Given three positive integer L, R, G. The task is to find the count of the pair (x,y) having GCD(x,y) = G and x, y lie between L and R.
Input : L = 1, R = 11, G = 5 Output : 3 (5, 5), (5, 10), (10, 5) are three pair having GCD equal to 5 and lie between 1 and 11. So answer is 3. Input : L = 1, R = 10, G = 7 Output : 1
A simple solution is to go through all pairs in [L, R]. For every pair, find its GCD. If GCD is equal to g, then increment count. Finally return count.
An efficient solution is based on the fact that, for any positive integer pair (x, y) to have GCD equal to g, x and y should be divisible by g.
Observe, there will be at most (R – L)/g numbers between L and R which are divisible by g.
So we find numbers between L and R which are divisible by g. For this, we start from ceil(L/g) * g and with increment by g at each step while it doesn’t exceed R, count numbers having GCD equal to 1.
ceil(L/g) * g = floor((L + g - 1) / g) * g.
Below is the implementation of above idea :
This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.