01背包N

Description

Many years ago , in Teddy’s hometown there was a man who was called “Bone Collector”. This man like to collect varies of bones , such as dog’s , cow’s , also he went to the grave …  The bone collector had a big bag with a volume of V ,and along his trip of collecting there are a lot of bones , obviously , different bone has different value and different volume, now given the each bone’s value along his trip , can you calculate out the maximum of the total value the bone collector can get ?  

 

Input

The first line contain a integer T , the number of cases.  Followed by T cases , each case three lines , the first line contain two integer N , V, (N <= 1000 , V <= 1000 )representing the number of bones and the volume of his bag. And the second line contain N integers representing the value of each bone. The third line contain N integers representing the volume of each bone.

 

Output

One integer per line representing the maximum of the total value (this number will be less than 2 ³¹).

 

Sample Input

1

5 10

1 2 3 4 5

5 4 3 2 1

 

Sample Output

14

 

 

 

思路：

       状态转移方程：val[j]=max{val[j],val[j-weight[i]]+p[i]}

       val[j]表示：前i个物体在容量为vol最大的装载量

 

源代码：

 

#include<iostream>
#include<algorithm>
#include<string>
#include<cstring>
#include<cmath>
using namespace std;
#define maxn 1000+10
int val[maxn], weight[maxn], p[maxn];
int main()
{
    int T;
    cin >> T;
    while (T--)
    {
        int n, vol;
        cin >> n >> vol;
        for (int i = 1; i <= n; i++)
        {
            cin >> p[i];
        }
        for (int j = 1; j <= n; j++)
        {
            cin >> weight[j];
        }
        for (int j = 0; j <= vol; j++)
        {
            val[j] = 0;
        }
        for (int i = 1; i <= n; i++)  
        {
            for (int j = vol; j >= weight[i]; j--)
            {
                val[j] = max(val[j], val[j - weight[i]] + p[i]);

            }
        }
        cout << val[vol] << endl;  

    }
       return 0;

}

心得：

 背包入门~~~~理解一个方程还是挺费劲的，/(ㄒoㄒ)/~~不过终于比之前好多了。。。。给自己一个赞！不过还是觉得好神奇

                                      (*^__^*) 嘻嘻……