What is the optimal time complexity of solving Search a 2D 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 Search a 2D 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 Search a 2D 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 Search a 2D 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.

Back to Practice Dashboard

Top 150 InterviewEasy

Search a 2D Matrix

Learn how to solve the 'Search a 2D Matrix' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Easy

You are given an m x n integer matrix matrix with the following two properties:

- Each row is sorted in non-decreasing order.

- The first integer of each row is greater than the last integer of the previous row.

Given an integer target, return True if target is in matrix or False otherwise.

You must write a solution in O(log(m * n)) time complexity.

Write a function searchMatrix(matrix: List[List[int]], target: int) -> bool.

Constraints

•m == len(matrix)
•n == len(matrix[i])
•1 <= m, n <= 100
•-10^4 <= matrix[i][j], target <= 10^4

Examples

Example 1

Input

matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]], target = 3

Output

True

Explanation

3 is found in the first row at index 1.

Example 2

Input

matrix = [[1, 3, 5, 7], [10, 11, 16, 20], [23, 30, 34, 60]], target = 13

Output

False

Explanation

13 is not present in the 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

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor