Is there something wrong with my id array?

Question

This program pulls two columns from the input.txt file where the first column indicates the value of the object, and the second column represents the weight. The values are imported and placed into two arrays: the value array and the weight array. The knapsack calculations are then made. There are 23 objects in total represented by the rows of the arrays. My code correctly calculates the total value that is being held in the knapsack, and will print out the correct IDs if the weight capacity entered is 5, but for any other weight the IDs being held in the id array are not correct, but the total value printed out is. Here is my code for both files, and if anyone is able to figure out how to correctly save and print the IDs being held in the knapsack please let me know . . .

input.txt file:

17  5
12  8
15  22
17  11
33  21
43  15
15  4
44  35
23  19
10  23
55  39
8   6
21  9
20  28
20  13
45  29
18  16
21  19
68  55
10  16
33  54
3   1
5   9

knapsack.java file:

//We did borrow concepts from:

// http://www.sanfoundry.com/java-program-solve-knapsack-problem-using-dp/

import java.util.Scanner;
import java.util.*;
import java.lang.*;
import java.io.*;

public class knapsack
{
    static int max(int a, int b) 
    { 
        if(a > b)
        {
            //System.out.println(a);
            return a;
        }
        else
            //System.out.println(b);
            return b;
    }
    static int knapSack(int maxCapacity, int weight[], int value[], int n)
    {
        int track = 0;
        int i, w;
        int foo1 = 0;
        int foo2 = 0;
        K = new int[n+1][maxCapacity+1];

        // Build table K[][] in bottom up manner
        for (i = 0; i <= n; i++)
        {
            for (w = 0; w <= maxCapacity; w++)
            {
                if (i==0 || w==0)
                K[i][w] = 0;
                else if (weight[i-1] <= w)
            {
                //K[i][w] = max(value[i-1] + K[i-1][w-weight[i-1]],  K[i-1][w]);
                if(value[i-1] + K[i-1][w-weight[i-1]] > K[i-1][w])
                {
                    K[i][w] = value[i-1] + K[i-1][w-weight[i-1]];
                    //System.out.println("A: "+i);

                }
                else
                {
                    K[i][w] = K[i-1][w];
                    id[track++] = i;
                    //System.out.println("B: "+i);
                }

            }
            else
            {
                K[i][w] = K[i-1][w];

            }

        }
        //System.out.println(K[foo1][foo2]);
    }

    return K[n][maxCapacity];
}

public static void main(String args[])throws java.io.FileNotFoundException
{
    Scanner sc = new Scanner(System.in);
    int n = 23;
    File file = new File("input.txt");
    Scanner scanner = new Scanner(file);
    id = new Integer [n]; 
    //knapval = new int[n];
    //knapweight = new int [n];
    int []value = new int[n]; 
    int []weight = new int[n];
    for(int i=0; i<n; i++)
    {
        value[i] = scanner.nextInt();
        weight[i] = scanner.nextInt();

    }

    System.out.println("Enter the maximum capacity: ");
    int maxCapacity = sc.nextInt();
    System.out.println("The maximum value that can be put in a knapsack with a weight capacity of "+maxCapacity+" is: " + knapSack(maxCapacity, weight, value, n));
    System.out.println();
    System.out.println("IDs Of Objects Held In Knapsack: ");
    //System.out.println();
    for(int z = 0; z < n && id[z] != null; z++)
    {
        System.out.println(id[z]);
    }
    if(id[0] == null)
        System.out.println("All objects are too heavy, knapsack is empty.");
    sc.close();
    scanner.close();


}
protected static Integer [] id;
protected static int [][]K;
}

Answer 1

Your way of recording your solution in the id array is flawed. At the time you do id[track++] = i; , you don't yet know whether i will be in your final solution. Because of the nested loops you may even add i more than once. This in turn may lead to overflowing the array with a java.lang.ArrayIndexOutOfBoundsException: 23 (this happens for max capacity 12 and above).

I suggest instead of using id , after your solution is complete you track your way backward through the K array (by Java naming conventions, it should be a small k ). It holds all the information you need to find out which objects were included in the maximum value.

private static void printKnapsack(int maxCapacity, int weight[], int value[], int n) {
    if (K[n][maxCapacity] == 0) {
        System.out.println("No objects in knapsack");
    } else {
        int w = maxCapacity;
        for (int i = n; i > 0; i--) {
            if (K[i][w] > K[i - 1][w]) { // increased value from object i - 1
                System.out.format("ID %2d value %2d weight %2d%n", i, value[i - 1], weight[i - 1]);
                // check that value in K agrees with value[i - 1] 
                assert K[i - 1][w - weight[i - 1]] + value[i - 1] == K[i][w];
                w -= weight[i - 1];
            }
        }
    }
}

The above prints the objects backward. Example run:

Enter the maximum capacity: 
13
The maximum value that can be put in a knapsack with a weight capacity of 13 is: 36

ID 13 value 21 weight  9
ID  7 value 15 weight  4

If you want the objects in forward order, inside the for loop put them into a list (you may for instance use id from your old attempt), and then print the items from the list in opposite order.