Co-prime or mutually prime pair are those pair of numbers whose GCD is 1. Given a number n represent the number as the sum of a Co-prime pair ( A, B) such that A – B is minimum .
Input : 12 Output : 5 7 Possible co-prime pairs are (5, 7), (1, 11) but difference between 5 and 7 is minimum Input : 13 Output : 6 7 Possible co-prime pairs are (6, 7), (5, 8), (4, 9), (3, 10), (2, 11) and (1, 12) but difference between 6 and 7 is minimum
A simple solution is to iterate through all number from 1 to n-1. For every number x, check if n – x and x are co-primes. If yes, then update the result if difference between these two is less than minimum difference so far.
An efficient solution is based on the fact that the numbers with minimum difference should be close to n/2. We loop from n/2 to 1. Check every possible pair and when first possible Co-prime pair is found display it and stop the loop.
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