# leetcode390.Elimination Game

## 题目要求

``````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``````

## 思路一：递归

``````1 2 3 4 5 6 7
2   4   6
4``````

``````    public int lastRemaining(int n) {
return lastRemaining(n, true);
}

public int lastRemaining(int n, boolean left) {
if(n == 1) {
return 1;
}
if(n % 2 == 1) {
return lastRemaining(n / 2, !left) * 2;
}else{
if( left ) {
return lastRemaining(n/2, !left) * 2;
}else {
return lastRemaining(n/2, !left) * 2 -1;
}
}
}
``````

## 思路二

``````从左往右开始删除
1 2 3 4 5 6
2   4   6
4

1 2 3 4 5 6
1   3   5
3 ``````

``````    public int lastRemaining2(int n) {
return n == 1 ? 1 : (1 + n / 2 - lastRemaining2(n/2)) * 2;
}``````