elimination-game

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Algorithms

You have a list <code>arr</code> of all integers in the range <code>[1, n]</code> sorted in a strictly increasing order. Apply the following algorithm on <code>arr</code>:

<ul>
	<li>Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.</li>
	<li>Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.</li>
	<li>Keep repeating the steps again, alternating left to right and right to left, until a single number remains.</li>
</ul>

Given the integer <code>n</code>, return the last number that remains in <code>arr</code>.

&nbsp;
Example 1:

<pre>
Input: n = 9
Output: 6
Explanation:
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
arr = [2, 4, 6, 8]
arr = [2, 6]
arr = [6]
</pre>

Example 2:

<pre>
Input: n = 1
Output: 1
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 109</code></li>
</ul>

lastRemaining

Elimination Game

Min Max Game

min-max-game

极大极小游戏

Recursion

Math

列表 <code>arr</code> 由在范围 <code>[1, n]</code> 中的所有整数组成，并按严格递增排序。请你对 <code>arr</code> 应用下述算法：

<div class="original__bRMd">
<div>
<ul>
	<li>从左到右，删除第一个数字，然后每隔一个数字删除一个，直到到达列表末尾。</li>
	<li>重复上面的步骤，但这次是从右到左。也就是，删除最右侧的数字，然后剩下的数字每隔一个删除一个。</li>
	<li>不断重复这两步，从左到右和从右到左交替进行，直到只剩下一个数字。</li>
</ul>

给你整数 <code>n</code> ，返回 <code>arr</code> 最后剩下的数字。

&nbsp;

示例 1：

<pre>
输入：n = 9
输出：6
解释：
arr = [1, 2, 3, 4, 5, 6, 7, 8, 9]
arr = [2, 4, 6, 8]
arr = [2, 6]
arr = [6]
</pre>

示例 2：

<pre>
输入：n = 1
输出：1
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= n &lt;= 109</code></li>
</ul>
</div>
</div>