Given an array of positive numbers, the task is to calculate the absolute difference between sum of non-prime numbers and prime numbers.
Note: 1 is neither prime nor non-prime.
Input : 1 3 5 10 15 7 Output : 10 Explanation: Sum of non-primes = 25 Sum of primes = 15 Input : 3 4 6 7 Output : 0
Naive Approach: A simple solution is to traverse the array and keep checking for every element if it is prime or not. If number is prime, then add it to sum S2 which represents the sum of primes else check if its not 1 then add it to sum of non-primes let’s say S1. After traversing the whole array, take the absolute difference between the two(S1-S2).
Time complexity: O(Nsqrt(N))
Efficient Approach: Generate all primes up to the maximum element of the array using the sieve of Eratosthenes and store them in a hash. Now, traverse the array and check if the number is present in the hash map. Then, add these numbers to sum S2 else check if it’s not 1, then add it to sum S1.
After traversing the whole array, display the absolute difference between the two.
Time Complexity: O(Nlog(log(N))
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