Two non repeating elements in an array (#2381)

Maths/NonRepeatingElement.java

@@ -0,0 +1,71 @@
+package Maths;
+import java.util.Scanner;
+
+/*
+ * Find the 2 elements which are non repeating in an array
+ * Reason to use bitwise operator: It makes our program faster as we are operating on bits and not on
+ * actual numbers.  
+ */
+public class NonRepeatingElement {
+
+  public static void main(String[] args) {
+
+    Scanner sc = new Scanner(System.in);
+    int i, res = 0;
+    System.out.println("Enter the number of elements in the array");
+    int n = sc.nextInt();
+    if((n & 1) == 1)
+    {
+        //Not allowing odd number of elements as we are expecting 2 non repeating numbers
+        System.out.println("Array should contain even number of elements");
+        return;
+    }
+    int arr[] = new int[n];
+
+    System.out.println("Enter "+n+" elements in the array. NOTE: Only 2 elements should not repeat");
+    for(i = 0; i <n;i++){
+        arr[i] = sc.nextInt();
+    }
+
+    try{
+        sc.close();
+    }catch(Exception e){
+        System.out.println("Unable to close scanner"+e);
+    }
+
+    //Find XOR of the 2 non repeating elements
+    for(i = 0 ; i < n; i++)
+        res^=arr[i];
+
+    //Finding the rightmost set bit
+    res = res & (-res);
+    int num1=0,num2=0;
+
+    for(i = 0 ; i < n; i++){
+        if((res & arr[i]) > 0)//Case 1 explained below
+        num1^=arr[i];
+        else 
+        num2^=arr[i];//Case 2 explained below
+
+    }
+
+    System.out.println("The two non repeating elements are "+num1+" and "+num2);
+
+  }
+
+  /* 
+  Explanation of the code:
+  let us assume we have an array [1,2,1,2,3,4]
+  Property of XOR: num ^ num = 0. 
+  If we XOR all the elemnets of the array we will be left with 3 ^ 4 as 1 ^ 1 and 2 ^ 2 would give 0.
+  Our task is to find num1 and num2 from the result of 3 ^ 4 = 7.
+  We need to find two's complement of 7 and find the rightmost set bit. i.e. (num & (-num))
+  Two's complement of 7 is 001 and hence res = 1.
+  There can be 2 options when we Bitise AND this res with all the elements in our array
+  1. Result will come non zero number
+  2. Result will be 0.
+  In the first case we will XOR our element with the first number (which is initially 0)
+  In the second case we will XOR our element with the second number(which is initially 0)
+  This is how we will get non repeating elements with the help of bitwise operators. 
+  */
+}