<endl;
    }
    return 0;
}