Bone Collector 【01背包问题 java】

Problem 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 231).

Sample Input

5 10

1 2 3 4 5

5 4 3 2 1

Sample Output

问题：输入t组数据，每组数组有两个输入N和V，代表N个石头，V是背包的容量，下面两组第一行是石头的价值，第二行是对应的重量，找到背包所能装下的最大价值。

简单的01背包问题，设f[v]表示容量为v的背包可以获得的最大价值，所以有：

for i=1..N
   for v=V..0
        f[v]=max{f[v],f[v-c[i]]+w[i]};

import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            int max = in.nextInt();

            int[] c = new int[n + 1];
            int[] v = new int[n + 1];

            for (int i = 1; i <= n; i++) {
                v[i] = in.nextInt();
            }
            for (int i = 1; i <= n; i++) {
                c[i] = in.nextInt();
            }
            //使用一维数组来表示
            int[] f = new int[max + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = max; j >= c[i]; j--) {
                    f[j] = Math.max(f[j], f[j - c[i]] + v[i]);
                }
            }
            System.out.println(f[max]);
        }
    }
}

Bone Collector 【01背包问题 java】

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