Welcome back! Today, we are focusing on solving complex algorithmic problems using Python dictionaries — the data structure that enables us to store data in key-value pairs. This powerful data structure facilitates lightning-fast retrieval and insertion operations, playing a pivotal role in algorithm efficiency. We will be tackling two carefully selected problems designed to highlight the practical uses of dictionaries: "Majority Vote Problem" and "Implement a Keyword Index". These problems serve to illustrate real-world applications of dictionaries, helping us understand them in a deeper, more meaningful way. Let's dive in!

Our first problem is about identifying the "majority" element in a list. The "majority element" in a list is an element that appears more than n / 2 times. Given a list of integers, our aim is to identify the majority element.

This problem could arise on numerous occasions. Imagine running a survey where each participant selects a number from 1 to n to rate a product. After the survey, you want to find out if there is a feature that received more than n / 2 votes. Or, consider an internet voting system for an online event. You may need to identify if a candidate is leading by more than half the total votes.

One naive approach is for each element, iterate over the entire list, and count the number of occurrences. However, this approach could lead to time complexity, which is not suitable for a large dataset, where is the size of the list.