What is the optimal time complexity of solving Spiral Matrix?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Spiral Matrix?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Spiral Matrix?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Spiral Matrix?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Spiral Matrix

Learn how to solve the 'Spiral Matrix' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

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

Implement a function spiralOrder(matrix: list) -> list that returns the elements in spiral order.

Constraints

•m == matrix.length
•n == matrix[i].length
•1 <= m, n <= 10
•-100 <= matrix[i][j] <= 100

Examples

Example 1

Input

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

Output

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

Explanation

Spiral order: right across top [1,2,3], down right side [6,9], left across bottom [8,7], up left side [4], then center [5].

Example 2

Input

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

Output

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

Explanation

Spiral order through a 3x4 matrix.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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