背包问题（java)实现

1、01背包

import java.util.Scanner;

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

2、完全背包

import java.util.Scanner;

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

}
}

 3、多重背包1

数据范围 

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
       Scanner scan=new Scanner(System.in);
       int n=scan.nextInt();
       int m=scan.nextInt();
       int[][] dp=new int[n+1][m+1];
       int[] v=new int[n+1]; //体积
       int[] w=new int[n+1]; //价值
       int[] c=new int[n+1]; //重量
       for(int i=1;i<=n;i++) {
    	   v[i]=scan.nextInt();
    	   w[i]=scan.nextInt();
    	   c[i]=scan.nextInt();
       }
       for(int i=1;i<=n;i++) {
    	 for(int j=1;j<=m;j++) {
    		 dp[i][j]=dp[i-1][j];
    		 for(int k=1;k<=c[i]&&v[i]*k<=j;k++) {
    			 dp[i][j]=Math.max(dp[i][j], dp[i-1][j-v[i]*k]+w[i]*k);
    			 
    		 }
    		 System.out.print(dp[i][j]+" ");
    		 
    	 }
    	 System.out.println();
  }    
       System.out.println(dp[n][m]);

}
}

4、多重背包2

数据范围

import java.util.Scanner;
import java.util.ArrayList;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), m = in.nextInt();
        // 使用列表存储二进制优化后的物品
        int[] newV = new int[2000*11];
        int[] newW = new int[2000*11];
        int[] dp = new int[m + 1];
        int count = 0;

        // 二进制优化处理
        for (int i = 1; i <= n; i++) {
            int v = in.nextInt();
            int w = in.nextInt();
            int c = in.nextInt();

            // 二进制拆分（将数量c分解为1,2,4...的幂次方组合）
            for (int k = 1; k <= c; k *= 2) {
                newV[count]=(v * k);
                newW[count]=(w * k);
                c -= k;
                count++;
            }
            if (c > 0) {
                newV[count]=(v * c);
                newW[count]=(w * c);
                count++;
            }
        }

        // 转化为01背包问题
        for (int i = 0; i < count; i++) {
            // 01背包处理逻辑
            for (int j = m; j >= newV[i]; j--) {
                dp[j] = Math.max(dp[j], dp[j - newV[i]] + newW[i]);
            }
        }
        System.out.println(dp[m]);
    }
}