1.背包问题

1）01背包问题

 

二维： 

import java.util.*;
public class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int v = scan.nextInt();
        
        int[] a = new int[n + 1];
        int[] b = new int[n + 1];
        for(int i = 1 ; i <= n; i ++){
            a[i] = scan.nextInt();
            b[i] = scan.nextInt();
        }
        
        scan.close();
        
        int[][] dp = new int[n + 1][v + 1];
        dp[0][0] = 0;
        for(int i = 1; i <= n ; i ++){
            for(int j = 1; j <= v; j ++){
                if (j >= a[i]){
                    dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - a[i]] + b [i]);
                }else{
                    dp[i][j] = dp[i - 1][j];
                }
            }
        }
        System.out.println(dp[n][v]);
    }
}

二维优化为一维： 

import java.util.*;
public class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int v = scan.nextInt();
        
        int[] a = new int[n + 1];
        int[] b = new int[n + 1];
        for(int i = 1 ; i <= n; i ++){
            a[i] = scan.nextInt();
            b[i] = scan.nextInt();
        }
        
        scan.close();
        
        int[] dp = new int[v + 1];
        dp[0] = 0;
        for(int i = 1; i <= n ; i ++){
            for(int j = v; j >= a[i]; j --){
                dp[j] = Math.max(dp[j], dp[j - a[i]] + b [i]);
            }
        }
        System.out.println(dp[v]);
    }
}

2）完全背包问题

import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int v = scan.nextInt();
        
        int[] a = new int[n + 1];
        int[] b = new int[n + 1];
        for(int i = 1; i <= n; i ++){
            a[i] = scan.nextInt();
            b[i] = scan.nextInt();
        }
        
        int[][] dp = new int[n + 1][v + 1];
        for(int i = 1; i <= n; i ++){
            for(int j = 0; j <= v; j ++){
                for(int k = 0; k * a[i] <= j;  k ++){
                    dp[i][j] = Math.max(dp[i][j], dp[i - 1][j - k * a[i]] + k * b[i]);
                }
            }
        }
        System.out.println(dp[n][v]);
        
    }
}

  稍作优化

import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int v = scan.nextInt();
        
        int[] a = new int[n + 1];
        int[] b = new int[n + 1];
        for(int i = 1; i <= n; i ++){
            a[i] = scan.nextInt();
            b[i] = scan.nextInt();
        }
        
        int[][] dp = new int[n + 1][v + 1];
        for(int i = 1; i <= n; i ++){
            for(int j = 0; j <= v; j ++){
                if(a[i] <= j){
                    dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - a[i]] + b[i]);
                }else{
                    dp[i][j] = dp[i - 1][j];
                }
            }
        }
        System.out.println(dp[n][v]);
        
    }
}

3）多重背包问题

2.线性DP