ACM: dp题 poj 1276  go on 动态规…

                                                                     
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 3 350

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.

 

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;

  
   
   
   
   
 }

  
   
   
   
 }

  
   
   
 }

  
   
 }