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Algorithms

There is an exam room with <code>n</code> seats in a single row labeled from <code>0</code> to <code>n - 1</code>.

When a student enters the room, they must sit in the seat that maximizes the distance to the closest person. If there are multiple such seats, they sit in the seat with the lowest number. If no one is in the room, then the student sits at seat number <code>0</code>.

Design a class that simulates the mentioned exam room.

Implement the <code>ExamRoom</code> class:

<ul>
	<li><code>ExamRoom(int n)</code> Initializes the object of the exam room with the number of the seats <code>n</code>.</li>
	<li><code>int seat()</code> Returns the label of the seat at which the next student will set.</li>
	<li><code>void leave(int p)</code> Indicates that the student sitting at seat <code>p</code> will leave the room. It is guaranteed that there will be a student sitting at seat <code>p</code>.</li>
</ul>

&nbsp;
Example 1:

<pre>
Input
[&quot;ExamRoom&quot;, &quot;seat&quot;, &quot;seat&quot;, &quot;seat&quot;, &quot;seat&quot;, &quot;leave&quot;, &quot;seat&quot;]
[[10], [], [], [], [], [4], []]
Output
[null, 0, 9, 4, 2, null, 5]

Explanation
ExamRoom examRoom = new ExamRoom(10);
examRoom.seat(); // return 0, no one is in the room, then the student sits at seat number 0.
examRoom.seat(); // return 9, the student sits at the last seat number 9.
examRoom.seat(); // return 4, the student sits at the last seat number 4.
examRoom.seat(); // return 2, the student sits at the last seat number 2.
examRoom.leave(4);
examRoom.seat(); // return 5, the student sits at the last seat number 5.

</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 109</code></li>
	<li>It is guaranteed that there is a student sitting at seat <code>p</code>.</li>
	<li>At most <code>104</code> calls will be made to <code>seat</code> and <code>leave</code>.</li>
</ul>

Exam Room

Maximize Distance to Closest Person

maximize-distance-to-closest-person

到最近的人的最大距离

Design

Ordered Set

Heap (Priority Queue)

在考场里，有&nbsp;<code>n</code>&nbsp;个座位排成一行，编号为 <code>0</code> 到 <code>n - 1</code>。

当学生进入考场后，他必须坐在离最近的人最远的座位上。如果有多个这样的座位，他会坐在编号最小的座位上。(另外，如果考场里没有人，那么学生就坐在 <code>0</code> 号座位上。)

设计一个模拟所述考场的类。

实现&nbsp;<code>ExamRoom</code>&nbsp;类：

<ul>
	<li><code>ExamRoom(int n)</code> 用座位的数量&nbsp;<code>n</code> 初始化考场对象。</li>
	<li><code>int seat()</code> 返回下一个学生将会入座的座位编号。</li>
	<li><code>void leave(int p)</code> 指定坐在座位 <code>p</code> 的学生将离开教室。保证座位 <code>p</code> 上会有一位学生。</li>
</ul>

&nbsp;

示例 1：

<pre>
输入：
["ExamRoom", "seat", "seat", "seat", "seat", "leave", "seat"]
[[10], [], [], [], [], [4], []]
输出：
[null, 0, 9, 4, 2, null, 5]
解释：
ExamRoom examRoom = new ExamRoom(10);
examRoom.seat(); // 返回 0，房间里没有人，学生坐在 0 号座位。
examRoom.seat(); // 返回 9，学生最后坐在 9 号座位。
examRoom.seat(); // 返回 4，学生最后坐在 4 号座位。
examRoom.seat(); // 返回 2，学生最后坐在 2 号座位。
examRoom.leave(4);
examRoom.seat(); // 返回 5，学生最后坐在 5 号座位。
</pre>

&nbsp;

提示：

<ol>
	<li><code>1 &lt;= n &lt;= 109</code></li>
	<li>保证有学生正坐在座位 <code>p</code> 上。</li>
	<li><code>seat</code>&nbsp;和&nbsp;<code>leave</code>&nbsp;最多被调用&nbsp;<code>104</code>&nbsp;次。</li>
</ol>