1 题目编号：1018
2 题目内容：
Problem 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. <br><br>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! <br>
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. <br>
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.". <br>
Sample Input
310 11021 130 5010 11021 150 301 6210 320 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.
3 题意：用一堆给定面值的硬币a1,a2,...,aN,(ai和aj的面值可以相同)，组合成恰好质量为W的最小总面值
4 解题思路形成过程：设选择范围为前i个硬币组成质量恰好为j的最小面值为dp(j)=max(dp(j),dp(j-w[i])+p[i]),(j>=w[i])；由于罐里每种硬币可以有多个（即完全背包模型），因此j从0开始遍历这样dp[i][j]可以从d[i-1][j-w[i]]中得到更新，也可以从dp[i][j-w[i]]中更新，正好符合每种物体可以取无穷多个，但一定注意不能用二维数组，否则dp[i][j]只能从dp[i-1][j-w[i]]中得到更新，而不能从dp[i][j-w[i]]更新，不符合dp[i][j]的前一个状态是dp[i][j-w[i]]，就变成01背包了，而不是完全背包
5 代码：
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<ctype.h>
using namespace std;
const int maxn=510;
const int INF=1000100;
int T;
int E,F;
int N;
int p[maxn],w[maxn];
int dp[INF];
int main()
{
cin>>T;
while(T--){
cin>>E>>F>>N;
for(int i=1;i<=N;i++){
cin>>p[i]>>w[i];
}
for(int i=0;i<=F-E;i++) dp[i]=INF;
dp[0]=0;
for(int i=1;i<=N;i++){
for(int j=w[i];j<=F-E;j++){
dp[j]=min(dp[j-w[i]]+p[i],dp[j]);
}
}
if(dp[F-E]!=INF) cout<<"The minimum amount of money in the piggy-bank is "<<dp[F-E]<<"."<<endl;
else cout<<"This is impossible."<<endl;
}
return 0;
}
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