12. Euclidean algorithm. ChocolatesByNumbers.swift

import Foundation
import Glibc

// Solution @ Sergey Leschev, Belarusian State University

// 12. Euclidean algorithm. ChocolatesByNumbers.

// Two positive integers N and M are given. Integer N represents the number of chocolates arranged in a circle, numbered from 0 to N − 1.
// You start to eat the chocolates. After eating a chocolate you leave only a wrapper.
// You begin with eating chocolate number 0. Then you omit the next M − 1 chocolates or wrappers on the circle, and eat the following one.
// More precisely, if you ate chocolate number X, then you will next eat the chocolate with number (X + M) modulo N (remainder of division).
// You stop eating when you encounter an empty wrapper.

// For example, given integers N = 10 and M = 4. You will eat the following chocolates: 0, 4, 8, 2, 6.

// The goal is to count the number of chocolates that you will eat, following the above rules.

// Write a function:
// class Solution { public int solution(int N, int M); }
// that, given two positive integers N and M, returns the number of chocolates that you will eat.

// For example, given integers N = 10 and M = 4. the function should return 5, as explained above.

// Write an efficient algorithm for the following assumptions:
// N and M are integers within the range [1..1,000,000,000].

public func solution(_ N: Int, _ M: Int) -> Int {

    func greatestCommonDivisor(_ a: Int, _ b: Int) -> Int {
        if (a % b) == 0 { return b }
        return greatestCommonDivisor(b, a % b)
    }
    
        
    let divisor = greatestCommonDivisor(N, M)
    return N / divisor
}