Welcome back! Today, we're sharpening our algorithmic problem-solving skills, focusing on HashMaps in Java. Imagine HashMaps as the backbone of a social network app, ensuring that each user's data remains unique and instantly accessible. By the close of this lesson, you will be equipped to use Java's HashMap to efficiently solve problems that might otherwise seem daunting due to their complexity or data size.

Our journey begins with the Majority Element Finder. You're handed an array of integers, and your mission is simple yet intriguing: determine whether this array has a celebrity element. This integer appears more frequently than all others combined. More formally, we are looking for an element appearing more than n/2 times.

Why does this matter? Well, consider analyzing sales data to determine the most sold product in an online marketplace—knowing the majority of products could streamline marketing strategies and inventory management. That's the real-world relevance of the majority element problem.

Now, let's be savvy about this. Enter the HashMap: your sophisticated voting tally system. With it, you can keep a running total of each product's sales as you go through the transaction list once rather than reviewing the entire list for each product. It grants us the speed of an experienced cashier who knows customers' habits by heart.