Spiral Matrix III Python Solution with Tests

lcpy gen -n 885   # by problem number
lcpy gen -s spiral_matrix_iii   # by problem name

Input: rows = 5, cols = 6, rStart = 1, cStart = 4
Output: [[1,4],[1,5],[2,5],[2,4],[2,3],[1,3],[0,3],[0,4],[0,5],[3,5],[3,4],[3,3],[3,2],[2,2],[1,2],[0,2],[4,5],[4,4],[4,3],[4,2],[4,1],[3,1],[2,1],[1,1],[0,1],[4,0],[3,0],[2,0],[1,0],[0,0]]

Input: rows = 1, cols = 4, rStart = 0, cStart = 0
Output: [[0,0],[0,1],[0,2],[0,3]]

class Solution:
    # Time: O(max(rows, cols)^2)
    # Space: O(1) excluding output
    def spiral_matrix_iii(
        self, rows: int, cols: int, r_start: int, c_start: int
    ) -> list[list[int]]:
        result = [[r_start, c_start]]
        r, c, steps, direction = r_start, c_start, 1, 0
        directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]
        while len(result) < rows * cols:
            for _ in range(2):
                dr, dc = directions[direction]
                for _ in range(steps):
                    r, c = r + dr, c + dc
                    if 0 <= r < rows and 0 <= c < cols:
                        result.append([r, c])
                direction = (direction + 1) % 4
            steps += 1
        return result