Sort Every Concentric Matrix Border Clockwise

Problem

For each concentric border of a rectangular integer matrix, sort that border's values in ascending order and write them back clockwise starting at the border's top-left cell. Process every valid border through the center and return the transformed matrix.

Function Contract

Implement sort_matrix_borders(matrix) -> list[list[int]]. Do not mutate the input.

Constraints

• 1 <= rows, columns <= 200 and all rows have equal length.
• Border k has top row k, bottom row rows-1-k, left column k, and right column columns-1-k.
• Clockwise order is top left-to-right, right top-to-bottom, bottom right-to-left, then left bottom-to-top, without visiting a cell twice.
• A one-row or one-column center is one border vector.

Examples

• [[4,3],[2,1]] returns [[1,2],[4,3]] because clockwise cells are top-left, top-right, bottom-right, bottom-left.
• A one-row matrix is returned as that row sorted ascending.

Edge Cases

• Odd dimensions can leave one center cell.
• A rectangular center may be a one-row or one-column vector.
• Duplicates and negative values retain their multiplicities.