Easy Python Solution
Intuition\n Describe your first thoughts on how to solve this problem. \nThe problem requires us to traverse a matrix in a spiral order starting from a given ce
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe problem requires us to traverse a matrix in a spiral order starting from a given cell, collecting the coordinates of all the cells in the matrix as we move. The challenge is to handle the direction changes and ensure that we cover the entire matrix efficiently.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n**Direction Management**: We maintain an array directions to represent the four possible movements: right (East), down (South), left (West), and up (North). These directions will be used cyclically as we traverse the matrix.\n\n**Step Management**: As we move in a spiral, the number of steps we take in each direction increases in a specific pattern. For example, after moving right, we move down, and then we increase the steps by 1 when changing direction after every two directions (i.e., after moving right and down, or left and up).\n\n**Boundary Checking**: As we move, we need to ensure that the current cell lies within the boundaries of the matrix. If it does, we add it to the result list.\n\n**Early Termination**: The loop terminates as soon as we\'ve collected all the cells in the matrix. This prevents unnecessary iterations.\n\n\n# Complexity\n- Time complexity: O(Rows\u2217Cols)\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\n- Space complexity: O(Rows\u2217Cols)\n# Code\n```\nclass Solution:\n    def spiralMatrixIII(self, rows: int, cols: int, rStart: int, cStart: int) -> List[List[int]]:\n        directions = [(0, 1), (1, 0), (0, -1), (-1, 0)]  # East, South, West, North\n        result = [[rStart, cStart]]\n        total_cells = rows * cols\n        steps = 0\n        direction_index = 0\n        \n        while len(result) < total_cells:\n            if direction_index % 2 == 0:\n                steps += 1\n            \n            for _ in range(steps):\n                rStart += directions[direction_index][0]\n                cStart += directions[direction_index][1]\n                \n                if 0 <= rStart < rows and 0 <= cStart < cols:\n                    result.append([rStart, cStart])\n                    if len(result) == total_cells:\n                        return result\n            \n            direction_index = (direction_index + 1) % 4\n        \n        return result\n\n```
['Python3']