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>

projectionArea

Projection Area of 3D Shapes

Geometry

Array

Math

Matrix

在<meta charset="UTF-8" />&nbsp;<code>n x n</code>&nbsp;的网格<meta charset="UTF-8" />&nbsp;<code>grid</code>&nbsp;中，我们放置了一些与 x，y，z 三轴对齐的<meta charset="UTF-8" />&nbsp;<code>1 x 1 x 1</code>&nbsp;立方体。

每个值&nbsp;<code>v = grid[i][j]</code>&nbsp;表示 <code>v</code>&nbsp;个正方体叠放在单元格&nbsp;<code>(i, j)</code>&nbsp;上。

现在，我们查看这些立方体在 <code>xy</code>&nbsp;、<code>yz</code>&nbsp;和 <code>zx</code>&nbsp;平面上的投影。

投影&nbsp;就像影子，将 三维 形体映射到一个 二维 平面上。从顶部、前面和侧面看立方体时，我们会看到“影子”。

返回 所有三个投影的总面积 。

&nbsp;

<ul>
</ul>

<ul>
</ul>

<ul>
</ul>

<ul>
</ul>

示例 1：

<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/02/shadow.png" style="height: 214px; width: 800px;" />

<pre>
输入：[[1,2],[3,4]]
输出：17
解释：这里有该形体在三个轴对齐平面上的三个投影(“阴影部分”)。
</pre>

示例&nbsp;2:

<pre>
输入：grid = [[2]]
输出：5
</pre>

示例 3：

<pre>
输入：[[1,0],[0,2]]
输出：8
</pre>

&nbsp;

提示：

<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>