Leetcode 54: Spiral Matrix

 

1. Problem Statement (Simple Explanation):

You’re given an m x n matrix.

You must return all elements in spiral order, starting from the top-left corner and spiraling:

• Right → down → left → up → and so on, layer by layer.

2. Examples:

Example 1:

Input:

matrix = [

  [1,2,3],

  [4,5,6],

  [7,8,9]

]

Spiral order:

1 → 2 → 3 → 6 → 9 → 8 → 7 → 4 → 5

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

Example 2:

Input:

matrix = [

  [1, 2, 3, 4],

  [5, 6, 7, 8],

  [9,10,11,12]

]

Spiral order:

1 → 2 → 3 → 4 → 8 → 12 → 11 → 10 → 9 → 5 → 6 → 7

Output: [1,2,3,4,8,12,11,10,9,5,6,7]

3. Approach – Boundary Tracking (Layer by Layer):

We can simulate walking around the matrix in layers, maintaining four boundaries:

• top – index of current top row not yet traversed.

• bottom – index of current bottom row not yet traversed.

• left – index of current left column not yet traversed.

• right – index of current right column not yet traversed.

Process in this order while top <= bottom and left <= right:

1. Traverse top row from left to right. Then top++.

2. Traverse right column from top to bottom. Then right--.

3. If top <= bottom:

• Traverse bottom row from right to left. Then bottom--.

4. If left <= right:

• Traverse left column from bottom to top. Then left++.

Repeat until boundaries cross.

Pseudo-code:

Complexity:

Let m = rows, n = columns:

• Time: We visit each element once → O(m⋅n).

• Space: O(1) extra (excluding the output list).

4. Java code:

5. C code:

6. C++ code:

7. Python code:

8. JavaScript code: