poj1276多重背包
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D - Cash Machine
Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64uDescription
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.
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.
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
题意:有一个取款机,里面有n种纸币,每样纸币数量各不相同,现在我们要取款m元,这个取款机只能吐出小于等于m元的纸币,问最多可以取到多少钱;
这是一个有一点点限制的多重背包,限制上线为m元,然后按照多重背包写就可以了,之前有一篇介绍多重背包的详细题目,几天不在讲述具体思想,多重背包详解;
ac代码:
#include <iostream>#include <stdio.h>#include <string.h>#include <math.h>using namespace std;const int maxn=1e5+10,maxm=1e3+100;int dp[maxn],num[maxm],v[maxm],val[maxn];int tw[50];int main(){ int tot,n, w; for(int i=0;i<30;i++) { tw[i]=(1<<i); } while(~scanf("%d%d",&w,&n)) { tot=0; for(int i=0;i<n;i++) { scanf("%d%d",&num[i],&v[i]); } if(w==0||n==0) { printf("0\n"); goto endW; } for(int i=0;i<n;i++) { for(int j=0;;j++) { int temp=tw[j]-1; if(tw[j]>(num[i]-temp)) { val[tot++]=(num[i]-temp)*v[i]; break; } else val[tot++]=tw[j]*v[i]; } } memset(dp,0,sizeof(dp)); for(int i=0;i<tot;i++) { for(int j=w;j>=val[i];j--) { if(dp[j]<dp[j-val[i]]+val[i]&&dp[j-val[i]]+val[i]<=w) dp[j]=dp[j-val[i]]+val[i]; } } printf("%d\n",dp[w]); endW:; } //cout << "Hello world!" << endl; return 0;}
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