# 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].

**The Idea:** Evolve a 3x3 filter along every element in the matrix. Sum the elements as you go, and count the number of active cells to avoid boundary issues.

**Complexity:** O(n\*m) time and O(1) space

```python
class Solution:
    def imageSmoother(self, M):
        """
        :type M: List[List[int]]
        :rtype: List[List[int]]
        """

        if not M:
            return M

        def is_valid(r, c):
            return r >= 0 and c >= 0 and c < len(M[0]) and r < len(M)

        n_rows = len(M)
        n_cols = len(M[0])

        M_new = [[0] * n_cols for _ in range(n_rows)]
        rotations = [(1, 1), (-1, 1), (1, -1), (0, 1), (0, -1), (1, 0), (-1, 0), (-1, -1)]

        for i in range(n_rows):
            for j in range(0, n_cols):
                n_active = 1
                summ = M[i][j]
                for x, y in rotations:
                    if is_valid(i + x, j + y):
                        n_active += 1
                        summ += M[i + x][j + y]
                M_new[i][j] = summ // n_active
        return M_new
```


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