hdu 2602Bone Collector(0/1背包)
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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 ?
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.
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
15 101 2 3 4 55 4 3 2 1
Sample Output
14
这是简单的0/1背包,用一维的比较快。0/1背包,每个物品只能使用一次。
这是最基础的背包问题,特点是:每种物品仅有一件,可以选择放或不放。
用子问题定义状态:即f[i][v]表示前i件物品恰放入一个容量为v的背包可以获得的最大价值。则其状态转移方程便是:
f[i][v]=max{f[i-1][v],f[i-1][v-c[i]]+w[i]}
代码:
#include<iostream>#include<cmath>using namespace std;int dp[1005];int w[1005],c[1005];int main(){ int i,j,n,v,t; scanf("%d",&t); while(t--) { scanf("%d%d",&n,&v); memset(dp,0,sizeof(dp)); for(i=1;i<=n;i++) scanf("%d",&w[i]); for(i=1;i<=n;i++) scanf("%d",&c[i]); for(i=1;i<=n;i++) { for(j=v;j>=c[i];j--) { dp[j]=max(dp[j],dp[j-c[i]]+w[i]); } } printf("%d\n",dp[v]); } return 0;}
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