There are n chocolates in a circle: count the number of chocolates you will eat
ℹ️ © Codility, 2009-2018
Problem
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 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)).
Solution
C#
class Solution { public int solution(int n, int m) { return n / f(n, m); } private int f(int n, int m) { return n % m == 0 ? m : f(m, n % m); } }
Java
class Solution { public int solution(int n, int m) { return n / f(n, m); } private int f(int n, int m) { return n % m == 0 ? m : f(m, n % m); } }
JavaScript
function solution(n, m) { return n / f(n, m); } function f(n, m) { return n % m == 0 ? m : f(m, n % m); }
PHP
function solution($n, $m) { return $n / f($n, $m); } function f($n, $m) { return $n % $m == 0 ? $m : f($m, $n % $m); }