使用java语言解决基于回溯法的0-1背包问题，记录物品选择结果、程序运行时间、访问节点数

以下是基于回溯法的0-1背包问题的Java代码，其中记录了物品选择结果、程序运行时间和访问节点数：

import java.util.*;

public class KnapsackProblemBacktracking {
    
    private static int capacity;
    private static int[] weights;
    private static int[] values;
    private static boolean[] solution;
    private static int maxProfit;
    private static int nodeCount;

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);

        System.out.print("Enter the capacity of the knapsack: ");
        capacity = scanner.nextInt();

        System.out.print("Enter the number of items: ");
        int n = scanner.nextInt();

        weights = new int[n];
        values = new int[n];
        solution = new boolean[n];

        System.out.println("Enter the weight and value of each item:");

        for (int i = 0; i < n; i++) {
            weights[i] = scanner.nextInt();
            values[i] = scanner.nextInt();
        }

        long startTime = System.currentTimeMillis();
        nodeCount = 0;
        knapsack(0, 0, 0);
        long endTime = System.currentTimeMillis();

        System.out.println("\nMaximum profit: " + maxProfit);

        System.out.println("Selected items (1 if selected, 0 otherwise):");
        for (int i = 0; i < n; i++) {
            System.out.print((solution[i] ? 1 : 0) + " ");
        }

        System.out.println("\nTotal time taken: " + (endTime - startTime) + "ms");
        System.out.println("Total nodes visited: " + nodeCount);

        scanner.close();
    }

    private static void knapsack(int i, int profit, int weight) {

        nodeCount++;

        if (weight <= capacity && profit > maxProfit) {
            maxProfit = profit;
            for (int j = 0; j < solution.length; j++) {
                solution[j] = (j == i) || solution[j];
            }
        }

        if (i == weights.length || weight >= capacity) {
            return;
        }

        knapsack(i + 1, profit + values[i], weight + weights[i]);

        knapsack(i + 1, profit, weight);
    }
}

在此代码中，`knapsack` 方法实现了回溯算法。其中，`i` 表示当前考虑到的物品编号，`profit` 表示当前背包中物品的总价值，`weight` 表示当前背包中物品的总重量。`nodeCount` 记录访问的节点数，`maxProfit` 记录当前最大价值，`solution` 记录选中的物品。

程序输入背包容量、物品个数、每个物品的重量和价值，然后计算最大价值、选中的物品、程序运行时间和访问节点数。