Saddle Points2026-04-30

My Solution: Exercism Saddle Points solution

Instructions

Find all saddle points in a matrix.

A saddle point is an element that is the largest value in its row and the smallest value in its column.

Rules:

• Return a list of saddle points as objects with 1-based row and column values.
• Return an empty list for an empty matrix.
• Raise ValueError("irregular matrix") if the rows are not all the same length.

Solution

def saddle_points(matrix):

    if not matrix:
        return []

    target_len = len(matrix[0])
    for row in matrix:
        if len(row) != target_len:
            raise ValueError("irregular matrix")
    
    max_rows = [max(row) for row in matrix]
    min_cols = [min(col) for col in zip(*matrix)]

    spots = []
    for r in range(len(matrix)):
        for c in range(len(matrix[r])):
            if matrix[r][c] == max_rows[r] and matrix[r][c] == min_cols[c]:
                spots.append({"row": r + 1, "column": c + 1})

    return spots

Syntax Notes

• The empty-matrix check comes first so the rest of the logic can assume at least one row exists.
• max_rows stores the largest value from each row.
• zip(*matrix) transposes the matrix so each column can be analyzed as a sequence.
• min_cols stores the smallest value from each column.
• A point qualifies only when its value matches both the row maximum and the column minimum.