Spiral Matrix
Given an $m \times n$ matrix, return all elements of the matrix in spiral order.
Why Interviewers Ask This
Uber engineers frequently ask the Spiral Matrix problem to assess a candidate's ability to manage complex boundary conditions and state transitions without external libraries. It specifically evaluates spatial reasoning, precision in loop logic, and the capacity to maintain code clarity while handling edge cases like single-row or single-column matrices.
How to Answer This Question
1. Clarify the input: Confirm if the matrix can be empty or contain non-square dimensions, as Uber values robustness against invalid inputs.
2. Visualize the path: Mentally trace the spiral (right, down, left, up) on a small example to identify when boundaries shift.
3. Define state variables: Establish four pointers for top, bottom, left, and right boundaries that contract inward after each direction traversal.
4. Implement the loop: Use a while loop continuing until all elements are collected, checking the current row/column against the shrinking boundaries before moving.
5. Handle termination: Ensure the logic breaks immediately once the count of added elements equals the total matrix size to prevent re-adding elements.
6. Optimize complexity: Verify your solution runs in O(m*n) time with O(1) extra space, excluding the output array, demonstrating efficiency awareness.
Key Points to Cover
- Explicitly handling edge cases like empty matrices or single-row/column inputs
- Using four boundary pointers instead of modifying the input array
- Ensuring the loop terminates precisely when all elements are visited
- Maintaining O(m*n) time complexity and O(1) auxiliary space
- Demonstrating clear visualization of the shrinking spiral path
Sample Answer
To solve the Spiral Matrix problem efficiently, I first validate the input to ensure it's not null or empty, which aligns with Uber's focus on production-ready code. I propose using a boundary-tracking approach rather than modifying the matrix directly to preserve data integrity. I initialize four pointers: top, bottom, left, and right. The algorithm proceeds by iterating through the matrix in four directions sequentially: traversing from left to right along the top row, then top to bottom along the right column, followed by right to left on the bottom row, and finally bottom to top on the left column. After each directional pass, I adjust the corresponding pointer inward to shrink the active area. Crucially, I add a check after every movement to ensure the new boundaries haven't crossed; this prevents infinite loops or duplicate additions in scenarios like single-row matrices. For example, in a 3x3 matrix, the outer layer is processed first, then the inner 1x1 element remains. This approach guarantees O(m*n) time complexity since we visit every cell exactly once, and O(1) auxiliary space beyond the result list. This method demonstrates clear logic flow and handles edge cases gracefully, which is essential for high-scale systems at Uber.
Common Mistakes to Avoid
- Failing to update boundary pointers correctly, causing infinite loops or skipped elements
- Not checking for crossing boundaries inside the loop, leading to index out-of-bounds errors
- Modifying the original matrix by marking visited cells, which violates the O(1) space constraint
- Ignoring the scenario where the remaining sub-matrix is a single row or column
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