Category: C# Coding Test Tutorials

C# Coding Test Course, Finding the Lowest Common Ancestor 2

Author: [Author Name]

Written on: [Date]

Introduction

In this course, we will discuss how to solve the ‘Lowest Common Ancestor (LCA)’ problem using the C# programming language.
The Lowest Common Ancestor refers to the deepest node that is a common ancestor of two nodes in a binary tree.
We will explain the process of solving this problem in detail using specific algorithms and data structures.

Problem Description

The problem is to find the lowest common ancestor of two given nodes A and B in a given binary tree.
The binary tree is non-empty, and all nodes have unique values.
Additionally, nodes A and B are assumed to exist in the tree.

Input Format

                - First line: Number of nodes in the tree N (1 ≤ N ≤ 10^5)
                - Second line: N space-separated integers representing the node values of the tree
                - Third line: Two integers A, B (A, B exist in the tree)

Output Format

                - The value of the lowest common ancestor of A and B

Example Problem

                Input:
                7
                3 5 1 6 2 0 8
                5 1

                Output:
                3

Solution Method

There are various methods to find the lowest common ancestor, but it is generally effective to explore the tree
using Depth First Search (DFS) while considering the depth of the tree.
In the case of a Binary Search Tree (BST), it is possible to efficiently find the ancestor by determining which
subtree A and B belong to. However, in a general binary tree, utilizing information from the parent nodes is necessary.

Algorithm Design

The main steps of the algorithm are as follows.

  1. Construct the tree given in the input.
  2. Store the parent node for each node in a map or array.
  3. Record the path from node A to the root.
  4. Record the path from node B to the root.
  5. Find the first common node in the two paths.

C# Code Implementation

Below is the C# code implementing the above algorithm. 

                
using System;
using System.Collections.Generic;

class TreeNode {
    public int Value;
    public TreeNode Left, Right;
    
    public TreeNode(int value) {
        this.Value = value;
        this.Left = null;
        this.Right = null;
    }
}

class Program {
    static Dictionary nodeMap = new Dictionary();
    static TreeNode root;

    public static void Main(string[] args) {
        int N = Convert.ToInt32(Console.ReadLine());
        int[] values = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int A = Convert.ToInt32(Console.ReadLine());
        int B = Convert.ToInt32(Console.ReadLine());

        BuildTree(values, 0, N);
        TreeNode ancestor = FindLCA(root, A, B);
        Console.WriteLine(ancestor.Value);
    }

    static TreeNode BuildTree(int[] values, int index, int N) {
        if (index < N) {
            TreeNode node = new TreeNode(values[index]);
            nodeMap[values[index]] = node;
            node.Left = BuildTree(values, 2 * index + 1, N);
            node.Right = BuildTree(values, 2 * index + 2, N);
            return node;
        }
        return null;
    }

    static TreeNode FindLCA(TreeNode node, int A, int B) {
        if (node == null) return null;
        if (node.Value == A || node.Value == B) return node;

        TreeNode leftLCA = FindLCA(node.Left, A, B);
        TreeNode rightLCA = FindLCA(node.Right, A, B);

        if (leftLCA != null && rightLCA != null) return node;
        return (leftLCA != null) ? leftLCA : rightLCA;
    }
}

Code Explanation

1. TreeNode Class: Represents a node in a binary tree. Each node has a value and left and right children.

2. Main Method: The starting point of the program. It receives input from the user and builds the tree, then finds the LCA.

3. BuildTree Method: Constructs the binary tree using an array. It is called recursively to build the tree.

4. FindLCA Method: Recursively traverses the tree to find the lowest common ancestor of the two nodes A and B.

Time Complexity

The time complexity of this algorithm is O(N).
It increases proportionally to the number of nodes since it visits each node once while traversing the tree.
The space complexity is also O(N), which is due to the space used by the recursive call stack and for storing node information.

Conclusion

In this course, we learned how to solve the lowest common ancestor problem using C#.
By understanding the principles of the algorithm and implementing the code, you would have gained insights on how to effectively tackle similar tree problems in coding tests.
In the next session, we will delve deeper into other data structures or algorithm problems.
Thank you.

C# Coding Test Course, Finding the Kth Number in an Array

Hello, everyone preparing for coding tests! Today, we will discuss a problem where we need to find the K-th largest number in an array. This problem is one of the common types that frequently appears in coding tests and is very helpful in understanding the concepts of arrays and sorting. In this article, we will explain the problem in detail and step by step, we will explore how to solve it using C#.

Problem Description

We have a problem of finding the K-th largest number in a given array. The array consists of integers, and K is an index starting from 1. It is assumed that the objects are sorted in size order. For example, if the array is [3, 1, 2, 4, 5] and K is 2, then the 2nd largest number is 4.

Input

  • The first line contains the size of the array N (1 ≤ N ≤ 1000).
  • The second line contains N integers. (Each integer is -10000 ≤ x ≤ 10000)
  • The third line contains the integer K. (1 ≤ K ≤ N)

Output

Print the K-th largest number.

Example Input

5
3 1 2 4 5
2

Example Output

4

Approach to the Problem

To solve this problem, we can follow these steps:

  1. Sort the given array.
  2. Find the K-th largest number in the sorted array.

Step 1: Sort the Array

There are several ways to sort an array, but we can use the Array.Sort() method provided by C#. This method sorts the array in ascending order by default.

Step 2: Find the K-th Number

Finding the K-th number in the sorted array is quite simple. If K is 2, the K-th number will be the one located at the index K – 1 in the sorted array.

C# Code Implementation

Now let’s implement the C# code based on the above methods:


using System;

class KthLargestNumber
{
    static void Main()
    {
        // Get input
        int N = int.Parse(Console.ReadLine());
        int[] arr = new int[N];

        string[] input = Console.ReadLine().Split();
        for (int i = 0; i < N; i++)
        {
            arr[i] = int.Parse(input[i]);
        }

        int K = int.Parse(Console.ReadLine());

        // Sort the array
        Array.Sort(arr);

        // Find the K-th number
        Console.WriteLine(arr[N - K]);
    }
}

Code Explanation

1. The using System; statement allows us to use various classes from the System namespace.

2. int N = int.Parse(Console.ReadLine()); reads the input from the first line and stores the size of the array N.

3. int[] arr = new int[N]; declares an integer array of length N.

4. Console.ReadLine().Split(); method receives the input from the second line and stores the space-separated strings in an array.

5. Array.Sort(arr); sorts the array in ascending order.

6. Console.WriteLine(arr[N - K]); prints the K-th largest number. Here, the number at the index N – K corresponds to the K-th largest number.

Time Complexity Analysis

The time complexity of this problem is determined by the process of sorting the array. The time complexity of the sorting algorithm is O(N log N) in the worst case. The process of finding the K-th number takes O(1), so the overall time complexity is O(N log N).

Conclusion

In this tutorial, we learned how to find the K-th number in an array. We learned to use array sorting and indexing to solve the problem. This problem frequently appears in coding tests, so I encourage you to solve various variations to improve your skills. I will return with more informative topics in the next tutorial. Thank you!

References

C# Coding Test Course, Helping the Less Fortunate

Hello! Today, we will take some time to solve an easy algorithm problem related to helping the less fortunate using C#. In this course, we will cover various aspects including problem definition, approach to solving the problem, algorithm implementation, and optimized code.

Problem Definition

Problem: Achieving the Donation Goal for Helping the Less Fortunate

Given a donation goal, this problem determines whether several individuals can achieve this goal through their donations.

Input:

  • goal: The donation target amount (integer)
  • donations: The donation history of contributors (array of integers)

Output:

  • Return true if the donation goal can be achieved, otherwise return false.

Approach to Solving the Problem

The core of this problem is to check whether we can reach the target amount with the given donations. We can solve the problem using the following steps:

  1. Calculate the sum of the amounts donated by the contributors.
  2. If the sum is greater than or equal to the target amount, we have achieved the goal, so return true.
  3. Otherwise, return false.

Algorithm Implementation

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

using System;

class Program
{
    static void Main(string[] args)
    {
        int goal = 100000; // Target amount
        int[] donations = { 25000, 30000, 50000, 35000 }; // Contributors' donation history

        bool result = CanAchieveGoal(goal, donations);
        Console.WriteLine(result ? "We have achieved the goal!" : "We did not achieve the goal.");
    }

    static bool CanAchieveGoal(int goal, int[] donations)
    {
        int total = 0;
        foreach (var donation in donations)
        {
            total += donation;
        }
        return total >= goal;
    }
}

Code Analysis

The above code first defines the target amount and the contributors’ donation history. Then, it calculates the total amount of donations using the CanAchieveGoal function, compares it with the target amount, and prints the final result. This code is straightforward and easy to understand.

Performance Optimization

The current code has a time complexity of O(n) depending on the length of the donation history. There won’t be performance issues even if the number of contributors increases. However, if further optimization is needed, for example, a way to confirm early that we have reached the target amount, we can stop the loop when the total reaches the goal.

static bool CanAchieveGoal(int goal, int[] donations)
{
    int total = 0;
    foreach (var donation in donations)
    {
        total += donation;
        if (total >= goal)
        {
            return true; // Confirm the goal has been achieved early
        }
    }
    return false;
}

Conclusion

In this article, we solved an algorithm problem to determine whether we can achieve a donation goal related to helping the less fortunate using C#. We explored various approaches, implementation code, and performance optimization. Such problems are often presented in actual coding tests, so sufficient practice is necessary.

Finally, I hope that through this course, you learned valuable insights about donations and the basics of C# programming. I will return with more problems in the next session. Thank you!

C# Coding Test Course, Floyd-Warshall

Date: October 1, 2023

Introduction

Algorithm problems are one of the important elements in coding tests, especially graph algorithms are used effectively in many situations.
In this article, we will solve a problem using the Floyd-Warshall algorithm.
The Floyd-Warshall algorithm is used to find the shortest path between all pairs of vertices and mainly uses dynamic programming techniques.

Problem Description

Problem: Finding the Shortest Path

All campuses of your university are represented as vertices, and the roads connecting the campuses are represented as edges.
Calculate the distance of the shortest path from campus A to campus B. Follow the input format below. 

            Input:
            - First line: Total number of campuses N (1 ≤ N ≤ 100)
            - Second line: Number of roads M (1 ≤ M ≤ 10000)
            - The next M lines: Information about each road in the form (A, B, C), meaning the length of the road from A to B is C.
            
            Output:
            - Print the distance matrix of the shortest paths between campuses.

Algorithm Overview

The Floyd-Warshall algorithm is based on the following fundamental principle.
For every pair of vertices (i, j), it compares the distance from i to j through k with the direct path distance and updates the shortest path. 

            D[i][j] = min(D[i][j], D[i][k] + D[k][j])

This algorithm has a time complexity of O(N^3) and can efficiently compute the shortest paths between all pairs of vertices.

Problem Solving Process

Step 1: Input Handling

To handle input, initialize the array and receive road information.
After initializing the distances to infinity, set the distances between directly connected campuses.
This creates the initial distance matrix D.

Step 2: Implementing the Floyd-Warshall Algorithm

Update the minimum distances between each pair of campuses through three nested loops.
In each iteration, check if there is a shorter path via k, and if so, update the distance matrix.

Step 3: Output the Result

Print the updated distance matrix. Remaining infinite distances indicate unreachable campuses.

C# Code Implementation

            
            using System;
            using System.Linq;

            class Program
            {
                const int INF = 987654321; // Define infinity value

                static void Main(string[] args)
                {
                    // Input handling
                    int N = int.Parse(Console.ReadLine());
                    int M = int.Parse(Console.ReadLine());

                    int[,] D = new int[N + 1, N + 1];

                    // Initialize distance array
                    for (int i = 1; i <= N; i++)
                    {
                        for (int j = 1; j <= N; j++)
                        {
                            if (i == j) D[i, j] = 0;
                            else D[i, j] = INF; // Initialize to infinity
                        }
                    }

                    // Input road information into distance array
                    for (int i = 0; i < M; i++)
                    {
                        var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                        int A = input[0], B = input[1], C = input[2];
                        D[A, B] = Math.Min(D[A, B], C); // Set to minimum value as there could be multiple roads
                    }

                    // Floyd-Warshall algorithm
                    for (int k = 1; k <= N; k++)
                    {
                        for (int i = 1; i <= N; i++)
                        {
                            for (int j = 1; j <= N; j++)
                            {
                                D[i, j] = Math.Min(D[i, j], D[i, k] + D[k, j]);
                            }
                        }
                    }

                    // Output results
                    for (int i = 1; i <= N; i++)
                    {
                        for (int j = 1; j <= N; j++)
                        {
                            if (D[i, j] == INF) Console.Write("INF ");
                            else Console.Write(D[i, j] + " ");
                        }
                        Console.WriteLine();
                    }
                }
            }

Conclusion

In this article, we discussed the shortest path problem using the Floyd-Warshall algorithm.
This algorithm is effective in finding the shortest paths between all pairs of vertices and is widely used in real situations.
It is important to understand and apply the Floyd-Warshall algorithm to solve various graph problems.

Author: Algorithm Blogger

C# Coding Test Course, Finding the Average

Hello! Today, we will discuss an algorithm problem related to calculating the average for those preparing for coding tests with C#. Many companies use algorithm problems when hiring developers, so it’s important to prepare well. In this lecture, we will define the problem, design the algorithm, implement the code in C#, and conduct performance analysis.

Problem Definition

The problem is to calculate the average of a given integer array. The array consists of various positive integers, and the final result should be expressed up to two decimal places. The method for calculating the average is as follows:

Add all the elements of the given array and divide by the number of elements to find the average.

Input Format

  • Length N (1 ≤ N ≤ 1000)
  • Integer array A = [a1, a2, …, aN] (1 ≤ ai ≤ 10,000)

Output Format

  • Average value (up to two decimal places)

Problem Examples

Example 1

Input: 5, array [10, 20, 30, 40, 50]

Output: 30.00

Example 2

Input: 3, array [5, 15, 25]

Output: 15.00

Algorithm Design

The algorithm to solve this problem is very simple. First, we sum all elements of the given array and then divide the sum by the number of elements in the array to calculate the average. To maintain two decimal places, we will use the Math.Round method.

Algorithm Steps:

  1. Receive an integer array.
  2. Calculate the total sum of the array.
  3. Divide the total sum by the number of elements (N) to find the average.
  4. Round the average to two decimal places and return it.

C# Code Implementation

Now, let’s implement the C# code based on the above algorithm.


using System;

class AverageCalculator
{
    public static void Main(string[] args)
    {
        // Get input
        Console.Write("Please enter the number of integers: ");
        int N = int.Parse(Console.ReadLine());
        int[] numbers = new int[N];

        Console.WriteLine("Please enter the integer array:");
        for (int i = 0; i < N; i++)
        {
            numbers[i] = int.Parse(Console.ReadLine());
        }

        double average = CalculateAverage(numbers);
        Console.WriteLine($"Average: {average:F2}");  // Output up to two decimal places
    }

    private static double CalculateAverage(int[] array)
    {
        double sum = 0;
        foreach (int number in array)
        {
            sum += number; // Calculate total sum of the array
        }
        return Math.Round(sum / array.Length, 2); // Round the average to two decimal places
    }
}

Code Explanation

The above C# code has the following structure:

  1. It receives the number of integers and the array elements from the user.
  2. It calculates the average in the CalculateAverage method.
  3. Finally, it prints the average up to two decimal places.

Performance Analysis

The time complexity of this problem is O(N). This is because it visits each element of the array only once. The space complexity is O(1) as it uses very little additional storage space. Therefore, this algorithm continues to work effectively even as the input data size increases.

Conclusion

Through this lecture, we learned how to solve the average calculation problem using C#. Since this is a commonly occurring problem in coding tests, it is important to practice thoroughly and ensure that it works correctly with various inputs. Keep solving more algorithm problems in the future!