Spiral Matrix

Problem

Given an m x n matrix, return all elements of the matrix in spiral order.

Examples

The brute-force approach

Track direction manually and visited cells. Rotate clockwise when you hit a boundary or visited cell.

directions = [(0,1),(1,0),(0,-1),(-1,0)]   # right, down, left, up
visited = [[False]*n for _ in range(m)]
r, c, d = 0, 0, 0
result = []
for _ in range(m*n):
    result.append(matrix[r][c])
    visited[r][c] = True
    nr, nc = r + directions[d][0], c + directions[d][1]
    if not (0<=nr<m and 0<=nc<n and not visited[nr][nc]):
        d = (d + 1) % 4
        nr, nc = r + directions[d][0], c + directions[d][1]
    r, c = nr, nc

O(m×n) but uses O(m×n) space for visited array. The boundary-shrinking approach below uses O(1) extra space.

Spotting the pattern

This is a Matrix Traversal problem. The key question to ask yourself:

After traversing the top row left-to-right, why do you increment top before traversing the right column? What would happen if you didn't?

Answering that is where it clicks, and it's exactly what the guided walkthrough below builds with you: the pattern reasoning, a progressive hint ladder that never spoils the answer, a row-by-row dry run, the optimized solution, and an in-browser editor to run your code against real test cases.