maximum-students-taking-exam

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Algorithms

Given a <code>m&nbsp;* n</code>&nbsp;matrix <code>seats</code>&nbsp;&nbsp;that represent seats distributions&nbsp;in a classroom.&nbsp;If a seat&nbsp;is&nbsp;broken, it is denoted by <code>&#39;#&#39;</code> character otherwise it is denoted by a <code>&#39;.&#39;</code> character.

Students can see the answers of those sitting next to the left, right, upper left and upper right, but he cannot see the answers of the student sitting&nbsp;directly in front or behind him. Return the maximum number of students that can take the exam together&nbsp;without any cheating being possible.

Students must be placed in seats in good condition.

&nbsp;
Example 1:
<img height="200" src="https://assets.leetcode.com/uploads/2020/01/29/image.png" width="339" />
<pre>
Input: seats = [[&quot;#&quot;,&quot;.&quot;,&quot;#&quot;,&quot;#&quot;,&quot;.&quot;,&quot;#&quot;],
&nbsp; [&quot;.&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;#&quot;,&quot;.&quot;],
&nbsp; [&quot;#&quot;,&quot;.&quot;,&quot;#&quot;,&quot;#&quot;,&quot;.&quot;,&quot;#&quot;]]
Output: 4
Explanation: Teacher can place 4 students in available seats so they don&#39;t cheat on the exam. 
</pre>

Example 2:

<pre>
Input: seats = [[&quot;.&quot;,&quot;#&quot;],
&nbsp; [&quot;#&quot;,&quot;#&quot;],
&nbsp; [&quot;#&quot;,&quot;.&quot;],
&nbsp; [&quot;#&quot;,&quot;#&quot;],
&nbsp; [&quot;.&quot;,&quot;#&quot;]]
Output: 3
Explanation: Place all students in available seats. 

</pre>

Example 3:

<pre>
Input: seats = [[&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;#&quot;],
&nbsp; [&quot;.&quot;,&quot;#&quot;,&quot;.&quot;,&quot;#&quot;,&quot;.&quot;],
&nbsp; [&quot;.&quot;,&quot;.&quot;,&quot;#&quot;,&quot;.&quot;,&quot;.&quot;],
&nbsp; [&quot;.&quot;,&quot;#&quot;,&quot;.&quot;,&quot;#&quot;,&quot;.&quot;],
&nbsp; [&quot;#&quot;,&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;#&quot;]]
Output: 10
Explanation: Place students in available seats in column 1, 3 and 5.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>seats</code>&nbsp;contains only characters&nbsp;<code>&#39;.&#39;&nbsp;and</code><code>&#39;#&#39;.</code></li>
	<li><code>m ==&nbsp;seats.length</code></li>
	<li><code>n ==&nbsp;seats[i].length</code></li>
	<li><code>1 &lt;= m &lt;= 8</code></li>
	<li><code>1 &lt;= n &lt;= 8</code></li>
</ul>