Welcome to this insightful session, where we aim to master the complexities of the illustrious applications of sorting algorithms. Today's voyage links two problems: "Find the K-th Ordinal Statistic in a List" and "Count the Number of Inversions in a List". These problems mirror practical scenarios, and the efficient techniques used to solve them present valuable demonstrations of the application of sort algorithms. Solving these two problems, we'll see how Quick Sort and Merge Sort knowledge applies here and helps provide efficient implementations for both questions.

Let's dive into these captivating problems!

Our first problem presents a list of integers and the number k. The challenge is finding the k-th smallest element in that given list. To further elucidate, k starts from 1, so for k = 1, you are seeking to find the smallest element; if k = 2, you're searching for the second smallest element, and so on. By the conclusion of this lesson, you'll be highly skilled at performing this task!

A primary instinctive solution could involve iteratively identifying and discarding the smallest element from the list until you reach the k-th smallest element. While it sounds straightforward, this approach, unfortunately, incurs high time complexity due to the repetitive scans of the list to locate the smallest element. This solution has a complexity.