## 661. Image Smoother

Given a 2D integer matrix M representing the gray scale of an image, you need to design a smoother to make the gray scale of each cell becomes the average gray scale (rounding down) of all the 8 surrounding cells and itself. If a cell has less than 8 surrounding cells, then use as many as you can.

Example 1:

```Input:
[[1,1,1],
[1,0,1],
[1,1,1]]
Output:
[[0, 0, 0],
[0, 0, 0],
[0, 0, 0]]
Explanation:
For the point (0,0), (0,2), (2,0), (2,2): floor(3/4) = floor(0.75) = 0
For the point (0,1), (1,0), (1,2), (2,1): floor(5/6) = floor(0.83333333) = 0
For the point (1,1): floor(8/9) = floor(0.88888889) = 0
```

Note:

1. The value in the given matrix is in the range of [0, 255].
2. The length and width of the given matrix are in the range of [1, 150].

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#### Approach #1: Iterate Through Grid

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Intuition and Algorithm

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For each cell in the grid, look at the immediate neighbors - up to 9 of them, including the original cell.

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Then, we will add the sum of the neighbors into `ans[r][c]` while recording `count`, the number of such neighbors. The final answer is the sum divided by the count.

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Complexity Analysis

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Time Complexity: , where is the number of pixels in our image. We iterate over every pixel.

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Space Complexity: , the size of our answer.

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Analysis written by: @awice.

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