Greetings, aspiring coders! Today, we're going to delve deeply into the complexities of data structures, specifically the RBTree, 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 RBTree operations and get our hands dirty with some interactive problem solving!

Before delving into the task, let's understand what an RBTree is and why we would use it. An RBTree (Red-Black Tree) is a balanced binary search tree, and it ensures that the tree remains balanced, with operations that are efficient for insertion, deletion, and lookups.

The advantages of using RBTree include the following:

1. Extracting minimum or maximum values is efficient using tree traversal.
2. Maintaining sorted order after every insertion or deletion, similar to a SortedSet, but typically offering better performance for lookups and modifications since it's inherently balanced.

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

Ruby's RBTree provides methods to handle elements efficiently. For example, locating the insertion point or finding bounds can be efficiently managed using the tree's structure.

Here is an example usage of RBTree:

Ruby
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1rbtree = RBTree.new
2
3rbtree[1] = true
4rbtree[2] = true
5rbtree[4] = true
6rbtree[6] = true
7rbtree[8] = true
8
9min_bound = rbtree.lower_bound(4).key rescue -1
10puts min_bound  # Output: 4

We aim to design a Ruby function named process_queries to process a series of distinct requests or queries efficiently. The queries consist of a list of two elements — the type of operation and the operand. The tree is initially empty when we start processing the queries.

There are three types of operations we'll handle:

• Adding an integer to the tree (operation type 0)
• Removing an integer from the tree (operation type 1). Whenever this operation is invoked, the integer is guaranteed to exist in the tree.
• 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 tree when the operation type is 0 or 1 and the smallest integer when the operation type is 2. If such an integer does not exist, the function should return -1.

Given a list of queries:

Ruby
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1[
2  [0, 10],
3  [2, 10],
4  [0, 20],
5  [1, 10],
6  [2, 10]
7]

The function should return: [1, 10, 2, 1, 20]

To start, we'll initialize our RBTree. We'll also create an empty array labeled results to store the outputs for each request.

Ruby
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1def process_queries(queries)
2  rbtree = RBTree.new
3  results = []
4end

Next, we utilize an each loop to iterate through all the queries. For operation type 0 or 1, we add or remove the given value from our red-black tree, respectively, and then append the current size of the tree to results.

Ruby
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1def process_queries(queries)
2  rbtree = RBTree.new
3  results = []
4  
5  queries.each do |query|
6    operation, value = query
7    
8    if operation == 0
9      rbtree[value] = true
10    elsif operation == 1
11      rbtree.delete(value)
12    end
13
14    results << rbtree.size
15  end
16end

Lastly, when the operation type is 2, we need to find the minimum bound, i.e., the smallest value greater than or equal to the given value in the tree. We achieve this by selecting the appropriate element using RBTree#lower_bound. If no such element exists, we append -1 to results.

Ruby
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1def process_queries(queries)
2  rbtree = RBTree.new
3  results = []
4  
5  queries.each do |query|
6    operation, value = query
7    
8    if operation == 0
9      rbtree[value] = true
10    elsif operation == 1
11      rbtree.delete(value)
12    elsif operation == 2
13      min_bound = rbtree.lower_bound(value).key rescue -1
14      results << (min_bound.nil? ? -1 : min_bound)
15      next
16    end
17    
18    results << rbtree.size
19  end
20  
21  results
22end

Well done! You've successfully navigated the complexities of RBTree operations and developed an understanding of how to handle various types of queries efficiently using Ruby. Resolving the problem involved incorporating Ruby arrays, conditional statements, and utilizing sorting and search logic within a tree structure.

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 with Ruby!