two repeating elements : comments added

Author: Ram swaroop

src/me/ramswaroop/arrays/TwoRepeatingElements.java

@@ -11,20 +11,38 @@
  */
 public class TwoRepeatingElements {
 
+    /**
+     * Finds the 2 repeating elements in an array {@param a} of 1 to n elements and n+2 length. This is
+     * similar to {@link me.ramswaroop.bits.TwoNonRepeatingElements}.
+     * <p/>
+     * EXPLANATION:
+     * Let the repeating numbers be X and Y, if we xor all the elements in the array and all integers from 1 to n,
+     * then the result is X xor Y.
+     * The 1’s in binary representation of X xor Y is corresponding to the different bits between X and Y.
+     * Suppose that the kth bit of X xor Y is 1, we can xor all the elements in the array and all integers
+     * from 1 to n, whose kth bits are 1. The result will be one of X and Y.
+     *
+     * @param a
+     * @return
+     */
     public static int[] getTwoRepeatingElements(int[] a) {
         int xor = a[0];
         int rightMostSetBit;
         int x = 0, y = 0;
-        
+
         for (int i = 1; i < a.length; i++) {
             xor ^= a[i];
         }
+
         for (int i = 1; i <= a.length - 2; i++) {
             xor ^= i;
         }
+
+        // now xor is X xor Y, therefore find any of its set bit
         rightMostSetBit = xor & ~(xor - 1);
 
         for (int i = 0; i < a.length; i++) {
+            // one number will have a set bit at that position and other wouldn't
             if ((a[i] & rightMostSetBit) == 0) {
                 x ^= a[i];
             } else {
@@ -33,6 +51,7 @@ public static int[] getTwoRepeatingElements(int[] a) {
         }
 
         for (int i = 1; i <= a.length - 2; i++) {
+            // one number will have a set bit at that position and other wouldn't
             if ((i & rightMostSetBit) == 0) {
                 x ^= i;
             } else {
@@ -45,5 +64,7 @@ public static int[] getTwoRepeatingElements(int[] a) {
 
     public static void main(String a[]) {
         System.out.println(Arrays.toString(getTwoRepeatingElements(new int[]{4, 2, 4, 5, 2, 3, 1})));
+        System.out.println(Arrays.toString(getTwoRepeatingElements(new int[]{2, 4, 5, 2, 3, 1, 6, 7, 7})));
+        System.out.println(Arrays.toString(getTwoRepeatingElements(new int[]{1, 2, 1, 2})));
     }
 }