POJ 1742 Coins 多重背包用单调队列优化

最新推荐文章于 2021-06-05 12:35:59 发布

原创最新推荐文章于 2021-06-05 12:35:59 发布 · 703 阅读

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#多重背包 #单调队列优化 #动态规划

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本文讨论了如何利用单调队列优化多重背包问题，提供了解决此类问题的有效方法。

多重背包用单调队列优化

Description

People in Silverland use coins.They have coins of value A1,A2,A3...An Silverland dollar.One day Tony opened his money-box and found there were some coins.He decided to buy a very nice watch in a nearby shop. He wanted to pay the exact price(without change) and he known the price would not more than m.But he didn't know the exact price of the watch.

You are to write a program which reads n,m,A1,A2,A3...An and C1,C2,C3...Cn corresponding to the number of Tony's coins of value A1,A2,A3...An then calculate how many prices(form 1 to m) Tony can pay use these coins.

Input

The input contains several test cases. The first line of each test case contains two integers n(1<=n<=100),m(m<=100000).The second line contains 2n integers, denoting A1,A2,A3...An,C1,C2,C3...Cn (1<=Ai<=100000,1<=Ci<=1000). The last test case is followed by two zeros.

Output

For each test case output the answer on a single line.

Sample Input

3 10
1 2 4 2 1 1
2 5
1 4 2 1
0 0

Sample Output

8
4#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn=100000+10;
int c[maxn],w[maxn],use[maxn],f[maxn];
int main()
{
	int n,m;
	while(scanf("%d%d",&n,&m)&&n&&m)
	{
		int ans=0;
		for(int i=1;i<=n;i++)
		{
			scanf("%d",&w[i]);
		}
		for(int i=1;i<=n;i++)
		{
			scanf("%d",&c[i]);
		}
		memset(f,0,sizeof(f));
		f[0]=1;
		for(int i=1;i<=n;i++)
		{
			memset(use,0,sizeof(use));
			for(int j=w[i];j<=m;j++)
			{
				if(!f[j]&&f[j-w[i]]&&(use[j-w[i]]+1<=c[i]))
				{
					f[j]=1;
					use[j]=use[j-w[i]]+1;
					ans++;
				}
			}
		}
		printf("%d\n",ans);
	}
	return 0;
}