🍑 算法题解专栏

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🍑 分组背包问题

输入

3 5
2
1 2
2 4
1
3 4
1
4 5

输出

8

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👨‍🏫 参考题解

🍑 终极简化版

import java.util.Scanner;

public class 分组背包极简版
{
	static int N = 110;
	static int[] f = new int[N];
	static int[] v = new int[N];
	static int[] w = new int[N];

	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();

		for (int i = 0; i < n; i++)
		{
			int s = sc.nextInt();
			for (int j = 1; j <= s; j++)
			{
				v[j] = sc.nextInt();
				w[j] = sc.nextInt();
			}
			for (int j = 1; j <= s; j++)// 枚举物品
				for (int k = m; k >= v[j]; k--)// 枚举体积
					f[k] = Math.max(f[k], f[k - v[j]] + w[j]);

		}
		System.out.println(f[m]);
	}
}

🍑 滚动数组优化

import java.util.Scanner;

public class Main
{
	static int N = 110;
	static int[] f = new int[N];
	static int[][] v = new int[N][N];
	static int[][] w = new int[N][N];
	static int[] s = new int[N];

	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		for (int i = 1; i <= n; i++)
		{
			s[i] = sc.nextInt();
			for (int j = 1; j <= s[i]; j++)
			{
				v[i][j] = sc.nextInt();
				w[i][j] = sc.nextInt();
			}
		}

		for (int i = 1; i <= n; i++)// 枚举每一组
			for (int j = m; j >= 1; j--)// 枚举体积（体积从大到小枚举【后边依赖于前边的】）
				for (int k = 1; k <= s[i]; k++)// 枚举选了哪个物品
					if (j >= v[i][k])
						f[j] = Math.max(f[j], f[j - v[i][k]] + w[i][k]);

		System.out.println(f[m]);
	}
}

🍑 朴素版

import java.util.*;

class Main{
    static int N = 110;
    static int[][] f = new int[N][N];
    static int[] s = new int[N];
    static int[][] w = new int[N][N];
    static int[][] v =new int[N][N];
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        for(int i = 1; i <= n; i++ ){
            s[i] = sc.nextInt();
            for(int j = 1; j <= s[i]; j++){
                v[i][j] = sc.nextInt();
                w[i][j] = sc.nextInt();
            }
        }
        
        for(int i =1 ; i <= n; i++){
            for(int j = 1; j <= m; j++){
                f[i][j] = f[i-1][j];
                for(int k = 1; k <= s[i]; k++){
                    if(j >= v[i][k])
                      f[i][j] = Math.max(f[i][j],f[i-1][j-v[i][k]] + w[i][k]);
                }
            }
        }        
        
        System.out.println(f[n][m]);   
    }
    
    
}