二维：

import java.util.Scanner;
public class Main{
    public static void main(String[] args){
        Scanner reader = new Scanner(System.in);
        //输入物品个数N和背包容量V
        int N = reader.nextInt();
        int V = reader.nextInt();
        //两个一维数组分别存储每个物品的体积与价值
        int[] v = new int[N + 1];
        int[] w = new int[N + 1];
        for(int i = 1; i <= N; i++){
            v[i] = reader.nextInt();
            w[i] = reader.nextInt();
        }
        reader.close();

        int[][] dp = new int[N + 1][V + 1];
        dp[0][0] = 0;//第0个物品，体积为0时，最大价值为0
        for(int i = 1; i <= N; i++){
            for(int j = 0; j <= V; j++){
                for(int k = 0; k * v[i] <= j; k++){
                    dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - k * v[i]] + k * w[i]);
                }
            }
        }
        System.out.println(dp[N][V]);
    }
} 

一维：优化后

import java.util.Scanner;
public class Main{
    public static void main(String[] args){
        Scanner reader = new Scanner(System.in);
        //输入物品个数N和背包容量V
        int N = reader.nextInt();
        int V = reader.nextInt();
        //两个一维数组分别存储每个物品的体积与价值
        int[] v = new int[N + 1];
        int[] w = new int[N + 1];
        for(int i = 1; i <= N; i++){
            v[i] = reader.nextInt();
            w[i] = reader.nextInt();
        }
        reader.close();

        int[][] dp = new int[N + 1][V + 1];
        dp[0][0] = 0;//第0个物品，体积为0时，最大价值为0
        for(int i = 1; i <= N; i++){
            for(int j = 0; j <= V; j++){
                for(int k = 0; k * v[i] <= j; k++){
                    dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - k * v[i]] + k * w[i]);
                }
            }
        }
        System.out.println(dp[N][V]);
    }
}