# 1329. Sort the Matrix Diagonally

#### Medium

***

A **matrix diagonal** is a diagonal line of cells starting from some cell in either the topmost row or leftmost column and going in the bottom-right direction until reaching the matrix's end. For example, the **matrix diagonal** starting from `mat[2][0]`, where `mat` is a `6 x 3` matrix, includes cells `mat[2][0]`, `mat[3][1]`, and `mat[4][2]`.

Given an `m x n` matrix `mat` of integers, sort each **matrix diagonal** in ascending order and return *the resulting matrix*.

 

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/01/21/1482_example_1_2.png)

<pre><code>Input: mat = [[3,3,1,1],[2,2,1,2],[1,1,1,2]]
<strong>Output:
</strong> [[1,1,1,1],[1,2,2,2],[1,2,3,3]]
</code></pre>

**Example 2:**

<pre><code>Input: mat = [[11,25,66,1,69,7],[23,55,17,45,15,52],[75,31,36,44,58,8],[22,27,33,25,68,4],[84,28,14,11,5,50]]
<strong>Output:
</strong> [[5,17,4,1,52,7],[11,11,25,45,8,69],[14,23,25,44,58,15],[22,27,31,36,50,66],[84,28,75,33,55,68]]
</code></pre>

&#x20;

**Constraints:**

* `m == mat.length`
* `n == mat[i].length`
* `1 <= m, n <= 100`
* `1 <= mat[i][j] <= 100`

```python
class Solution:
    def diagonalSort(self, mat: List[List[int]]) -> List[List[int]]:
        #.
        row, col = len(mat), len(mat[0])
        
        # This diagonal parse logic is important
        for i in range(1, row + col - 2):
            if i < row:
                start_row, start_col = row - i - 1, 0
            else:
                start_row, start_col = 0, i - row + 1
            
            # Add all diagonal elements to arr
            diag = []
            while start_row < row and start_col < col:
                diag.append(mat[start_row][start_col])
                start_row += 1
                start_col += 1
            # Sort array
            diag.sort()
            start_row -= 1
            start_col -= 1
            while start_row >= 0 and start_col >= 0:
                # Add back all sort diagonal elements back
                mat[start_row][start_col] = diag.pop()
                start_row -= 1
                start_col -= 1

        return(mat)
```