first-day-where-you-have-been-in-all-the-rooms

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Algorithms

There are <code>n</code> rooms you need to visit, labeled from <code>0</code> to <code>n - 1</code>. Each day is labeled, starting from <code>0</code>. You will go in and visit one room a day.

Initially on day <code>0</code>, you visit room <code>0</code>. The order you visit the rooms for the coming days is determined by the following rules and a given 0-indexed array <code>nextVisit</code> of length <code>n</code>:

<ul>
	<li>Assuming that on a day, you visit room <code>i</code>,</li>
	<li>if you have been in room <code>i</code> an odd number of times (including the current visit), on the next day you will visit a room with a lower or equal room number specified by <code>nextVisit[i]</code> where <code>0 &lt;= nextVisit[i] &lt;= i</code>;</li>
	<li>if you have been in room <code>i</code> an even number of times (including the current visit), on the next day you will visit room <code>(i + 1) mod n</code>.</li>
</ul>

Return the label of the first day where you have been in all the rooms. It can be shown that such a day exists. Since the answer may be very large, return it modulo <code>109 + 7</code>.

&nbsp;
Example 1:

<pre>
Input: nextVisit = [0,0]
Output: 2
Explanation:
- On day 0, you visit room 0. The total times you have been in room 0 is 1, which is odd.
&nbsp; On the next day you will visit room nextVisit[0] = 0
- On day 1, you visit room 0, The total times you have been in room 0 is 2, which is even.
&nbsp; On the next day you will visit room (0 + 1) mod 2 = 1
- On day 2, you visit room 1. This is the first day where you have been in all the rooms.
</pre>

Example 2:

<pre>
Input: nextVisit = [0,0,2]
Output: 6
Explanation:
Your room visiting order for each day is: [0,0,1,0,0,1,2,...].
Day 6 is the first day where you have been in all the rooms.
</pre>

Example 3:

<pre>
Input: nextVisit = [0,1,2,0]
Output: 6
Explanation:
Your room visiting order for each day is: [0,0,1,1,2,2,3,...].
Day 6 is the first day where you have been in all the rooms.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == nextVisit.length</code></li>
	<li><code>2 &lt;= n &lt;= 105</code></li>
	<li><code>0 &lt;= nextVisit[i] &lt;= i</code></li>
</ul>

firstDayBeenInAllRooms

First Day Where You Have Been in All the Rooms

Array

Dynamic Programming

你需要访问&nbsp;<code>n</code> 个房间，房间从 <code>0</code> 到 <code>n - 1</code> 编号。同时，每一天都有一个日期编号，从 <code>0</code> 开始，依天数递增。你每天都会访问一个房间。

最开始的第 <code>0</code> 天，你访问&nbsp;<code>0</code> 号房间。给你一个长度为 <code>n</code> 且 下标从 0 开始 的数组 <code>nextVisit</code> 。在接下来的几天中，你访问房间的 次序 将根据下面的 规则 决定：

<ul>
	<li>假设某一天，你访问&nbsp;<code>i</code> 号房间。</li>
	<li>如果算上本次访问，访问&nbsp;<code>i</code> 号房间的次数为 奇数 ，那么 第二天 需要访问&nbsp;<code>nextVisit[i]</code> 所指定的房间，其中 <code>0 &lt;= nextVisit[i] &lt;= i</code> 。</li>
	<li>如果算上本次访问，访问&nbsp;<code>i</code> 号房间的次数为 偶数 ，那么 第二天 需要访问&nbsp;<code>(i + 1) mod n</code> 号房间。</li>
</ul>

请返回你访问完所有房间的第一天的日期编号。题目数据保证总是存在这样的一天。由于答案可能很大，返回对 <code>109 + 7</code> 取余后的结果。

&nbsp;

示例 1：

<pre>
输入：nextVisit = [0,0]
输出：2
解释：
- 第 0 天，你访问房间 0 。访问 0 号房间的总次数为 1 ，次数为奇数。
&nbsp; 下一天你需要访问房间的编号是 nextVisit[0] = 0
- 第 1 天，你访问房间 0 。访问 0 号房间的总次数为 2 ，次数为偶数。
&nbsp; 下一天你需要访问房间的编号是 (0 + 1) mod 2 = 1
- 第 2 天，你访问房间 1 。这是你第一次完成访问所有房间的那天。
</pre>

示例 2：

<pre>
输入：nextVisit = [0,0,2]
输出：6
解释：
你每天访问房间的次序是 [0,0,1,0,0,1,2,...] 。
第 6 天是你访问完所有房间的第一天。
</pre>

示例 3：

<pre>
输入：nextVisit = [0,1,2,0]
输出：6
解释：
你每天访问房间的次序是 [0,0,1,1,2,2,3,...] 。
第 6 天是你访问完所有房间的第一天。
</pre>

&nbsp;

提示：

<ul>
	<li><code>n == nextVisit.length</code></li>
	<li><code>2 &lt;= n &lt;= 105</code></li>
	<li><code>0 &lt;= nextVisit[i] &lt;= i</code></li>
</ul>