Knapsack01

import java.util.Scanner;

public class Knapsack01 {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

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

        // Input weights and values of items
        int[] weights = new int[n];
        int[] values = new int[n];
        
        System.out.println("Enter the weights of the items:");
        for (int i = 0; i < n; i++) {
            weights[i] = scanner.nextInt();
        }

        System.out.println("Enter the values of the items:");
        for (int i = 0; i < n; i++) {
            values[i] = scanner.nextInt();
        }

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

        // Solve the 0/1 Knapsack problem
        int maxProfit = knapsack(weights, values, capacity, n);

        System.out.println("Maximum profit: " + maxProfit);
        
        scanner.close();
    }

    public static int knapsack(int[] weights, int[] values, int capacity, int n) {
        int[][] dp = new int[n + 1][capacity + 1];

        // Fill the DP table
        for (int i = 1; i <= n; i++) {
            for (int w = 1; w <= capacity; w++) {
                if (weights[i - 1] <= w) {
                    // Include the item and maximize the profit
                    dp[i][w] = Math.max(values[i - 1] + dp[i - 1][w - weights[i - 1]], dp[i - 1][w]);
                } else {
                    // Exclude the item
                    dp[i][w] = dp[i - 1][w];
                }
            }
        }

        // Backtrack to find the items that are included
        int[] solution = new int[n];
        int w = capacity;
        
        for (int i = n; i > 0 && w > 0; i--) {
            // If the item is included in the optimal solution
            if (dp[i][w] != dp[i - 1][w]) {
                solution[i - 1] = 1; // Mark as included
                w -= weights[i - 1];
            } else {
                solution[i - 1] = 0; // Mark as not included
            }
        }

        // Print the solution array
        System.out.print("Solution array (1 means included, 0 means not included): ");
        for (int i = 0; i < n; i++) {
            System.out.print(solution[i] + " ");
        }
        System.out.println();

        return dp[n][capacity];
    }
}