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 1Sample Output
14
題意:01揹包問題,求物品放入揹包能獲得的最大價值
題解:
F[i,j]:前i件物品放入容量爲v的揹包,故可以將問題轉化爲動態問題中的自底向上,也就是說考慮第i-1件的問題
考慮如果第i件物品放不放?
如果不放,則F[i-1,v]
如果放,則F[i-1,v-C[i]]
#include<iostream>
#include<algorithm>
#include<string.h>
using namespace std;
//物品價值
int val[1005];
//物品體積
int vol[1005];
int dp[1005][1005];
int main(){
int t;
cin>>t;
while(t--){
//揹包可容納的總數量
int n;
//揹包可容納的總體積
int v;
cin>>n>>v;
for(int i=1;i<=n;i++)
cin>>val[i];
for(int i=1;i<=n;i++)
cin>>vol[i];
//初始化
for(int i=0;i<=n;i++)
dp[i][0]=0;
for(int j=0;j<=v;j++)
dp[0][j]=0;
memset(dp,0,sizeof(dp));
for(int i=1;i<=n;i++)
for(int j=0;j<=v;j++)
if(j<vol[i])
dp[i][j]=dp[i-1][j];
else
dp[i][j]=max(dp[i-1][j],dp[i-1][j-vol[i]]+val[i]);
cout<<dp[n][v]<<endl;
}
return 0;
}