ACM: dp题 poj 1276  go on 动态规…

                                                                     Cash Machine

Description

A Bank plans to install a machine for cash withdrawal. Themachine is able to deliver appropriate @ bills for a requested cashamount. The machine uses exactly N distinct bill denominations, sayDk, k=1,N, and for each denomination Dk the machine has a supply ofnk 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 deliverand write a program that computes the maximum amount of cash lessthan or equal to cash that can be effectively delivered accordingto the available bill supply of the machine.

Notes:
@ is the symbol of the currency delivered by the machine. Forinstance, @ may stand for dollar, euro, pound etc.

Input

The program input is from standard input. Each data set in theinput stands for a particular transaction and has the format:

cash N n1 D1 n2 D2 ... nN DN

where 0 <= cash <= 100000 is theamount of cash requested, 0 <=N <= 10is the number of bill denominations and 0 <= nk<= 1000 is the number of available bills for the Dkdenomination, 1 <= Dk <= 1000, k=1,N.White spaces can occur freely between the numbers in the input. Theinput data are correct.

Output

For each set of data the program prints the result to thestandard output on a separate line as shown in the examplesbelow.

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 ofcash requested is @735. The machine contains 3 bill denominations:4 bills of @125, 6 bills of @5, and 3 bills of @350. The machinecan deliver the exact amount of requested cash.

In the second case the bill supply of the machine does not fit theexact amount of cash requested. The maximum cash that can bedelivered is @630. Notice that there can be several possibilitiesto combine the bills in the machine for matching the deliveredcash.

In the third case the machine is empty and no cash is delivered. Inthe fourth case the amount of cash requested is @0 and, therefore,the machine delivers no cash.

 

题意: 现在给你一个询问值. 要求你在N种值中寻找尽量能凑出询问值.如果不行请计算最接近的值.

        N种值的每一种的个数会给出.

 

解题思路:

               1.动态规划题--> 背包问题. 状态标记就可以了.

               2. d[i] 表示是否达到i值.

               3. 规划的起点是d[0]; 当满足当前 j+d[i]*k > s 就dp[j+d[i]*k  ]标记.

                   j是当前枚举的“询问值” (0<= j <= s);    d[i]是第i种值.k是d[i]个数 (1<=k<= n[i])

                   n[i]是第i种值的总个数.

               4. 从dp[s] 开始往下搜索.

代码:

#include <cstdio>
#include <iostream>
#include <cstring>
using namespace std;
#define MAX 100005

int s, N;
int n[10], d[10];
bool dp[MAX];

int main()
{
//   freopen("input.txt","r",stdin);
   while(scanf("%d%d",&s,&N) != EOF)
    {
      for(int i = 1; i <= N; ++i)
      {
         scanf("%d%d",&n[i],&d[i]);
      }
      
      memset(dp,false,sizeof(dp));
      dp[0] = true;
      
      for(int i = 1; i <= N; ++i)
      {
         for(int j = s; j >= 0; --j)
         {
            if(dp[j])
            {
               for(int k = 1; k <= n[i];++k)
               {
                  if( (j+d[i]*k) > s)
                     break;
                  dp[j+d[i]*k] = true;
               }
            }
         }
      }
      
      for(int i = s; i >= 0; --i)
      {
         if(dp[i])
         {
            printf("%d\n",i);
            break;
         }
      }
    }
    return0;
}