Greetings, aspiring coders! Today, we're going to delve deep into the complexities of data structures, specifically the SortedSet in Scala, and explore how to handle queries efficiently. This is a common problem, often encountered in numerous data science and algorithmic problems. So, let's gear up to unravel the mysteries of sorted set operations and get our hands dirty with some interactive problem-solving!

Before delving into the task, let's understand what a SortedSet (or TreeSet) is and why we would use it in Scala. A SortedSet is a collection that maintains its elements in sorted order at all times. In Scala, the most common implementation is TreeSet, which is backed by a balanced binary search tree.

Advantages of using SortedSet or TreeSet:

1. Extracting the minimum (set.headOption) or maximum (set.lastOption) values is a constant or logarithmic time operation, as the set is always kept in sorted order.
2. Inserting or removing elements is efficient, with a time complexity of $O(\log N)$ per operation, since the underlying tree structure maintains order automatically.
3. Searching for the existence of an element, or finding the smallest element greater than or equal to a given value, can also be performed efficiently.

Understanding these operations can help us utilize efficiently for our problem.

Unlike some languages, Scala's SortedSet does not provide direct methods like bisect_left or bisect_right to find insertion points. However, we can still efficiently find the smallest element greater than or equal to a given value using the from method, which returns a view of the set starting from a specific value.

For example, if we have a TreeSet as TreeSet(1, 2, 4, 6, 8), we can find the smallest element greater than or equal to 4 by calling set.from(4).headOption. This will return Some(4), since 4 is present in the set. If we call set.from(5).headOption, it will return Some(6), as 6 is the next greater element.

Both insertion and search operations in a TreeSet are performed in $O(\log N)$ time.

We are tasked with designing a Scala function named processQueries that can process a series of distinct requests or queries efficiently. The queries comprise a list of two integers — the type of operation and the operand.

There are three types of operations we'll handle:

• Adding an integer to the set (operation type 0)
• Removing an integer from the set (operation type 1). Whenever this operation is invoked, we can guarantee that the integer exists in the set.
• Finding the smallest integer that is greater than or equal to a given value (operation type 2).

The function should return the current size of the set when the operation type is 0 or 1, and the smallest possible integer when the operation type is 2. If such an integer does not exist, the function should return -1.

Given a list of queries:

The function should return: List(1, 10, 2, 1, 20)

To start, we'll initialize our TreeSet in Scala. We'll also create an empty ListBuffer labeled results to store the outputs for each request.

Next, we utilize a for loop to traverse through all the queries. For an operation type of 0 or 1, we either add or remove the provided value from our sorted set. Subsequently, we append the size of the current set to results.

Lastly, when the operation type is 2, we need to find the minimum bound, i.e., the smallest value greater than or equal to our provided value in the set. We perform this using the from method and headOption from our TreeSet. If such a value does not exist, we append -1 to results.

Well done! You've successfully navigated the complexities of SortedSet operations and developed an understanding of how to handle various types of queries efficiently using Scala. Resolving the problem involved incorporating Scala's immutable collections, pattern matching, and efficient search within a sorted set.

The next step in your learning journey involves tackling similar challenges on your own using the concepts that you've just learned. Be sure to review this lesson as needed, and always remember: practice and apply these concepts. Happy coding!