HDU 1114：Piggy-Bank ← 完全背包问题

【题目概述】
给定一个数T，表示T个样例。
针对每个样例，第一行两个值，分别为小猪存钱罐空时的重量E，满时的重量F。
第二行一个值，表示小猪存钱罐中钱币的种类N。
接下来N行，每行两个值，分别某种钱币的面值P，某种钱币的单个重量W。
求小猪存钱罐中钱币的最小值。

数据范围：1<= E<= F<=10000，1<=N<= 500，1<= P<= 50000, 1<= W<=10000

From：http://acm.hdu.edu.cn/showproblem.php?pid=1114

【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.
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, P and 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 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.

【Code】

#include <bits/stdc++.h>
using namespace std;

const int inf=0x3f3f3f3f;
const int maxv=10005;
const int maxn=505;

int c[maxv];
int val[maxn],vol[maxn];

int main() {
	int T;
	scanf("%d",&T);
	while(T--) {
		int empty,full,V;
		scanf("%d%d",&empty,&full);
		V=full-empty;

		int n;
		scanf("%d",&n);
		for(int i=1; i<=n; i++) {
			scanf("%d%d",&val[i],&vol[i]);
		}

		memset(c,inf,sizeof(c));
		c[0]=0;
		for(int i=1; i<=n; i++) {
			for(int j=vol[i]; j<=V; j++) {
				c[j]=min(c[j],c[j-vol[i]]+val[i]);
			}
		}

		if(c[V]==inf) {
			printf("This is impossible.\n");
		} else {
			printf("The minimum amount of money in the piggy-bank is %d.\n",c[V]);
		}
	}

	return 0;
}


/*
in:
3
10 110
2
1 1
30 50
10 110
2
1 1
50 30
1 6
2
10 3
20 4

out:
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.
*/

【Reference】
https://blog.csdn.net/weixin_44756457/article/details/98470225
https://blog.csdn.net/pmt123456/article/details/53350173/