885. Spiral Matrix III

How to solve Spiral Matrix III (LeetCode 885): the approach in brief

The problem

You start at the cell (rStart, cStart) of an rows x cols grid facing east. The northwest corner is at the first row and column in the grid, and the southeast corner is at the last row and column.

Pattern

Spiral Matrix III is a Array/Matrix Manipulation Patterns problem, in the Spiral Traversal subpattern. The pattern covers in-place operations, hashing, prefix sums, spiral traversal, and cyclic sort

Master spiral traversal pattern for 2D matrices. Learn to traverse matrices in spiral order for interview problems.

Approach outline

1. Visualize the grid and consider how to represent your path as you move in a spiral pattern; think about how to keep track of visited cells efficiently.
2. Since the movement is in a clockwise spiral, identify the four possible directions (east, south, west, north) and how direction changes occur after a certain number of steps.
3. Notice that the number of steps you take in a given direction increases after every two direction changes; this pattern helps you know when to change direction and how far to move.

Complexity

The reference solution runs in O(rows * cols) time and O(rows * cols) space.

Asked at

Spiral Matrix III has been reported in interviews at Facebook.