390. Elimination Game

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 92 4 6 82 66Output:6

思路：约瑟夫环的变种，核心思想是通过index的变换，以此来递归

http://www.cnblogs.com/EricYang/archive/2009/09/04/1560478.html

public class Solution {    public int lastRemaining(int n) {    return lastRemaining(n, 0);    }public int lastRemaining(int n, int i) {if(n == 1)return 1;if(i == 0)return 2 * lastRemaining(n/2, 1);if(i == 1)return n + 1 - 2 * lastRemaining(n/2, 1);return 0;}}