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package leetcode;

/**

* Project Name : Leetcode

* Package Name : leetcode

* File Name : EliminationGame

* Creator : Edward

* Date : Oct, 2017

* Description : 390. Elimination Game

*/

public class EliminationGame {

/**

* Example:

Input:

n = 8,

1 2 3 4 5 6 7 8

2 4 6 8 res = 2

2 6 res = 2

6 res = 6

1 2 3 4 5 6 7

2 4 6

4

Output:

6

time : O(logn)

space : O(1)

* @param n

* @return

*/

public int lastRemaining(int n) {

boolean left = true;

int remaining = n;

int step = 1;

int res = 1; // head

while (remaining > 1) {

if (left || remaining % 2 == 1) {

res = res + step;

}

remaining = remaining / 2;

step = step * 2;

left = !left;

}

return res;

}

}