Majority Element

Problem Description

Given an array nums of size n, return the majority element. The majority element is the element that appears more than ⌊n / 2⌋ times. You may assume that the majority element always exists in the array.

Key Insights

• The majority element appears more than half the time in the array.
• There are multiple approaches to solve the problem, including using hash tables, sorting, and the Boyer-Moore Voting Algorithm.
• The problem can be solved in linear time while using constant space, which is optimal for this case.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem of finding the majority element, we can use the Boyer-Moore Voting Algorithm. This algorithm allows us to find the majority element in linear time while requiring only constant space. The algorithm works by maintaining a candidate for the majority element and a count of how many times that candidate has been encountered. It iterates through the array, adjusting the candidate and count based on the elements seen.

1. Initialize a candidate variable and a count variable.
2. Iterate through the array:
   • If the count is zero, set the current element as the candidate.
   • If the current element is equal to the candidate, increment the count.
   • If the current element is different, decrement the count.
3. Return the candidate as the majority element.

Code Solutions