find-the-child-who-has-the-ball-after-k-seconds.cpp

// Time:  O(1)
// Space: O(1)

// math
class Solution {
public:
    int numberOfChild(int n, int k) {
        const int q = k / (n - 1), r = k % (n - 1);
        return (q & 1) == 0 ? r : (n - 1) - r;
    }
};

// Time:  O(1)
// Space: O(1)
// math
class Solution2 {
public:
    int numberOfChild(int n, int k) {
        const int r = k % (2 * (n - 1));
        return r <= n - 1 ? r : (n - 1) - (r - (n - 1));
    }
};