Sort Every Concentric Matrix Border Clockwise

Question

The question asks the candidate to implement a function that sorts the borders of concentric matrices in a clockwise direction.

Codemia · Accepted Answer

To solve the problem, we need to extract the borders of the concentric matrices, sort them, and then place them back in their respective positions. We can achieve this by iterating through the matrix layers, starting from the outermost layer and moving inward. For each layer, we will collect the border elements, sort them, and then reinsert them into the matrix.

1. Initialize an empty list to hold the sorted borders. 
2. Loop through each layer of the matrix. 
   - For each layer, extract the top row, right column, bottom row, and left column. 
3. Combine these border elements into a single list, sort it, and then place them back in the matrix. 
4. Repeat this for all layers until the entire matrix is processed.

The time complexity of this solution is O(n * m log(m)), where n is the number of rows and m is the number of columns in the matrix. This is due to the sorting step for each layer. The space complexity is O(min(n, m)) for storing the border elements temporarily.

```python
def sort_concentric_matrix(matrix):
    if not matrix or not matrix[0]:
        return matrix
    rows, cols = len(matrix), len(matrix[0])
    layers = min(rows, cols) // 2
    for layer in range(layers):
        border = []
        # Top row
        for col in range(layer, cols - layer):
            border.append(matrix[layer][col])
        # Right column
        for row in range(layer + 1, rows - layer - 1):
            border.append(matrix[row][cols - layer - 1])
        # Bottom row
        for col in range(cols - layer - 1, layer - 1, -1):
            border.append(matrix[rows - layer - 1][col])
        # Left column
        for row in range(rows - layer - 2, layer, -1):
            border.append(matrix[row][layer])
        border.sort()
        index = 0
        # Place sorted border back
        for col in range(layer, cols - layer):
            matrix[layer][col] = border[index]
            index += 1
        for row in range(layer + 1, rows - layer - 1):
            matrix[row][cols - layer - 1] = border[index]
            index += 1
        for col in range(cols - layer - 1, layer - 1, -1):
            matrix[rows - layer - 1][col] = border[index]
            index += 1
        for row in range(rows - layer - 2, layer, -1):
            matrix[row][layer] = border[index]
            index += 1
    return matrix
```

It's important to handle edge cases such as empty matrices or matrices with only one row or column. In such cases, the function should return the matrix as is, since there are no borders to sort.

Sort Every Concentric Matrix Border Clockwise

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