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g0801_0900.s0883_projection_area_of_3d_shapes.readme.md Maven / Gradle / Ivy

883\. Projection Area of 3D Shapes

Easy

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

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

We view the projection of these cubes onto the `xy`, `yz`, and `zx` planes.

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

Return _the total area of all three projections_.

**Example 1:**

![](https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/02/shadow.png)

**Input:** grid = [[1,2],[3,4]]

**Output:** 17

**Explanation:** Here are the three projections ("shadows") of the shape made with each axis-aligned plane.

**Example 2:**

**Input:** grid = [[2]]

**Output:** 5

**Example 3:**

**Input:** grid = [[1,0],[0,2]]

**Output:** 8

**Constraints:**

*   `n == grid.length == grid[i].length`
*   `1 <= n <= 50`
*   `0 <= grid[i][j] <= 50`