Minimum difference between any two primes from the given range

Given two integers L and R, the task is to find the minimum difference between any two prime numbers in the range [L, R].

Examples: 

Input: L = 21, R = 50 
Output: 2 
(29, 31) and (41, 43) are the only valid pairs 
that give the minimum difference.

Input: L = 1, R = 11 
Output: 1 
The difference between (2, 3) is minimum. 
 

Approach:  

• Find all the prime numbers upto R using Sieve of Eratosthenes.
• Now starting from L, find the difference between any two prime numbers within the range and update minimum difference so far.
• If the number of primes in the range were < 2 then print -1.
• Else print the minimum difference.

Below is the implementation of the above approach:  

2

Time Complexity: O((R - L) + sqrt(10⁵))

Auxiliary Space: O(10⁵)