POJ 1276 Cash Machine

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 350633 4  500 30  6 100  1 5  0 1735 00 3  10 100  10 50  10 10

Sample Output

73563000

背包问题，大意是有各种不同面值的货币，每种面值的货币有有限的数量，把这些货币组成最多但不超过cash的数。

从面值从小到大做多重背包 。从cash开始dp，rcnt记录当前总价时的剩余的当前价值货币的个数。

#include<iostream>#include<algorithm>#include<cstdio>#include<cstring>#include<cstdlib>using namespace std;typedef struct node{int c,p;}q;bool cmp(q a,q b){return a.p<b.p;}char dp[100001];int rcnt[100001];int main(){q p[11];int cash,n,i,j;while(scanf("%d%d",&cash,&n)!=EOF){if(!n){printf("0\n");continue;}for(i=0;i<n;i++)scanf("%d%d",&p[i].c,&p[i].p);p[n].c=0;if(!cash){printf("0\n");continue;}sort(p,p+n,cmp);memset(dp,0,sizeof(dp));memset(rcnt,0,sizeof(rcnt));dp[cash]=1;rcnt[cash]=p[0].c;for(i=0;i<n;i++){for(j=cash;j>=p[i].p;j--){if(dp[j]){if(rcnt[j]&&!dp[j-p[i].p]){rcnt[j-p[i].p]=rcnt[j]-1;dp[j-p[i].p]=1;}rcnt[j]=p[i+1].c;}}} i=0;  while(dp[i]==0)  {   i++;  }  printf("%d\n",cash-i);}return 0;}