POJ 1276-CashMachine 背包问题

题目来源：http://acm.pku.edu.cn/JudgeOnline/problem?id=1276

 

解题报告：

 

设f[k]=1代表可以组成金额为k的钱。

 

从第一个D1开始，有f[1*n1]=1, f[2*n1]=1, ..., f[D1*n1]=1

 

然后到Dk，就应该在之前所有可以组成的钱币的情况下，将可以组成的钱币再加上1*nk, 2*nk, .. Dk*nK，得到新的可以组成的更多的金额，另外，为了区分本轮新添加的金额和之前一轮就已经可以组成的金额，将 f[新的金额]设为2，等一轮结束后，在重新全部设为1即可（我因为忘了这个，一次WA）。

 

#include <iostream>using namespace std;int main(){int cash;while(scanf("%d",&cash)!=EOF){int N;cin >> N;int *n=new int[N];int *d=new int[N];for(int i=0;i<N;i++)cin >> n[i] >> d[i];int *f=new int[cash+1];f[0]=1;for(int i=0;i<N;i++){for(int k=0;k<cash+1;k++){if(f[k]==1){for(int j=1;j<=n[i];j++){int temp=j*d[i]+k;if(temp > cash)break;else if(f[temp]!=1)f[temp]=2;}}}for(int k=0;k<cash+1;k++)if(f[k]==2)f[k]=1;}for(int i=cash;i>=0;i--){if(f[i]==1){cout << i << endl;break;}}}}

 

附录：

Cash Machine

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 12018 Accepted: 4078

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

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.