POJ 1276 Cash Machine

Cash Machine

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 23136		Accepted: 8093

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

 

   题意 ：一台免费的现金输出机器，先输入一个金额cash，里面有N种货币，数量为num[i]，面值为val[i]，问最多输出多少现金？

   // 多重背包

// 将 每种票值同时当做所占用的容量
// 然后二进制优化
#include <iostream>
#include <algorithm>
#include <queue>
#include <math.h>
#include <stdio.h>
#include <string.h>
using namespace std;
#define MOD 1000000007
#define maxn 100010
int dp[maxn];
//int num[20],val[20];
int main()
{
    int cash,N;
    while(scanf("%d %d",&cash,&N)!=EOF){
        int i,j,k;
        int tp;
        int num,val;
        for(i=0;i<=cash;i++)
          dp[i]=0;
        for(i=1;i<=N;i++){
          scanf("%d %d",&num,&val);
           k=1;
           while(k<=num){
            tp=k*val;
            for(j=cash;j>=tp;j--)
                dp[j]=max(dp[j],dp[j-tp]+tp);
            num-=k;
            k=k<<1;
           }
           if(num>0){
            k=num;
            tp=k*val;
            for(j=cash;j>=tp;j--)
                dp[j]=max(dp[j],dp[j-tp]+tp);
           }
        }
        printf("%d
",dp[cash]);
    }


    return 0;
}