The Maximum Prime Difference interview question is a combination of array traversal and number theory. You are given an array of integers, and you need to find the maximum distance (difference between indices) between any two prime numbers in the array. Essentially, you want to find the index of the first prime number and the index of the last prime number and calculate the absolute difference between them.
If there is only one prime or no primes, the difference is typically 0.
This Maximum Prime Difference coding problem tests two things: your ability to efficiently identify prime numbers and your ability to traverse arrays to find extremas. Companies like Unstop use it to see if you can implement a standard mathematical check (is_prime) and apply it within a simple optimization task. It also evaluates if you can optimize the prime check (e.g., checking up to square root) to ensure the overall solution is performant.
The Array, Math, Number Theory interview pattern is applied here.
i where arr[i] is prime.j where arr[j] is prime.j - i (if two or more primes are found).Array: [4, 2, 9, 5, 3, 8, 10]
first_prime_idx = 1.last_prime_idx = 4.Maximum Prime Difference is 3.
In the Maximum Prime Difference coding problem, candidates often forget that 1 is not a prime number. Another common mistake is using an inefficient prime-checking algorithm (like checking all divisors up to N), which can lead to TLE if the numbers in the array are very large. Some might also forget to handle the cases where there are zero or one prime numbers in the array.
Always have a clean, optimized is_prime function in your toolkit. Remember: handle 0 and 1 as special cases, check 2 separately, and then loop through odd numbers up to the square root. This is a common sub-routine in many "Math + Array" interview questions.