背包问题---DP

Problem 2214 Knapsack problem

Accept: 412 Submit: 1650
Time Limit: 3000 mSec Memory Limit : 32768 KB

Problem Description

Given a set of n items, each with a weight w[i] and a value v[i], determine a way to choose the items into a knapsack so that the total weight is less than or equal to a given limit B and the total value is as large as possible. Find the maximum total value. (Note that each item can be only chosen once).

Input

The first line contains the integer T indicating to the number of test cases.

For each test case, the first line contains the integers n and B.

Following n lines provide the information of each item.

The i-th line contains the weight w[i] and the value v[i] of the i-th item respectively.

1 <= number of test cases <= 100

1 <= n <= 500

1 <= B, w[i] <= 1000000000

1 <= v[1]+v[2]+...+v[n] <= 5000

All the inputs are integers.

Output

For each test case, output the maximum value.

Sample Input

5 15

12 4

2 2

1 1

4 10

1 2

Sample Output

代码如下:

/*
    0-1背包问题：
    因为重量太大，肯定不能按照原来的标准模型套用，开不了那么大的数组
    但是总价值却小于5000;

    根据价值构造dp方程,找到最小的重量能够得到这个价值
    dp[100]=15,就是代表使得价值为100的最小重量为15;
*/


#include <iostream>
#include<cstring>
#include<cstdio>
using namespace std;
const int maxs = 600;
int n,B;
int w[maxs];
int v[maxs];
int dp[5005];
int main()
{
    freopen("in.txt","r",stdin);
    int T;
    cin>>T;
    while(T--)
    {
        int sum = 0;
        scanf("%d%d
",&n,&B);
        for(int i=1;i<=n;i++)
            scanf("%d%d",&w[i],&v[i]),sum+=v[i];
        memset(dp,0x3f,sizeof(dp));
        dp[0]=0;
        for(int i=n;i>=1;i--)
            for(int j=sum;j>=v[i];j--)
                dp[j]=min(dp[j],dp[j-v[i]]+w[i]);
        for(int i=sum;i>=0;i--)
            if(dp[i]<=B)
            {
                printf("%d
",i);
                break;
            }

    }
    return 0;
}