dp入门

dp入门经典——01背包问题（1）

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 2 ³¹).

Sample Input

15 101 2 3 4 55 4 3 2 1

Sample Output

14

#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;const int maxn = 1e3+5;int vol[maxn];int val[maxn];int dp[maxn];int main(){    int T,N,V;    scanf("%d",&T);    while(T--)    {        memset(dp,0,sizeof(dp));        scanf("%d%d",&N,&V);        for(int i=0;i<N;i++)            scanf("%d",&val[i]);        for(int i=0;i<N;i++)            scanf("%d",&vol[i]);        for(int i=0;i<N;i++)            for(int j=V;j>=vol[i];j--)                dp[j]=max(dp[j],dp[j-vol[i]]+val[i]);        printf("%d\n",dp[V]);    }    return 0;}