三种背包问题

1.0-1背包

import java.util.*;
public class Main{
    public static void main(String[] args) {  
        int N=5;
        int max=10;
        int[] weights={2,2,6,5,4};
        int[] values={6,3,5,4,6};
        int[] c=new int[max+1];
        c[0]=0;
        for(int i=0;i<N;i++){
            for(int j=max;j>0;j--){
                if(weights[i]<=j){
                    c[j]=Math.max(c[j],c[j-weights[i]]+values[i]);
                }else{
                    c[j]=c[j];
                }
            }
        }
        System.out.println(c[max]);
    }
}

2.完全背包

import java.util.*;
public class Main{
    public static void main(String[] args) {  
        int N=5;
        int max=10;
        int[] weights={2,2,6,5,4};
        int[] values={4,3,5,4,6};
        int[] c=new int[max+1];
        c[0]=0;
        for(int i=0;i<N;i++){
            for(int j=max;j>0;j--){
                int count=max/weights[i];
                for(int k=0;k<=count;k++){
                    if(weights[i]*k<=j){
                        c[j]=Math.max(c[j],c[j-weights[i]*k]+values[i]*k);
                    }
                }
            }
        }
        System.out.println(c[max]);
    }
}

3.多重背包

import java.util.*;
public class Main{
    public static void main(String[] args) {  
        int N=5;
        int max=10;
        int[] weights={2,2,6,5,4};
        int[] values={4,3,5,4,6};
        int[] counts={2,3,1,2,3};
        int[] c=new int[max+1];
        c[0]=0;
        for(int i=0;i<N;i++){
            for(int j=max;j>0;j--){
                for(int k=0;k<=counts[i];k++){
                    if(weights[i]*k<=j){
                        c[j]=Math.max(c[j],c[j-weights[i]*k]+values[i]*k);
                    }
                }
            }
        }
        System.out.println(c[max]);
    }
}