What is the optimal time complexity of solving Set Matrix Zeroes?

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 Set Matrix Zeroes?

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 Set Matrix Zeroes?

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 Set Matrix Zeroes?

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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Set Matrix Zeroes

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

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Problem Statement

Easy

Given an m x n integer matrix matrix, if an element is 0, set its entire row and column to 0's.

You must do it in place.

Implement a function setZeroes(matrix: list) -> list that modifies the matrix in place and returns it.

Constraints

•m == matrix.length
•n == matrix[0].length
•1 <= m, n <= 200
•-2^31 <= matrix[i][j] <= 2^31 - 1

Examples

Example 1

Input

[[1,1,1],[1,0,1],[1,1,1]]

Output

[[1,0,1],[0,0,0],[1,0,1]]

Explanation

The element at position (1,1) is 0. So the entire row 1 and column 1 are set to 0.

Example 2

Input

[[0,1,2,0],[3,4,5,2],[1,3,1,5]]

Output

[[0,0,0,0],[0,4,5,0],[0,3,1,0]]

Explanation

Elements at (0,0) and (0,3) are 0. Row 0 becomes all zeros. Columns 0 and 3 become all zeros.

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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