Spiral Matrix - Video Solutions

Problem Overview: Given an m × n matrix, return all elements in spiral order. The traversal starts at the top-left corner, moves right across the first row, then down the last column, then left across the bottom row, and continues inward layer by layer until every element is visited.

Approach 1: Iterative Boundary Management (O(m×n) time, O(1) space)

This approach simulates the spiral traversal by maintaining four boundaries: top, bottom, left, and right. You iterate across the top row, then move down the right column, then traverse the bottom row in reverse, and finally move up the left column. After completing each direction, adjust the corresponding boundary inward. The key insight is that every spiral layer shrinks the valid traversal region. Each matrix element is visited exactly once, giving O(m×n) time with constant extra space. This method fits naturally with problems involving array traversal and matrix boundary processing.

Approach 2: Recursive Divide and Conquer (O(m×n) time, O(m+n) recursion space)

The matrix can also be processed layer by layer using recursion. Each recursive call handles one outer ring of the matrix: traverse the top row, right column, bottom row (reverse), and left column (reverse). After processing the outer layer, the recursion continues with the inner submatrix defined by updated boundaries. The recursive structure mirrors the spiral pattern directly, which can make the logic easier to reason about. The tradeoff is additional recursion stack usage proportional to the number of layers, typically O(min(m,n)). This approach is a natural fit when practicing simulation or divide-and-conquer thinking.

Recommended for interviews: Iterative boundary management is the expected solution. Interviewers want to see careful boundary updates and correct handling of edge cases when rows or columns collapse. The recursive version demonstrates conceptual clarity but rarely improves performance. Showing the iterative solution proves you can control indices precisely and implement efficient matrix traversal.