chocolates_by_numbers.py

"""
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:

    def solution(N, 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)).
"""


def solution(N, M):
    x = 0
    while x != 1:
        x = N
        y = M
        while y != 0:
            (x, y) = (y, x % y)
        N = N // x
        M = M // x
    return N