projection-area-of-3d-shapes

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Algorithms

You are given an <code>n x n</code> <code>grid</code> where we place some <code>1 x 1 x 1</code> cubes that are axis-aligned with the <code>x</code>, <code>y</code>, and <code>z</code> axes.

Each value <code>v = grid[i][j]</code> represents a tower of <code>v</code> cubes placed on top of the cell <code>(i, j)</code>.

We view the projection of these cubes onto the <code>xy</code>, <code>yz</code>, and <code>zx</code> planes.

A projection is like a shadow, that maps our 3-dimensional figure to a 2-dimensional plane. We are viewing the &quot;shadow&quot; when looking at the cubes from the top, the front, and the side.

Return the total area of all three projections.

&nbsp;
Example 1:
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/02/shadow.png" style="width: 800px; height: 214px;" />
<pre>
Input: grid = [[1,2],[3,4]]
Output: 17
Explanation: Here are the three projections (&quot;shadows&quot;) of the shape made with each axis-aligned plane.
</pre>

Example 2:

<pre>
Input: grid = [[2]]
Output: 5
</pre>

Example 3:

<pre>
Input: grid = [[1,0],[0,2]]
Output: 8
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 50</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 50</code></li>
</ul>