POJ1384完全背包

Description

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

3
10 110
2
1 1
30 50
10 110
2
1 1
50 30
1 6
2
10 3
20 4

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.

这题我WA了好多次
原因是这样的，我被那个背包必须满的条件给限制住了
一开始我的dp数组是初始化为0，然后这个dp我就写不出来了…
再后来换了一种想法，我把dp的对象作为重量
按照max来dp
如果他最终的时候重量为n那么就更新一次sum
但是这样又不对了，因为你只是疯狂的增大了他的重量，
并没有给出可以更新sum的数据
所以疯狂WA
按照完全背包从前向后的放来看，只要dp[n]被更新过那么就一定存在着题目要求
因此直接求最小值就可以

#include<iostream>
#include<cmath>
#include<queue>
#include<algorithm>
#include<cstdlib>
using namespace std;
int zhi[501];
int zhong[501];
long long  dp[10001];
int dpz[10001];
int main()
{
    int T;
    cin >> T;
    while (T--)
    {
        memset(zhi, 0, sizeof(zhi));
        memset(zhong, 0, sizeof(zhong));
        for (int a = 1;a <= 10001;a++)dp[a] = 100000000;
        int w1, w2;
        cin >> w1 >> w2;
        int m;
        cin >> m;
        int n = w2 - w1;
        if (n == 0)
        {
            printf("The minimum amount of money in the piggy-bank is 0.\n");
            continue;
        }
        long long sum = 100000000;
        for (int a = 1;a <= m;a++)cin >> zhi[a] >> zhong[a];
        for (int a = 1;a <= m;a++)
        {
            for (int b = 1;b <= n;b++)
            {
                if (b - zhong[a] >= 0)
                {
                    if (dp[b] > dp[b - zhong[a]] + zhi[a] ) //&& dpz[n] <= n
                    {
                        dp[b] = dp[b - zhong[a]] + zhi[a];
                        if (b == n)
                        {
                            sum = min(sum, dp[b]);
                        }
                    }
                }
            }
        }
        if (sum == 100000000)
        {
            cout << "This is impossible." << endl;
        }
        else
        {
            printf("The minimum amount of money in the piggy-bank is %lld.\n", sum);
        }
    }
    return 0;
}