# 1. Introduction

The "Majority Element" problem is a common question in data analysis and algorithm design, requiring the identification of an element that appears more than half the time in an array. This problem is a test of one's ability to efficiently find a frequent element in a collection, often leading to the exploration of various algorithmic approaches.

## Problem

Given an array nums of size n, the task is to return the majority element. The majority element is defined as the element that appears more than ⌊n / 2⌋ times in the array. It is assumed that the majority element always exists in the array.

# 2. Solution Steps

1. Use the Boyer-Moore Voting Algorithm, which is a space-efficient method for finding the majority element.

2. Initialize two variables: one for storing the candidate element (candidate) and another for counting (count).

3. Iterate through the array.

4. If the count is 0, set the current element as the candidate.

5. If the current element is the same as the candidate, increment the count; otherwise, decrement it.

6. The candidate at the end of the array iteration is the majority element.

# 3. Code Program

``````def majorityElement(nums):
candidate, count = None, 0

for num in nums:
if count == 0:
candidate = num
count += (1 if num == candidate else -1)

return candidate

# Example Usage
print(majorityElement([3,2,3]))  # Output: 3
print(majorityElement([2,2,1,1,1,2,2]))  # Output: 2

``````

```3
2
```

### Explanation:

1. Boyer-Moore Voting Algorithm: Efficiently finds the majority element without extra space.

2. Candidate Tracking: Keeps track of the potential majority element.

3. Count Adjustment: Adjusts the count based on whether the current element matches the candidate.

4. Efficient Computation: The algorithm traverses the array once, achieving O(n) time complexity.

5. Assumption Verification: The assumption that there is always a majority element in the array ensures the correctness of the algorithm.

6. Practical Usage: Demonstrates an efficient technique for majority voting problems, applicable in areas like data analysis and machine learning.