Question.java

package Question5_7;

import java.util.ArrayList;
import java.util.Random;

public class Question {
    /* Create a random array of numbers from 0 to n, but skip 'missing' */
    public static ArrayList<BitInteger> initialize(int n, int missing) {
        BitInteger.INTEGER_SIZE = Integer.toBinaryString(n).length();
        ArrayList<BitInteger> array = new ArrayList<BitInteger>();
        
        for (int i = 1; i <= n; i++) {
        	array.add(new BitInteger(i == missing ? 0 : i));
        }

        // Shuffle the array once.
        for (int i = 0; i < n; i++){
            int rand = i + (int) (Math.random() * (n-i));
            array.get(i).swapValues(array.get(rand));
        }
        
        return array;
    }


    public static int findMissing(ArrayList<BitInteger> array) {
       return findMissing(array, BitInteger.INTEGER_SIZE - 1);
    }        

    private static int findMissing(ArrayList<BitInteger> input, int column) {
    	if (column < 0) { // Base case and error condition
    		return 0;
    	}
    	ArrayList<BitInteger> oddIndices = new ArrayList<BitInteger>(input.size()/2);
    	ArrayList<BitInteger> evenIndices = new ArrayList<BitInteger>(input.size()/2);
        for (BitInteger t : input) {
            if (t.fetch(column) == 0) {
                evenIndices.add(t);
            } else {
                oddIndices.add(t);
            }
        }
        if (oddIndices.size() >= evenIndices.size()) {
            return (findMissing(evenIndices, column - 1)) << 1 | 0;
        } else {
            return (findMissing(oddIndices, column - 1)) << 1 | 1;
        }
    }

    // Test harness
    public static void main(String[] args) {
        Random rand = new Random(); 
        int n = rand.nextInt(300000) + 1;
        int missing = rand.nextInt(n+1);
        ArrayList<BitInteger> array = initialize(n, missing);
        System.out.println("The array contains all numbers but one from 0 to " + n + ", except for " + missing);
        
        int result = findMissing(array);
        if (result != missing) {
            System.out.println("Error in the algorithm!\n" + "The missing number is " + missing + ", but the algorithm reported " + result);
        } else {
            System.out.println("The missing number is " + result);
        }
    }
}