What is the optimal time complexity of solving Majority Element?

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 Majority Element?

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 Majority Element?

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 Majority Element?

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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DSA SectionEasy

Majority Element

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

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Problem Statement

Easy

Write a function find_majority_element(arr) that takes a list of integers arr and returns the majority element (the element that appears more than n // 2 times). You may assume that the majority element always exists in the array.

Constraints

•1 <= len(arr) <= 5 * 10^4
•-10^9 <= arr[i] <= 10^9

Examples

Example 1

Input

arr = [3, 2, 3]

Output

Explanation

3 appears twice, which is more than 3 // 2 = 1 time.

Example 2

Input

arr = [2, 2, 1, 1, 1, 2, 2]

Output

Explanation

2 appears 4 times, which is more than 7 // 2 = 3 times.

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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