Spiral Matrix III

Spiral Matrix III

What is this problem about?

The Spiral Matrix III interview question takes the spiral concept into an infinite grid. Starting at a specific coordinate (rStart, cStart), you are tasked with visiting every cell in a spiral fashion within a grid of size rows x cols. Because you start at an arbitrary point, the spiral might often go outside the boundaries of the rows x cols rectangle. The goal is to return the coordinates of the cells in the order they are visited, but only if they are within the given grid boundaries.

Why is this asked in interviews?

This Spiral Matrix III coding problem is a favorite at companies like Uber and Apple because it adds a layer of complexity to basic matrix simulation. It tests your ability to handle "out-of-bounds" scenarios gracefully and requires a more sophisticated direction-management strategy than the previous versions. It's an excellent way to evaluate if a candidate can maintain logical consistency when a problem's constraints are expanded.

Algorithmic pattern used

The Simulation interview pattern is modified here to use a step-based approach. Unlike the previous spiral problems where boundaries defined the movement, here the "step size" increases every two turns.

1. Move right 1 step, then move down 1 step.
2. Move left 2 steps, then move up 2 steps.
3. Move right 3 steps, then move down 3 steps. After each individual move, you check if the current coordinate is within the rows x cols bounds. If it is, you record it. The process continues until you have recorded all rows * cols cells.

Example explanation

Suppose we have a 5x6 grid and start at (1, 4).

1. Move right (1, 5). Within bounds? Yes.
2. Move down (2, 5). Within bounds? Yes.
3. Move left 2 steps: (2, 4), (2, 3). Both are within bounds.
4. Move up 2 steps: (1, 3), (0, 3). Both are within bounds.
5. Move right 3 steps: (0, 4), (0, 5), (0, 6). (0, 4) and (0, 5) are within bounds, but (0, 6) is not. The simulation continues, skipping the storage of out-of-bounds coordinates but still performing the movement.

Common mistakes candidates make

• Termination Condition: Forgetting that the simulation should only stop when rows * cols valid coordinates have been found, not just when a boundary is hit.
• Step Increment Logic: Mismanaging when to increase the step size, leading to an incorrect spiral shape.
• Boundaries Check: Forgetting to check if the current (r, c) is valid before adding it to the result list.
• Efficiency: Over-allocating memory or using inefficient data structures to store the results.

Interview preparation tip

For problems where you move in a pattern (right, down, left, up), use a direction array like dx = [0, 1, 0, -1] and dy = [1, 0, -1, 0]. This allows you to change directions using a simple index (d + 1) % 4, making your code much cleaner and easier to manage.