What is the optimal time complexity of solving Boyer Moore Voting?

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 Boyer Moore Voting?

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 Boyer Moore Voting?

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 Boyer Moore Voting?

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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Boyer Moore Voting

Learn how to solve the 'Boyer Moore Voting' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function boyer_moore_majority(arr) that implements the Boyer-Moore Majority Vote Algorithm to find the majority element (the element that appears more than n // 2 times) in a list of integers arr. If no majority element exists, return -1.

Constraints

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

Examples

Example 1

Input

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

Output

Explanation

1 appears 3 times which is greater than 5 // 2 = 2 times.

Example 2

Input

arr = [1, 2, 3]

Output

-1

Explanation

No element appears more than 3 // 2 = 1 time.

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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