01背包问题及其拓展

求背包的最大价值，并求其由哪些物品组成（拓展）

//01背包问题
public class Main{
    static int m = 8;
    static int n = 4;
    static int[] value = { 0 , 3 , 4 , 5 , 6 };
    static  int[] weight = { 0 , 2 , 3 , 4 , 5 };
    static int[][] dp = new int[n+1][m+1];
    static int[] item = new int[5];
    public static void main(String[] args) {
        findMax();
        System.out.println("-------------");
        findWhat(4,8);
        print();
        System.out.println("-------------");
        print2();

    }
    //最优解
    static void findMax(){
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                if (j >= weight[i]){
                    int a = dp[i-1][j];
                    int b = dp[i-1][j-weight[i]]+value[i];
                    dp[i][j] = a > b ? a : b;
                }
                else{
                    dp[i][j] = dp[i-1][j];
                }
            }
        }
        System.out.println(dp[n][m]);
    }

    //最优解组成回溯
    static void findWhat(int i, int j) {                //最优解情况
        if (i > 0) {
            if (dp[i][j] == dp[i - 1][j]) {
                item[i] = 0;
                findWhat(i - 1, j);
            }
            else if (j - weight[i] >= 0 && dp[i][j] == dp[i - 1][j - weight[i]] + value[i]) {
                item[i] = 1;
                findWhat(i - 1, j - weight[i]);
            }
        }
    }

    //最优解二维表打印
    static void print(){
        int count = 0;
        for (int i = 0; i < 5; i++) {
            for (int j = 0; j < 9; j++) {
                System.out.print(dp[i][j]+" ");
                count++;
                if (count==9){
                    count = 0;
                    System.out.println();
                }
            }
        }
    }

    //背包由哪些物品组成 1代表有该物品，0代表没有该物品
    static void print2(){
        int count = 0;
        for (int i = 0; i < n+1; i++) {
            System.out.println(item[i]);
        }
    }
    
}

输出结果：

 

参考博客：https://blog.csdn.net/qq_38410730/article/details/81667885

                  https://blog.csdn.net/lanyu_01/article/details/79815801

如果对背包问题求解思路和如何填表仍有疑问的同学，推荐看这一篇文章：

                  https://blog.csdn.net/huyang0304/article/details/82286279