Sort Matrix Diagonals By Their Values

Question

The question asks the candidate to sort the diagonals of a matrix based on their values, returning a new matrix with the sorted diagonals.

Codemia · Accepted Answer

To solve the problem of sorting matrix diagonals, we first need to identify the elements that belong to each diagonal. A diagonal in a matrix can be identified by the difference between its row and column indices. We will store the elements of each diagonal in a dictionary where the key is the diagonal index (row - column). After collecting the elements, we will sort each diagonal and then reconstruct the matrix with the sorted values.

1. Initialize a dictionary to hold the diagonals.
2. Loop through each element in the matrix and populate the dictionary with the corresponding diagonal index.
3. Sort each list of diagonal elements in the dictionary.
4. Create a new matrix and fill it with the sorted diagonal values based on their original positions.

Here is a Python implementation:
```python
def sort_diagonals(matrix):
    from collections import defaultdict
    diagonals = defaultdict(list)
    rows, cols = len(matrix), len(matrix[0]) if matrix else 0

for r in range(rows):
        for c in range(cols):
            diagonals[r - c].append(matrix[r][c])

for key in diagonals:
        diagonals[key].sort()

sorted_matrix = [[0] * cols for _ in range(rows)]
    for r in range(rows):
        for c in range(cols):
            sorted_matrix[r][c] = diagonals[r - c].pop(0)

return sorted_matrix
```

The time complexity of this solution is O(N log N) where N is the total number of elements in the matrix. This is due to the sorting step for each diagonal. The space complexity is O(D) where D is the number of diagonals, which can be at most min(rows, cols). This ensures that we are efficiently using space to store the diagonal elements.

It is important to consider edge cases such as:
- An empty matrix, which should return an empty matrix.
- Non-square matrices, where the number of rows and columns differ. The algorithm handles this by using the diagonal index as a key, ensuring all diagonals are processed correctly regardless of the matrix shape.

Interviewers look for clarity in the candidate's thought process and their ability to break down the problem into manageable parts. They also assess the candidate's coding skills, particularly their ability to write clean, efficient code. Additionally, interviewers are interested in how candidates handle edge cases and their understanding of algorithm complexity.

Sort Matrix Diagonals By Their Values

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