In many real-world applications and coding challenges, identifying the majority element in an array is a common task. The majority element is defined as the element that appears more than ⌊n / 2⌋ times in an array of size n In this blog post, we’ll explore a highly efficient algorithm for solving this problem: the Boyer-Moore Voting Algorithm.

Problem Statement

Given an array nums of size n, return the majority element. The majority element is the one that appears more than ⌊n / 2⌋ times. For this problem, we can assume that there is always a majority element in the array.

Example 1:

Example 2:

Solution Approach

To tackle this problem efficiently, we can use the Boyer-Moore Voting Algorithm. This algorithm operates in linear time (O(n)) and requires constant space (O(1)), making it ideal for this problem.

How It Works

The Boyer-Moore Voting Algorithm works by maintaining a candidate for the majority element and a count to keep track of how many times this candidate appears.

Here’s a step-by-step explanation of the algorithm:

Code Implementation

Here’s how you can implement the Boyer-Moore Voting Algorithm in TypeScript:

Example Walkthrough

Let’s go through an example to illustrate how the algorithm works:

Example: [2, 2, 1, 1, 1, 2, 2]

Conclusion

The Boyer-Moore Voting Algorithm is an elegant solution for finding the majority element in a sorted array. Its linear time complexity and constant space usage make it an efficient choice for this problem. By understanding and applying this algorithm, you can handle majority element problems effectively in various coding scenarios.