Find two Missing Numbers in a Sequence of Consecutive Numbers
Objective : Write an algorithm to find two Missing Numbers in a Sequence of Consecutive Numbers
Input: Array, arrA[] with two missing numbers and Range
Output : Two missing numbers
Approach:

 Approach is very simple, Add all the given numbers say S
 Calculate sum of N numbers by formula n(n+1)/2 , say N
 Find sum of two missing numbers a+b = NS
 Now take the product of all given numbers say P
 Now take the product of N numbers , say Np;
 Find the product of two missing numbers ab = NpP
 Now we have a+b and ab , we can easily calculate a and b
Example :
Given array : {10,2,3,5,7,8,9,1}; Range : 10 N (Sum of 1 to 10 ) = 55 S (Sum of given elements ) = 45 a+b = 10(1) Np(Product of 1 to 10) = 3628800 P(Product of given elements) = 151200 So a*b = 24(2) Now we have two equations and two variables, if we solve we will get values 6 and 4.
Complete Code:
Output:
Missing numbers are :6 and 4