Category: C# Coding Test Tutorials

Hello, everyone! Today we will discuss one of the important topics in coding tests using C#, which is ‘Range Sum’. The range sum problem is about efficiently calculating the sum of a specific range in an array. This problem is a very useful topic that frequently appears in many algorithm problems and practical work.

Problem Definition

Before we start the problem, let me briefly explain what a range sum is. A range sum means calculating the sum of a specific range of a given array (e.g., from array[i] to array[j]). Such problems can be presented in various ways.

Example Problem

Let’s assume we have an array like the following.

int[] arr = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

Now we will solve a problem that requests the range sum of the given array. For example, if i and j are 2 and 5 respectively, we must calculate the sum from arr[2] to arr[5], which is 3 + 4 + 5 + 6 = 18.

Approach to Solving the Problem

The first method to calculate the range sum is to use a simple loop. We can traverse the elements of the array to calculate the sum of the range corresponding to the values of i and j. However, this has the disadvantage of being inefficient with a time complexity of O(N). So how can we calculate the range sum more efficiently?

Preprocessing Method

To efficiently solve the range sum problem, we use the concept of a ‘prefix sum array’. A prefix sum array is an array that stores the sum up to each index, allowing us to easily calculate the range sum. Using a prefix sum array allows us to calculate the range sum in O(1) time complexity.

Example of a Prefix Sum Array

Let’s look at how to create a prefix sum array.

    int[] prefixSum = new int[arr.Length + 1];
    for (int i = 0; i < arr.Length; i++)
    {
        prefixSum[i + 1] = prefixSum[i] + arr[i];
    }
    

In the above code, we store the sum of the arr array up to the i-th index in the i+1-th index of the prefixSum array. Now the sum of a specific range [i, j] can be easily calculated as prefixSum[j + 1] – prefixSum[i].

Implementation

Now let’s implement the range sum algorithm using the prefix sum array in C#.

    using System;

    public class Program
    {
        public static void Main()
        {
            int[] arr = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
            int[][] queries = { new int[] { 2, 5 }, new int[] { 0, 9 }, new int[] { 4, 7 } };

            int[] result = RangeSum(arr, queries);
            foreach (var sum in result)
            {
                Console.WriteLine(sum);
            }
        }

        public static int[] RangeSum(int[] arr, int[][] queries)
        {
            int[] prefixSum = new int[arr.Length + 1];
            for (int i = 0; i < arr.Length; i++)
            {
                prefixSum[i + 1] = prefixSum[i] + arr[i];
            }

            int[] results = new int[queries.Length];
            for (int i = 0; i < queries.Length; i++)
            {
                int l = queries[i][0];
                int r = queries[i][1];
                results[i] = prefixSum[r + 1] - prefixSum[l];
            }

            return results;
        }
    }
    

When the above code is executed, the range sums for each query can be calculated. It is important to ensure that the index ranges are always valid.

Time Complexity Analysis

The time complexity of the algorithm described above is as follows.

• Creating the prefix sum array: O(N)
• Query processing: O(1) (accessing state information for each query)

As a result, this algorithm has a time complexity of O(N + Q), where Q is the number of queries. Thus, the range sum problem can be solved very efficiently through the prefix sum array.

Practical Exercise

Now test how well you understand the range sum problem. We encourage you to create and solve problems like the one below.

Problem: Finding the Maximum Value in a Specific Range

Try to solve the problem of finding the maximum value within a specific range of a given array. Use the prefix sum to solve this problem.

Conclusion

The range sum problem is a fundamental algorithm problem about calculating the sum within a range of an array. We learned how to use the prefix sum array to handle arrays efficiently. Such techniques can be usefully applied to more complex problems, so make sure to practice enough.

I hope this article helps you in your C# coding test preparation. Try solving more algorithm problems to improve your skills!

1. Introduction

As programming languages have grown, a variety of data structures and algorithms have become necessary. Among them, the trie is a data structure specialized in efficiently handling strings, mainly used for string search, autocomplete features, and storing prefix sets. In this article, we will introduce algorithm problems using the trie data structure and solve them using C#.

2. Understanding the Trie Data Structure

A trie has polymorphic properties, with nodes representing each character. Tries have the following characteristics:

• The ability to store all words.
• The ability to easily search for prefixes of words.
• A structure that can group words with the same prefix.

A trie is typically structured as follows:

class TrieNode {
    Dictionary Children;
    bool IsEndOfWord;

    public TrieNode() {
        Children = new Dictionary();
        IsEndOfWord = false;
    }
}
    
class Trie {
    private TrieNode root;

    public Trie() {
        root = new TrieNode();
    }

    public void Insert(string word) {
        TrieNode current = root;
        foreach (char c in word) {
            if (!current.Children.ContainsKey(c)) {
                current.Children[c] = new TrieNode();
            }
            current = current.Children[c];
        }
        current.IsEndOfWord = true;
    }

    public bool Search(string word) {
        TrieNode current = root;
        foreach (char c in word) {
            if (!current.Children.ContainsKey(c)) {
                return false;
            }
            current = current.Children[c];
        }
        return current.IsEndOfWord;
    }

    public bool StartsWith(string prefix) {
        TrieNode current = root;
        foreach (char c in prefix) {
            if (!current.Children.ContainsKey(c)) {
                return false;
            }
            current = current.Children[c];
        }
        return true;
    }
}
    

3. Problem Introduction

The problem we will cover in this lecture is as follows:

Problem: Count the Number of Words with a Specific Prefix

Given a list of words and a specific prefix, write a function that returns the number of words that start with this prefix.

Input:

• Word list: [“apple”, “app”, “application”, “apricot”]
• Prefix: “app”

Output: 3 (The words “app”, “apple”, and “application” are in the word list.)

4. Problem-Solving Process

To solve the problem, we will use the trie data structure to insert words and implement a function to count the number of words that start with a specific prefix.

1. **Insert Words**: First, we need to insert all the words into the trie. This will create child nodes for each character of every word.

2. **Prefix Search**: Implement the logic to count the number of words that start with the specific prefix by performing a deep search.

3. **Return Result**: Return the count of words that start with the prefix.

4.1 Code Implementation

Below is the complete code implemented in C#:

class Solution {
    public int CountWordsWithPrefix(string[] words, string prefix) {
        Trie trie = new Trie();
        
        // Insert all words into the trie
        foreach (string word in words) {
            trie.Insert(word);
        }
        
        // Counting the number of words that start with the prefix
        return CountWordsStartingWithPrefix(trie, prefix);
    }

    private int CountWordsStartingWithPrefix(Trie trie, string prefix) {
        TrieNode current = trie.Root;
        foreach (char c in prefix) {
            if (!current.Children.ContainsKey(c)) {
                return 0; // Return 0 if there are no words corresponding to the prefix
            }
            current = current.Children[c];
        }
        return CountAllWords(current); // Count all words below the prefix
    }

    private int CountAllWords(TrieNode node) {
        int count = 0;
        
        if (node.IsEndOfWord) {
            count++; // Increase word count if the current node is the end of a word
        }
        
        foreach (var child in node.Children) {
            count += CountAllWords(child.Value); // Recursively explore all child nodes
        }
        
        return count;
    }
}
    

5. Time Complexity Analysis

The time complexity for inserting a word into the trie is O(m), where m is the length of the word.
Searching for a prefix takes O(k) time (where k is the length of the prefix).
Thus, the overall time complexity is O(n * m + k), where n is the number of words.

6. Test Cases

Here are a few test cases:

string[] words = {"apple", "app", "application", "apricot"};
string prefix = "app";
Solution solution = new Solution();
Console.WriteLine(solution.CountWordsWithPrefix(words, prefix)); // Output: 3

words = new string[] {"banana", "bandana", "band"};
prefix = "ban";
Console.WriteLine(solution.CountWordsWithPrefix(words, prefix)); // Output: 3

words = new string[] {"car", "cart", "cat"};
prefix = "ca";
Console.WriteLine(solution.CountWordsWithPrefix(words, prefix)); // Output: 3

words = new string[] {"dog", "deer", "dough"};
prefix = "do";
Console.WriteLine(solution.CountWordsWithPrefix(words, prefix)); // Output: 3
    

7. Conclusion

In this article, we explored how to solve string processing problems using the trie data structure. Tries are used for various purposes in many fields and are very useful for solving problems like string searches. We looked at the key ideas of tries along with their implementation in C#, and I hope that through various test cases, you can enhance your problem-solving skills.

Hello, everyone! Today, we will discuss a problem of finding the diameter of a tree using C#. This article will help you understand through problem definition, algorithm design, implementation, and testing process.

Problem Definition

The diameter of a tree refers to the length of the longest path between two nodes in the tree. The given tree is represented by the number of vertices n and n-1 edges.
Based on this, write a function to calculate the diameter of the tree.

Input

• n : Number of vertices (2 ≤ n ≤ 10^5)
• n-1 edges that make up the tree. Each edge is given in the form of u v w, where u and v are connected vertices, and w is the weight between the two vertices.

Output

An integer value representing the diameter of the tree.

Algorithm Design

The most common method to find the diameter of a tree is to use “two depth-first searches (DFS).”
Below is a summary of the simple procedure.

1. Run DFS from an arbitrary vertex to find the farthest vertex A.
2. Run DFS again from vertex A to find the farthest vertex B, and calculate the distance.

This method can efficiently determine the diameter of the tree. In the worst case, the time complexity is O(n).

C# Code Implementation

Below is the C# code based on the above algorithm:

using System;
using System.Collections.Generic;

class TreeDiameter
{
    static List>[] graph;
    static bool[] visited;
    static int maxDistance;
    static int furthestNode;

    public static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        graph = new List>[n + 1];

        for (int i = 1; i <= n; i++)
        {
            graph[i] = new List>();
        }

        for (int i = 0; i < n - 1; i++)
        {
            var edge = Console.ReadLine().Split();
            int u = int.Parse(edge[0]);
            int v = int.Parse(edge[1]);
            int w = int.Parse(edge[2]);
            graph[u].Add(new Tuple(v, w));
            graph[v].Add(new Tuple(u, w));
        }

        // Finding the farthest vertex using first DFS
        visited = new bool[n + 1];
        maxDistance = 0;
        DFS(1, 0);

        // Finding the diameter using second DFS
        visited = new bool[n + 1];
        maxDistance = 0;
        DFS(furthestNode, 0);
        
        // Output the result
        Console.WriteLine(maxDistance);
    }

    static void DFS(int node, int distance)
    {
        visited[node] = true;

        if (distance > maxDistance)
        {
            maxDistance = distance;
            furthestNode = node;
        }

        foreach (var neighbor in graph[node])
        {
            if (!visited[neighbor.Item1])
            {
                DFS(neighbor.Item1, distance + neighbor.Item2);
            }
        }
    }
}

Code Explanation

1. graph: An array to store the edges of the tree in an adjacency list format.
2. visited: An array to track visited vertices during DFS.
3. maxDistance: Stores the length of the longest path found so far.
4. furthestNode: Stores the ID of the farthest vertex.
5. Main(): Receives the tree structure input and calls DFS twice to calculate the diameter of the tree.
6. DFS(int node, int distance): Implements the depth-first search function to recursively explore each vertex while updating the distance.

Test Cases

Your code can be validated with the following test cases:

Test Input

5
1 2 3
1 3 2
3 4 4
3 5 1

Expected Output

9

Description

If we draw the tree from the above input, it looks like this:

          1
         / \
        2   3
           / \
          4   5

The diameter of the tree is the path starting from node 2 to node 4, with a total length of 3 + 2 + 4 = 9.

Conclusion

Today, we solved the problem of finding the diameter of a tree using C#.
This algorithm is a frequently encountered type in tree problems, so I encourage you to practice sufficiently.
Try various test cases to deepen your understanding.
Thank you!

Hello, everyone! Today we will learn how to solve algorithm problems using C#. The topic for this session is to find the number of leaf nodes in a binary tree. By solving this problem, you can enhance your understanding of data structures and recursive calls.

1. Problem Definition

The problem is as follows: Given a binary tree, write a function to count the number of leaf nodes (nodes with no children).

Example

• Input: A binary tree as follows

       1
      / \
     2   3
    / \
   4   5
    

• Output: 3 (Leaf nodes: 4, 5, 3)

2. Introduction to Binary Trees

A binary tree is a tree data structure in which each node can have at most two children. A binary tree has the following characteristics:

• Each node can have child nodes (left and right).
• A leaf node refers to a node that has no child nodes.
• A binary tree has a recursive structure.

3. Approach

To count the number of leaf nodes, let’s consider using a recursive function. The basic approach is as follows:

1. Examine the current node. If the current node is null, return 0.
2. If the current node is a leaf node (i.e., both left and right children are null), return 1.
3. If the current node is not a leaf node, recursively count the number of leaf nodes in the left and right subtrees and return the sum.

4. C# Code Implementation

Now, let’s implement the code in C# according to the approach described above.

using System;

class TreeNode
{
    public int Val;
    public TreeNode Left;
    public TreeNode Right;

    public TreeNode(int val)
    {
        Val = val;
        Left = null;
        Right = null;
    }
}

class Program
{
    public static int CountLeafNodes(TreeNode root)
    {
        // 1. If the current node is null
        if (root == null)
            return 0;

        // 2. If the current node is a leaf node
        if (root.Left == null && root.Right == null)
            return 1;

        // 3. Count leaf nodes in the left and right subtrees
        return CountLeafNodes(root.Left) + CountLeafNodes(root.Right);
    }

    static void Main(string[] args)
    {
        // Create the tree
        TreeNode root = new TreeNode(1);
        root.Left = new TreeNode(2);
        root.Right = new TreeNode(3);
        root.Left.Left = new TreeNode(4);
        root.Left.Right = new TreeNode(5);

        // Print the count of leaf nodes
        int leafCount = CountLeafNodes(root);
        Console.WriteLine($"Number of leaf nodes: {leafCount}");
    }
}

5. Code Explanation

The provided TreeNode class defines a node in the binary tree. Each node has a value (Val) and left (Left) and right (Right) child nodes. The CountLeafNodes function recursively calculates the number of leaf nodes for the given node.

• In the first conditional statement, if the current node is null, it returns 0 to terminate.
• In the second conditional statement, if the current node is a leaf node, it returns 1.
• Finally, it visits the left and right subtrees, sums up the results, and returns the total.

6. Time Complexity Analysis

The time complexity of this algorithm is O(N). Here, N represents the number of nodes in the tree. Since each node is visited only once, it has a linear time complexity.

7. Additional Considerations

• If the tree is empty, i.e., the root node is null, there are no leaf nodes.
• Both balanced binary trees and skewed binary trees can handle the problem in the same way.

8. Conclusion

We learned how to solve the problem of counting leaf nodes in a binary tree. We can easily resolve this using a recursive function, thereby enhancing our understanding of tree data structures.

Next time, we will tackle another algorithm problem and advance further. Thank you!

This article provides a detailed explanation of the problem type ‘Finding the K-th number’, which is frequently tested in coding interviews, along with methods for solving it.

Problem Description

Given an array arr and an integer K, the task is to find and return the K-th smallest number. The array uses zero-based indexing, and if there are multiple instances of the same number, any one of the K-th smallest numbers may be returned.

For example, if the array is [7, 10, 4, 3, 20, 15] and K=3, the 3rd smallest number is 7.

Input Format

The input is given in the following format:

• First line: Size of the array N (1 <= N <= 10^6)
• Second line: N integers (elements of the array range from -10^9 to 10^9)
• Third line: An integer K (1 <= K <= N)

Input Example

6
7 10 4 3 20 15
3
        

Output Format

The output should be the K-th smallest number in the array.

Output Example

7
        

Solution Process

Step 1: Understanding the Problem

We need to find the K-th smallest number in the given array. Since the array is not sorted, we need to find the value of the K-th element in a sorted state.

Step 2: Choosing the Algorithm

The most intuitive method is to sort the array and then return the K-th element. However, this method has a time complexity of O(N log N). There are various methods to optimize this:

• Quickselect algorithm (average O(N) time complexity)
• Using a heap data structure

In this tutorial, we will be using the Quickselect method.

Step 3: Quickselect Explanation

Quickselect is similar to the Quick Sort algorithm, which selects a pivot to divide the array into left and right parts. The result is derived based on the position of K.

Process of Quickselect

1. Select a pivot value.
2. Move values less than or equal to the pivot to the left and those greater to the right.
3. If K is equal to the pivot index, return the pivot.
4. If K is less than the pivot, recursively call Quickselect on the left part.
5. If K is greater than the pivot, recursively call Quickselect on the right part.

C# Code Implementation

using System;
using System.Linq;

class KthSmallest
{
    public static int QuickSelect(int[] arr, int left, int right, int k)
    {
        if (left == right) // If the array has only one element
            return arr[left];

        Random random = new Random();
        int pivotIndex = left + random.Next(right - left);
        int pivot = arr[pivotIndex];

        // Move pivot to the far right
        Swap(arr, pivotIndex, right);
        int storeIndex = left;

        for (int i = left; i < right; i++)
        {
            if (arr[i] < pivot)
            {
                Swap(arr, storeIndex, i);
                storeIndex++;
            }
        }

        Swap(arr, storeIndex, right); // Place pivot in its correct position

        if (k == storeIndex) return arr[k];
        else if (k < storeIndex) return QuickSelect(arr, left, storeIndex - 1, k);
        else return QuickSelect(arr, storeIndex + 1, right, k);
    }

    private static void Swap(int[] arr, int i, int j)
    {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }

    static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        int[] arr = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int K = int.Parse(Console.ReadLine()) - 1; // Convert K to a 0-based index

        int result = QuickSelect(arr, 0, N - 1, K);
        Console.WriteLine(result);
    }
}
        

Code Explanation

The above C# code uses the Quickselect algorithm to find the K-th number:

• QuickSelect method: Finds and returns the K-th smallest number in the array.
• Swap method: Swaps the positions of two elements.
• Main: Receives input and executes the program.

This algorithm has an average time complexity of O(N), which is very efficient.

Conclusion

In this tutorial, we learned how to solve the ‘Finding the K-th number’ problem using C#. By practicing the Quickselect algorithm, we have acquired a useful technique for coding interviews. Additionally, I encourage you to experience various algorithms and problems to further enhance your skills.