Spiral Matrix III

The problem is asking us to start at a given cell (rStart, cStart) and walk in a clockwise spiral shape to visit every position in a rows x cols grid, even if the walk takes us outside the grid.

The idea to solve this problem is to move in four directions (right, down, left, up) and gradually increase the steps while maintaining the current direction.

Here’s a step-by-step approach to solving the problem:

1. Initialize Variables: Start with an empty result list and current position (r, c) at (rStart, cStart). Also, initialize variables to track the current direction and number of steps.

2. Loop Until All Cells are Visited: Repeat the process until we have visited all rows * cols cells.

3. Four Directions: In each iteration, move in one of the four directions: right, down, left, up. Move a certain number of steps in the current direction. If the current cell is inside the grid, add it to the result.

4. Increase Steps and Change Direction: After moving in two directions (right and down, or left and up), increase the number of steps to take in the next directions. Change the direction in a clockwise manner.

5. Return Result: Return the coordinates representing the positions of the grid in the order you visited them.

Here’s the code:

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class Solution:
    def spiralMatrixIII(self, rows: int, cols: int, rStart: int, cStart: int) -> List[List[int]]:
        # Initialization
        result = []
        r, c = rStart, cStart
        steps = 0 # Number of steps to take in current direction
        total_cells = rows * cols
        direction = 0 # 0: right, 1: down, 2: left, 3: up

        # Loop until all cells are visited
        while len(result) < total_cells:
            # If we have moved right and down or left and up, increase the steps
            if direction == 0 or direction == 2:
                steps += 1

            # Move the required number of steps in the current direction
            for _ in range(steps):
                if 0 <= r < rows and 0 <= c < cols:
                    result.append([r, c])
                # Update the current position based on the current direction
                if direction == 0: c += 1
                elif direction == 1: r += 1
                elif direction == 2: c -= 1
                elif direction == 3: r -= 1

            # Change direction in a clockwise manner
            direction = (direction + 1) % 4

        return result

Key Takeaways

• This problem requires careful handling of the direction and the number of steps to take.
• Using a variable to represent the direction and updating it in a clockwise manner helps to maintain the required spiral shape.
• The time complexity of this solution is (O(\max(rows, cols)^2)), and the space complexity is (O(rows \times cols)).