Find Two Missing Numbers | Set 1 (An Interesting Linear Time Solution)

Given an array of n unique integers where each element in the array is in the range [1, n]. The array has all distinct elements and the size of the array is (n-2). Hence Two numbers from the range are missing from this array. Find the two missing numbers.

Examples : 

Input : arr[] = {1, 3, 5, 6}
Output : 2 4

Input : arr[] = {1, 2, 4}
Output : 3 5

Input : arr[] = {1, 2}
Output : 3 4

Method 1 - O(n) time complexity and O(n) Extra Space

Step 1: Take a boolean array mark that keeps track of all the elements present in the array. 
Step 2: Iterate from 1 to n, check for every element if it is marked as true in the boolean array, if not then simply display that element.

Two Missing Numbers are
2 4 

Method 2 - O(n) time complexity and O(1) Extra Space

The idea is based on this popular solution for finding one missing number. We extend the solution so that two missing elements are printed. 
Let’s find out the sum of 2 missing numbers:

arrSum => Sum of all elements in the array

sum (Sum of 2 missing numbers) = (Sum of integers from 1 to n) - arrSum
 = ((n)*(n+1))/2 – arrSum 

avg (Average of 2 missing numbers) = sum / 2;

• One of the numbers will be less than or equal to avg while the other one will be strictly greater than avg. Two numbers can never be equal since all the given numbers are distinct.
• We can find the first missing number as a sum of natural numbers from 1 to avg, i.e., avg*(avg+1)/2 minus the sum of array elements smaller than avg
• We can find the second missing number by subtracting the first missing number from the sum of missing numbers

Consider an example for better clarification 

Input : 1 3 5 6, n = 6
Sum of missing integers = n*(n+1)/2 - (1+3+5+6) = 6.
Average of missing integers = 6/2 = 3.
Sum of array elements less than or equal to average = 1 + 3 = 4
Sum of natural numbers from 1 to avg = avg*(avg + 1)/2
 = 3*4/2 = 6
First missing number = 6 - 4 = 2
Second missing number = Sum of missing integers-First missing number
Second missing number = 6-2= 4

Below is the implementation of the above idea.

Two Missing Numbers are
2 4

Note: There can be overflow issues in the above solution. 

In below set 2, another solution that is O(n) time, O(1) space, and doesn't cause overflow issues is discussed.
Find Two Missing Numbers | Set 2 (XOR based solution)