Cash Machine（多重背包）

Link：http://poj.org/problem?id=1276

Cash Machine Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 28815   Accepted: 10303 Description A Bank plans to install a machine for cash withdrawal. The machine is able to deliver appropriate @ bills for a requested cash amount. The machine uses exactly N distinct bill denominations, say Dk, k=1,N, and for each denomination Dk the machine has a supply of nk bills. For example,  N=3, n1=10, D1=100, n2=4, D2=50, n3=5, D3=10  means the machine has a supply of 10 bills of @100 each, 4 bills of @50 each, and 5 bills of @10 each.  Call cash the requested amount of cash the machine should deliver and write a program that computes the maximum amount of cash less than or equal to cash that can be effectively delivered according to the available bill supply of the machine.  Notes:  @ is the symbol of the currency delivered by the machine. For instance, @ may stand for dollar, euro, pound etc.  Input The program input is from standard input. Each data set in the input stands for a particular transaction and has the format:  cash N n1 D1 n2 D2 ... nN DN  where 0 <= cash <= 100000 is the amount of cash requested, 0 <=N <= 10 is the number of bill denominations and 0 <= nk <= 1000 is the number of available bills for the Dk denomination, 1 <= Dk <= 1000, k=1,N. White spaces can occur freely between the numbers in the input. The input data are correct.  Output For each set of data the program prints the result to the standard output on a separate line as shown in the examples below.  Sample Input 735 3 4 125 6 5 3 350 633 4 500 30 6 100 1 5 0 1 735 0 0 3 10 100 10 50 10 10 Sample Output 735 630 0 0 Hint The first data set designates a transaction where the amount of cash requested is @735. The machine contains 3 bill denominations: 4 bills of @125, 6 bills of @5, and 3 bills of @350. The machine can deliver the exact amount of requested cash.  In the second case the bill supply of the machine does not fit the exact amount of cash requested. The maximum cash that can be delivered is @630. Notice that there can be several possibilities to combine the bills in the machine for matching the delivered cash.  In the third case the machine is empty and no cash is delivered. In the fourth case the amount of cash requested is @0 and, therefore, the machine delivers no cash. Source Southeastern Europe 2002

解题思路：多重背包题，为费用与价值相等的特殊情况




AC  code：

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#define LL long long
#define MAXN 1000100
using namespace std;

int N;//物品个数
int V;//背包容量
int Weight[MAXN];
int Value[MAXN];
int Num[MAXN];
int f[MAXN];

/*
f[v]:表示把前i件物品放入容量为v的背包中获得的最大收益。
f[v] = max(f[v],f[v - Weight[i]] + Value[i]);
v的为逆序
*/
void ZeroOnePack(int nWeight,int nValue)
{
	for (int v = V;v >= nWeight;v--)
	{
		f[v] = max(f[v],f[v - nWeight] + nValue);
	}
}

/*
f[v]:表示把前i件物品放入容量为v的背包中获得的最大收益。
f[v] = max(f[v],f[v - Weight[i]] + Value[i]);
v的为增序
*/
void CompletePack(int nWeight,int nValue)
{
	for (int v = nWeight;v <= V;v++)
	{
		f[v] = max(f[v],f[v - nWeight] + nValue);
	}
}

int MultiKnapsack()
{
	int k = 1;
	int nCount = 0;
	for (int i = 1;i <= N;i++)
	{
		if (Weight[i] * Num[i] >= V)
		{
			//完全背包:该类物品原则上是无限供应，
			//此时满足条件Weight[i] * Num[i] >= V时，
			//表示无限量供应，直到背包放不下为止.
			CompletePack(Weight[i],Value[i]);
		}
		else
		{
			k = 1;
			nCount = Num[i];
			while(k <= nCount)
			{
				ZeroOnePack(k * Weight[i],k * Value[i]);
				nCount -= k;
				k *= 2;
			}
			ZeroOnePack(nCount * Weight[i],nCount * Value[i]);
		}
	}
	return f[V];
}
int main()
{
	while(cin>>V)
	{
		cin>>N;
		for(int i=1;i<=N;i++)
		{
			scanf("%d%d",&Num[i],&Value[i]);
			Weight[i]=Value[i];//费用与价值相等
		}
			
			memset(f,0,sizeof(f));
			int ans=MultiKnapsack();
			cout<<ans<<endl;
	}
	return 0;
}