Category: C# Coding Test Tutorials

Coding tests are a very important part of modern software engineering. Many companies include coding problems in technical interviews to assess applicants’ algorithmic and problem-solving skills. In this course, we will learn about Euler’s Totient Function, a mathematical concept.

Problem Description

The Euler’s Totient Function returns the number of positive integers m for a given integer n. m is an integer that is greater than or equal to 1 and less than or equal to n, and m and n are coprime integers. The goal is to determine the count of m that satisfies gcd(m, n) = 1.

Problem: Compute the Euler’s Totient Function for a given integer n.

Input Format

• 1 ≤ n ≤ 10⁶

Output Format

• The Euler’s Totient value of n

Example

6

2

Theoretical Background

The Euler’s Totient Function is defined as follows:

• If n is a prime number: ϕ(n) = n – 1
• If n is not a prime number, using the prime factors p of n: ϕ(n) = n × (1 – 1/p₁) × (1 – 1/p₂) × … × (1 – 1/p_k)

This allows us to find the prime factors of n and calculate ϕ(n) accordingly.

C# Implementation

Now, let’s implement the Euler’s Totient Function using C#. The time complexity of this algorithm is O(√n), which is efficient for finding the prime factors of n.

using System;

class Program
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        Console.WriteLine(EulerPhi(n));
    }

    static int EulerPhi(int n)
    {
        int result = n; // Set initial value to n
        for (int p = 2; p * p <= n; p++)
        {
            // Check if p is a prime factor of n
            if (n % p == 0)
            {
                // Remove prime factor by dividing n
                while (n % p == 0)
                {
                    n /= p;
                }
                result -= result / p; // Apply Euler's Totient formula
            }
        }
        // If the remaining n is a prime number
        if (n > 1)
        {
            result -= result / n;
        }

        return result; // Return the final result
    }
}

Code Explanation

The above code is for calculating the Euler’s Totient Function and consists of the following steps:

1. Read Input: Accept an integer n from the user.
2. Initialize Value: Initialize the result value to the input n.
3. Find Prime Factors: Iterate from 2 to the square root of n, checking if n is divisible by p.
4. Remove Prime Factors: Divide n by the prime factor p to remove it from n.
5. Apply Euler’s Totient Formula: Update the result value using the ϕ(n) formula for the current prime factor p.
6. Check Remaining Prime: If the remaining n value is greater than 1, exclude n from the result since it is prime.
7. Return Result: Return the final result value.

Performance Optimization

This algorithm operates very quickly within the specified range. However, for faster calculations on various inputs, we can precompute primes. Using the Sieve of Eratosthenes, we can find primes and use them to compute Euler’s Totient values.

By using an array to store primes, we can further improve the function. This method increases speed through comparisons with other numbers and optimizes memory usage.

Conclusion

The Euler’s Totient Function can be easily implemented in managed languages like C#, and by combining theory with code, we can solve algorithm problems more efficiently. In this course, you have learned how to compute the Euler’s Totient Function using various techniques, including basic functions in C# and the Euclidean algorithm for finding the greatest common divisor.

We hope you continue to practice regularly to solve more algorithm problems in future coding tests!

1. Problem Definition

Binary search is an algorithm for finding a specific value in a sorted array. It works by comparing the middle value of the array and halving the search range.
The time complexity of binary search is O(log n), making it very efficient. Let’s understand the principles of this algorithm by implementing it in practice.

2. Problem Description

The following problem involves finding a specific number using binary search:

        
            // Problem: Find a specific number in the given integer array.
            // The array is sorted in ascending order.
            // If the number is found, return its index, 
            // and return -1 if it is not found.
        
    

Example Input

• Input Array: [2, 3, 4, 10, 40]
• Value to Find: 10

Example Output

• Output: 3 (10 is located at index 3)

3. Problem Solving Strategy

The basic idea of binary search is as follows:

• Select the middle element of the array.
• Compare the middle element with the value to be found.
• If the value to be found is less than the middle element, reduce the search range to the left half of the array.
• If the value to be found is greater than the middle element, reduce the search range to the right half of the array.
• Repeat this process until the value to be found is found.

4. Algorithm Implementation

Now let’s implement the binary search algorithm in C#. The following code is an implementation of the binary search algorithm that finds a specific value in the given array.

        
            using System;

            class Program
            {
                static int BinarySearch(int[] arr, int target)
                {
                    int left = 0;
                    int right = arr.Length - 1;

                    while (left <= right)
                    {
                        int mid = left + (right - left) / 2;

                        // Compare mid value with the target value
                        if (arr[mid] == target)
                        {
                            return mid; // Return index if the value is found
                        }
                        else if (arr[mid] < target)
                        {
                            left = mid + 1; // Search in the right half of the array
                        }
                        else
                        {
                            right = mid - 1; // Search in the left half of the array
                        }
                    }

                    return -1; // Case when the value is not found
                }

                static void Main(string[] args)
                {
                    int[] arr = { 2, 3, 4, 10, 40 };
                    int target = 10;
                    int result = BinarySearch(arr, target);

                    if (result == -1)
                    {
                        Console.WriteLine("The value to be found does not exist.");
                    }
                    else
                    {
                        Console.WriteLine("Index of the value to be found: " + result);
                    }
                }
            }
        
    

5. Code Explanation

Let's take a closer look at how binary search is implemented in the C# code above.

• BinarySearch method takes two parameters: an integer array arr and the value to be found target.
• The variable left stores the starting index of the array, and right stores the ending index of the array.
• The loop while (left <= right) continues as long as there is a search range left.
• The middle index is calculated as int mid = left + (right - left) / 2;. This is one way to prevent index overflow in large arrays.
• By comparing the mid value with the target value, we modify the value of left or right based on the conditions.
• If the target value is found, the corresponding index is returned, and -1 is returned if the target value is not found.

6. Time Complexity

The time complexity of binary search is O(log n). This is because the data is halved during the search process.
Even if n is a very large number, binary search can derive the result with relatively few comparisons.

7. Conclusion

The binary search algorithm operates very efficiently when the data is sorted.
By understanding and implementing this algorithm well, it will be very helpful in various coding tests and development tasks.
I hope you enhance your skills in binary search by solving algorithm problems.

Hello! Today, we will address problems that may arise in coding tests using C# and discuss the importance of debugging to solve these issues. Through this tutorial, we will solve basic algorithm problems that you might encounter in coding tests, and in the process, we will explore debugging techniques and their significance.

Problem Definition: Sum of Two Numbers in an Array

The first problem I will introduce is “Return the indices of the two numbers in the given array that add up to a specific value.” This problem is one of the most frequently encountered in many coding interviews.

Problem Description

Given an integer array nums and an integer target, implement a function that returns the indices of the two numbers such that they add up to target in nums. Assume that you cannot use the same element twice, and that there is exactly one solution.

Example:
    Input: nums = [2, 7, 11, 15], target = 9
    Output: [0, 1]
    Explanation: Because nums[0] + nums[1] = 2 + 7 = 9, return [0, 1].

Problem Approach

There are several approaches to solve this problem, but the most common method is to use two nested loops. However, this is inefficient with a time complexity of O(n^2), so using a hashmap is a more efficient approach. Using a hashmap allows us to reduce the time complexity to O(n).

Solution Process

1. Create an empty hashmap.
2. Iterate through each element of the array.
3. Check if the ‘required complement’ of the current element exists in the hashmap. (target - nums[i])
4. If it exists, return the index of that element and the current index.
5. If not, add the current element and its index to the hashmap.

Code Implementation

Based on the approach described above, C# code can be written as follows:

using System;
    using System.Collections.Generic;

    public class Solution {
        public int[] TwoSum(int[] nums, int target) {
            Dictionary map = new Dictionary();
            for (int i = 0; i < nums.Length; i++) {
                int complement = target - nums[i];
                if (map.ContainsKey(complement)) {
                    return new int[] { map[complement], i };
                }
                map[nums[i]] = i;
            }
            throw new ArgumentException("No two sum solution");
        }
    }

Need for Debugging

Now that we have explained the process of solving the problem, let’s talk about the debugging process. Debugging is a crucial step in programming, allowing us to correct errors in the code we have written and optimize it. Good debugging enables us to quickly analyze and solve problems.

Debugging Techniques

There are several techniques that can be used during the debugging process. Here are a few:

• Print Debugging: You can print output at specific parts of the code to check the values of variables and the flow of execution.
• Using a Debugger: Use the built-in debugger in your IDE to set breakpoints and analyze the code execution step by step.
• Unit Testing: A systematic procedure for pre-testing each function to catch logical errors, not just syntax errors.

Debugging Steps

Debugging proceeds through the following steps:

1. Understand the problem and clarify the input values and expected results.
2. Execute the code and compare results to identify errors.
3. Locate the appropriate parts to fix the problem and make the corrections.
4. After making changes, retest the code to verify whether the problem is resolved.

Conclusion

Through this tutorial, we have examined the process of solving basic coding problems in C# and emphasized the importance of debugging. While solving algorithm problems is essential, effectively addressing the issues that arise in the process is equally important. Through debugging, you can become a better programmer and increase your chances of success in coding tests. In the next tutorial, we will tackle more complex problems and explore various methods for efficient solutions. Thank you!

Hello! In this post, we will discuss one of the problems frequently encountered in coding tests using C#: “Sorting Numbers”. This tutorial will explain the understanding of algorithm problems, the resolution process in detail, and finally how to implement C# code.

Problem Description

This problem requires you to input numbers equal to the given quantity and output those numbers sorted in ascending order. We will solve the problem using various methods along with a basic understanding of sorting algorithms.

Problem Input

• The first line contains the quantity of numbers N (1 ≤ N ≤ 100,000).
• From the second line onward, N lines will contain the numbers. Each number is an integer whose absolute value is less than or equal to 1,000,000.

Problem Output

Output the sorted results in ascending order from the first line to the Nth line.

Example

Input
5
5
2
3
1
4

Output
1
2
3
4
5

Problem Solving Process

This problem is simply about sorting the given numbers, and we can use various sorting algorithms. In this article, I will explain how to solve the problem using one of the basic sorting algorithms, “Merge Sort”, and “C#’s built-in sorting methods”.

1. Merge Sort

Merge Sort is a type of divide and conquer algorithm, which divides the given array into halves, sorts both halves, and then merges them back together. It has a time complexity of O(N log N) in both average and worst-case scenarios, and it is a stable sorting method.

Merge Sort Procedure

1. Recursively divide the array until it is split into single elements.
2. Sort and merge the split arrays.

Implementing Merge Sort

Now, let’s implement Merge Sort in C#.

public class MergeSort
{
    public static void Sort(int[] array, int left, int right)
    {
        if (left < right)
        {
            int mid = (left + right) / 2;

            // Divide the array elements
            Sort(array, left, mid);
            Sort(array, mid + 1, right);

            // Merge the sorted halves
            Merge(array, left, mid, right);
        }
    }

    public static void Merge(int[] array, int left, int mid, int right)
    {
        int n1 = mid - left + 1;
        int n2 = right - mid;

        int[] leftArray = new int[n1];
        int[] rightArray = new int[n2];

        for (int i = 0; i < n1; i++)
            leftArray[i] = array[left + i];

        for (int j = 0; j < n2; j++)
            rightArray[j] = array[mid + 1 + j];

        int k = left, l = 0, m = 0;

        while (l < n1 && m < n2)
        {
            if (leftArray[l] <= rightArray[m])
            {
                array[k] = leftArray[l];
                l++;
            }
            else
            {
                array[k] = rightArray[m];
                m++;
            }
            k++;
        }

        while (l < n1)
        {
            array[k] = leftArray[l];
            l++;
            k++;
        }

        while (m < n2)
        {
            array[k] = rightArray[m];
            m++;
            k++;
        }
    }
}

2. Using C# Built-in Sorting Method

In C#, using the built-in sorting methods allows for a simpler way to solve the problem.

using System;

class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());
        int[] numbers = new int[n];

        for (int i = 0; i < n; i++)
        {
            numbers[i] = int.Parse(Console.ReadLine());
        }

        Array.Sort(numbers);

        foreach (var num in numbers)
        {
            Console.WriteLine(num);
        }
    }
}

Analysis and Conclusion

This problem is a great opportunity to learn the basics of sorting. We learned how sorting occurs through Merge Sort and C#’s built-in methods, and which method is more efficient. Since this type of problem is frequently encountered in coding tests, it is advisable to practice often.

In the next post, we will cover more complex sorting problems or algorithms. I hope you continue to study and improve your abilities as a coding tester!

Hello everyone! Today, we will deeply explore how to implement Dijkstra’s algorithm using C# and how to solve algorithmic problems through it. This tutorial will provide a step-by-step explanation of the basic concepts of the algorithm, problem definition, C# code implementation, and optimization methods.

1. What is Dijkstra’s Algorithm?

Dijkstra’s algorithm is a method for finding the shortest path in a graph. It is particularly useful when the weights of all edges are greater than or equal to zero. This algorithm efficiently calculates the shortest path from a specific node to all other nodes.

The basic principle of Dijkstra’s algorithm is as follows:

1. Initialize the distance values from the starting node. Set the distance of the starting node to 0 and all other nodes to infinity.
2. When moving from the current node to adjacent nodes, update the distance value if the distance to reach the adjacent node through the current node is shorter.
3. Repeat this process until all nodes are visited.
4. Finally, output the shortest distances to each node.

2. Problem Definition

The problem we will solve together is “Finding the Shortest Path.” There is a given graph consisting of nodes and edges, and we need to find the shortest distance from a specific starting node to all other nodes.

The input for the problem is as follows:

• First line: Number of nodes N (1 <= N <= 100,000) and number of edges M (1 <= M <= 200,000)
• From the second line onward for M lines: Information for each edge (A, B, C), where A and B are node numbers and C is the distance between the two nodes.
• Last line: Starting node K

The output is the shortest distance to each node. Nodes that cannot be reached are marked as “INF”.

3. Algorithm Design

To implement Dijkstra’s algorithm in C#, we can use the following libraries and data structures:

• Priority Queue: Used for managing distance information.
• Graph Representation: Represent the graph using an adjacency list or an adjacency matrix.
• Distance Array: Used to store the shortest distance values for each node.

4. C# Code Implementation

First, let’s take a look at the complete code to implement Dijkstra’s algorithm in C#.

using System;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        int[] input = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int N = input[0];
        int M = input[1];

        List>[] graph = new List>[N + 1];
        for (int i = 0; i <= N; i++)
            graph[i] = new List>();

        for (int i = 0; i < M; i++)
        {
            input = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            graph[input[0]].Add(new Tuple(input[1], input[2]));
            graph[input[1]].Add(new Tuple(input[0], input[2])); // For undirected graphs
        }

        int K = int.Parse(Console.ReadLine());
        int[] distances = Dijkstra(graph, N, K);

        for (int i = 1; i <= N; i++)
        {
            Console.WriteLine(distances[i] == int.MaxValue ? "INF" : distances[i].ToString());
        }
    }

    static int[] Dijkstra(List>[] graph, int N, int start)
    {
        int[] distances = new int[N + 1];
        for (int i = 1; i <= N; i++)
            distances[i] = int.MaxValue;
        distances[start] = 0;

        PriorityQueue priorityQueue = new PriorityQueue();
        priorityQueue.Enqueue(start, 0);

        while (priorityQueue.Count > 0)
        {
            var current = priorityQueue.Dequeue();
            int currentNode = current.Item1;
            int currentDistance = current.Item2;

            if (currentDistance > distances[currentNode]) continue;

            foreach (var edge in graph[currentNode])
            {
                int nextNode = edge.Item1;
                int weight = edge.Item2;

                if (distances[currentNode] + weight < distances[nextNode])
                {
                    distances[nextNode] = distances[currentNode] + weight;
                    priorityQueue.Enqueue(nextNode, distances[nextNode]);
                }
            }
        }

        return distances;
    }
}

5. Code Explanation

The code above implements Dijkstra’s algorithm. Let’s explain the function of each part in detail.

5.1. Main Function

The main function takes input, constructs the graph, and then calls the Dijkstra function.

• Receives input to determine N and M.
• Initializes the graph represented as a list for each node.
• Constructs the graph based on the given edge information.
• Takes the starting node K as input and calls the Dijkstra function to return the shortest distance array.
• Outputs the shortest distance for each node. If unreachable, it displays “INF”.

5.2. Dijkstra Function

The Dijkstra function contains the core logic of the Dijkstra algorithm.

• Initializes the distance array.
• Uses a priority queue to store current node information and selects the node with the smallest distance.
• Performs shortest distance updates for adjacent nodes of the current node.

6. Test Cases

Now, let’s create some test cases to verify if Dijkstra’s algorithm works correctly.

6.1. Test Case 1

Input:

5 6
1 2 2
1 3 3
2 3 1
2 4 5
3 4 2
3 5 1
1

Output:

0
2
3
5
4

6.2. Test Case 2

Input:

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

Output:

0
3
1
4

7. Summary and Optimization

In this tutorial, we implemented Dijkstra’s algorithm using C# and solved the shortest path problem. To improve the efficiency of Dijkstra’s algorithm, we can consider the following optimization methods:

• Using a Fibonacci heap instead of a priority queue can achieve a worst-case time complexity of O(V log V).
• Using an adjacency list for sparse graphs can save memory.

The topic covered in the next tutorial will be “Bellman-Ford Algorithm”, which is useful for finding the shortest path when negative weight edges exist. I hope this helps improve your algorithm skills! Thank you.