Codility - Lesson 12 Euclidean Algorithm - 1. ChocolatesByNumbers

Source Link:
https://codility.com/programmers/lessons/12-euclidean_algorithm/chocolates_by_numbers/

Question:

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.

Assume that:

• N and M are integers within the range [1..1,000,000,000].

Complexity:

• expected worst-case time complexity is O(log(N+M));
• expected worst-case space complexity is O(log(N+M)).

My Solution:
Notes:
1. main idea:
// using "gcd(M, N)"
// the number of eaten chocolates = N / gcd(M,N) 
2. using "Euclidean Algorithm" (important)
public static int gcd(int a,int b){
if(a % b == 0)
return b; // case 1
else
return gcd(b,a % b); // case 2 (key point)
}