Introduction

Spiral Matrix means traversing all matrix elements in:

  • spiral order

The traversal starts from:

  • top row
  • right column
  • bottom row
  • left column

and continues layer by layer.

Example:

Input Matrix:1 2 3
4 5 6
7 8 9

Output:
1 2 3 6 9 8 7 4 5

Explanation:

Matrix elementare visited in clockwise spiral order.

This problem is one of the most important applications of:

Boundary Traversal

Constraints

1 <= Rows, Columns <= 10^3

Approach 1 : Brute Force (Using Visited Matrix)

Explanations:

Explanation:

The idea is:

  • move in spiral directions
  • mark visited cells

Steps:

  1. Traverse right.
  2. Traverse down.
  3. Traverse left.
  4. Traverse up.
  5. Repeat until completed.

This approach works but:

  • uses extra space

So boundary traversal is preferred.

Dry Run

Matrix:1 2 3
4 5 6
7 8 9

Spiral Order:

1 2 3
      6
      9
8 7 4
  5

Practice :

Complexity Analysis :

Time Complexity:- O(rows × cols)Explanation :
Every matrix element is visited once.

Space Complexity:- O(rows × cols)
Explanation :
Visited matrix is used.

Approach 2 : Optimal Solution(Boundary Traversal)

Explanations:

Explanation:

This is the most optimized and interview-preferred solution.

The idea is:

  • maintain boundaries
  • shrink boundaries after traversal

Boundaries:

  • top
  • bottom
  • left
  • right

This avoids:

  • extra visited matrix

Dry Run

Matrix:1 2 3
4 5 6
7 8 9

Top row:
1 2 3

Right column:
6 9

Bottom row:
8 7

Left column:
4

Center:
5

Practice :

Complexity Analysis :

Time Complexity:- O(rows × cols)Explanation :
Every matrix element is visited once.

Space Complexity:- O(1)
Explanation :
Only boundaries are used.

Why This Problem is Important

This problem builds the foundation for:

  • Matrix traversal
  • Boundary traversal
  • Grid manipulation
  • Simulation problems
  • Spiral algorithms

Real-World Applications

Spiral traversal concepts are used in:

  • Image scanning
  • Robot navigation
  • Game development
  • Matrix simulations
  • Graphics systems

Common Beginner Mistakes

  • Incorrect boundary updates
  • Infinite loops
  • Repeating elements
  • Missing center elements
  • Wrong traversal order

Interview Tip

Interviewers often expect:

  • boundary traversal logic
  • efficient matrix handling
  • edge case handling
  • O(1) space optimization

Always explain:

  • boundary shrinking logic
  • traversal order clearly

Related Questions

  • Set Matrix Zeroes
  • Matrix Traversal
  • Rotate Matrix
  • Spiral Order II
  • Search Matrix

Final Takeaway

The Spiral Matrix problem is one of the most important matrix traversal interview problems.

It teaches:

  • boundary traversal
  • spiral traversal
  • matrix manipulation
  • efficient grid traversal

Understanding this problem builds a strong foundation for:

  • advanced matrix problems
  • simulation algorithms
  • interview-level data structure questions.