C语言编程练习66：Bone Collector

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 2³¹).

Sample Input

1
5 10
1 2 3 4 5
5 4 3 2 1

Sample Output

14

动态规划的学习，但是我还是搞不太懂，如何推公式

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<cmath>
#include<iostream>
using namespace std;
struct BONE
{
    int val;
    int vol;
}bone[1011];
int N,V;
int dp[1011][1011];
int ans()
{
    memset(dp,0,sizeof(dp));
    for(int i=1;i<=N;i++)
    {
        for(int j=0;j<=V;j++)
        {
            if(bone[i].vol>j)
            {
                dp[i][j]=dp[i-1][j];
            }
            else
            {
                dp[i][j]=max(dp[i-1][j],dp[i-1][j-bone[i].vol]+bone[i].val);
            }
            
        }
    }
    return dp[N][V];
}
int main()
{
    int t;
    cin>>t;
    while(t--)
    {
        cin>>N>>V;
        for(int i=1;i<=N;i++)
        {
            cin>>bone[i].val;
        }
        for(int i=1;i<=N;i++)
        {
            cin>>bone[i].vol;
        }
        cout<<ans()<<endl;
    }
    
    return 0;
}