390. Elimination Game（約瑟夫環）

There is a list of sorted integers from 1 to n. Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.

Repeat the previous step again, but this time from right to left, remove the right most number and every other number from the remaining numbers.

We keep repeating the steps again, alternating left to right and right to left, until a single number remains.

Find the last number that remains starting with a list of length n.

Example:

Input:
n = 9,
1 2 3 4 5 6 7 8 9
2 4 6 8
2 6
6

Output:
6

重點在於比較每次開始的頭的下標在刪除前和刪除後的變化，update這個head的變化即可，通過n-1的head推n的head（通過n的head推n-1的head）。每次刪除的時候，看head怎麼變，head就是一定會留下的第一個人的編號，最後返回head編號即可。

class Solution {
    public int lastRemaining(int n) {
        int res = 1;
        int step = 1;
        boolean left = true;
        while (n > 1) {
            if (n % 2 == 1 || left) {
                res = res + step;
            }
            step *= 2;
            n /= 2;
            left = !left;
        }
        return res;
    }
}