Spiral Matrix

Return all elements of the matrix in spiral order.

10 min read

Time: O(n)

Space: O(1)

Solve on LeetCode

Problem Understanding

Given an m x n matrix, return all elements of the matrix in spiral order (Right -> Down -> Left -> Up).

Interactive Visualization

Step 1 / 1

Visualization data missing

Initializing...

Custom Input

Watch the path as we peel the matrix layer by layer.

Strategy

We can simulate the spiral movement by defining boundaries (top, bottom, left, right):

Move Right: Traverse from left to right. Increment top.
Move Down: Traverse from top to bottom. Decrement right.
Move Left: Traverse from right to left. Decrement bottom. (Check top <= bottom first)
Move Up: Traverse from bottom to top. Increment left. (Check left <= right first)

Initialize top=0, bottom=rows-1, left=0, right=cols-1.
Loop while top <= bottom and left <= right.

Dry Run

Matrix: [[1,2,3],[4,5,6],[7,8,9]]

Step	Action	Output After Step	Boundaries Update
1	Right	`[1, 2, 3]`	`top` becomes 1
2	Down	`[..., 6, 9]`	`right` becomes 1
3	Left	`[..., 8, 7]`	`bottom` becomes 1
4	Up	`[..., 4]`	`left` becomes 1
5	Right	`[..., 5]`	`top` becomes 2. Loop Ends.

Edge Cases & Common Mistakes

Watch out for:

Single Row/Column: Ensure the inner loops (left check, top check) prevent double-counting.
Empty Matrix: Handle gracefully.
Non-Square Matrix: Logic must hold for m != n.

Complexity Analysis

Time Complexity: O(M * N). Visit every element once.
Space Complexity: O(1). Output array doesn't count towards space.

Solution

Simulation with boundaries.

1class Solution:
2    def spiralOrder(self, matrix: List[List[int]]) -> List[int]:
3        result = []
4        if not matrix: return result
5        
6        top, bottom = 0, len(matrix) - 1
7        left, right = 0, len(matrix[0]) - 1
8        
9        while top <= bottom and left <= right:
10            # Move Right
11            for i in range(left, right + 1):
12                result.append(matrix[top][i])
13            top += 1
14            
15            # Move Down
16            for i in range(top, bottom + 1):
17                result.append(matrix[i][right])
18            right -= 1
19            
20            if top <= bottom:
21                # Move Left
22                for i in range(right, left - 1, -1):
23                    result.append(matrix[bottom][i])
24                bottom -= 1
25            
26            if left <= right:
27                # Move Up
28                for i in range(bottom, top - 1, -1):
29                    result.append(matrix[i][left])
30                left += 1
31                
32        return result

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