Greetings, aspiring coders! Today we're going to delve into the complexities of data structures, specifically handling queries efficiently using C#. This is a common challenge encountered in numerous data science and algorithmic problems. Let's explore how to efficiently manage sorted sets using C#'s powerful built-in data structures and engage in some interactive problem-solving!

In C#, you can directly employ the SortedSet class to achieve sorted set functionality without manually managing the sorting order. This class automatically maintains order for insertions and deletions.

To maintain a sorted set in C#:

• Adding an element to a SortedSet automatically inserts it in the correct position, ensuring O(log N) time complexity for insertion.
• Removing an element from a SortedSet also maintains O(log N) complexity.
• Finding the smallest element greater than or equal to a given value is efficiently performed by using the .GetViewBetween() method or other C# methods for accessing specific elements.

Understanding these operations allows us to leverage SortedSet efficiently for our problem.

We are tasked with designing a C# 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.

Let's go through a set of queries in detail using C#.

C#
Copy to clipboard
1using System;
2using System.Collections.Generic;
3
4public class QueryProcessor
5{
6    public static List<int> ProcessQueries(List<int[]> queries)
7    {
8        SortedSet<int> sortedSet = new SortedSet<int>();
9        List<int> results = new List<int>();
10
11        foreach (var query in queries)
12        {
13            int operation = query[0];
14            int value = query[1];
15
16            if (operation == 0)
17            {
18                sortedSet.Add(value);
19                results.Add(sortedSet.Count);
20            }
21            else if (operation == 1)
22            {
23                sortedSet.Remove(value);
24                results.Add(sortedSet.Count);
25            }
26            else if (operation == 2)
27            {
28                var view = sortedSet.GetViewBetween(value, Int32.MaxValue);
29                if (view.Count > 0)
30                {
31                    results.Add(view.Min);
32                }
33                else
34                {
35                    results.Add(-1);
36                }
37            }
38        }
39
40        return results;
41    }
42
43    public static void Main()
44    {
45        List<int[]> queries = new List<int[]>
46        {
47            new int[] { 0, 10 },  // Add 10 to the set
48            new int[] { 2, 10 },  // Find the smallest integer >= 10
49            new int[] { 0, 20 },  // Add 20 to the set
50            new int[] { 1, 10 },  // Remove 10 from the set
51            new int[] { 2, 10 }   // Find the smallest integer >= 10
52        };
53
54        List<int> results = ProcessQueries(queries);
55        Console.WriteLine(String.Join(", ", results)); // Output: 1, 10, 2, 1, 20
56    }
57}

To start, we initialize our set using C#'s SortedSet<int>. We'll also create a List<int> named results to store the outputs for each request.

C#
Copy to clipboard
1SortedSet<int> sortedSet = new SortedSet<int>();
2List<int> results = new List<int>();

We use a foreach loop to traverse all the queries. For an operation type of 0 or 1, we either add or remove the provided value from our set. The SortedSet class handles ordered insertion and deletion automatically. We then append the size of the current set to results.

C#
Copy to clipboard
1if (operation == 0)
2{
3    sortedSet.Add(value);
4    results.Add(sortedSet.Count);
5}
6else if (operation == 1)
7{
8    sortedSet.Remove(value);
9    results.Add(sortedSet.Count);
10}

When the operation type is 2, we find the minimum bound using the GetViewBetween method. This retrieves all elements greater than or equal to our provided value. If any elements exist in this view, the smallest is found using .Min. If not, we append -1 to results.

C#
Copy to clipboard
1else if (operation == 2)
2{
3    var view = sortedSet.GetViewBetween(value, Int32.MaxValue);
4    if (view.Count > 0)
5    {
6        results.Add(view.Min);
7    }
8    else
9    {
10        results.Add(-1);
11    }
12}

Well done! You've successfully navigated the complexities of sorted set operations and developed an understanding of how to handle various types of queries efficiently using C#. This involved using the SortedSet class to leverage automatic ordering, achieving efficient insertions, deletions, and lookups.

The next step in your learning journey involves tackling similar challenges independently using the concepts you've just learned. Review this lesson as needed, and remember: practice and apply these concepts. Happy coding!