Home/Blog/Interview Prep/Crack the top 45 C# data structure questions

Crack the top 45 C# data structure questions

Ryan Thelin

Mar 09, 2021

23 min read

content

Complexity Measures Questions 1. Big O complexity: Nested Addition 2. Big O complexity: Nested Multiplication 3. Big O with nested multiplication (advanced)C# Arrays 4. Remove even integers from an array 5. Find the minimum value in an array 6. Maximum subarray sum C# Linked Lists 7. Insertion at Tail 8. Remove Duplicates from a Linked List 9. Join two linked lists C# Stacks and Queues 10. Generate binary numbers from 1 to N 11. Implement a queue using stacks 12. Find the lowest value in a stack C# Graphs 13. Implement Depth First Search (DFS)14. Find a “Mother Vertex” in a graph 15. Remove edge Keep practicing C#.C# Trees and Tries 16. Find the lowest value in a Binary Search Tree 17. Find the height of a BST 18. 2-3 Trees vs. BST 19. Insertion in a Trie 20. Total words in a Trie C# Heaps and Hashing 21. Implement a Max-Heap 22. Find k smallest elements in an array 23. Trie vs. Hash Table 24. Subset Array Checker 25. Find two pairs with an equal sum 20 more questions for a C# coding interview What to learn next Continue reading about C#

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Data structure questions are some of the most commonly asked in coding interviews. These questions test your ability to implement, optimize, and adapt data structures to solve a unique situation. It’s essential to review common questions before your coding interview to ensure you’re not caught off guard with an unfamiliar question.

Today, we’ll help you brush up on your data structure skills by reviewing 45 of the top data structure questions you should practice before your next interview.

Here’s what we’ll cover today:

Complexity Measures Questions
C# Arrays
C# Linked Lists
C# Stacks and Queues
C# Graphs
C# Trees and Tries
C# Heaps and Hashing
20 more questions for C# coding interview
What to learn next

Ace your C# interview the first time
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Data Structures for Coding Interviews in C#

using System; 
namespace Chapter_1
{
    class Challenge_6
    {
        static void Main(string[] args)
        {
            int n = 10;
            int sum = 0;
            float pie = 3.14f;
            for (int i = 0; i < n; i++)
            {
                int j = 1;
                Console.WriteLine(pie);
                while (j < i)
                {
                    sum += 1;
                    j *= 2;
                }
            }
            Console.WriteLine(sum);
            return;
        }
    }
}

using System;
namespace Chapter_1
{
    class Challenge_7
    {
        static void Main(string[] args)
        {
            int n = 10;    // you can change the value of n
            int sum = 0;
            int j = 1;
            float pie = 3.14f;
            for (int i = 0; i < n; i++)
            {
                Console.WriteLine(pie);
                while (j < i)
                {
                    sum += 1;
                    j *= 2;
                }
            }
            Console.WriteLine(sum );
        }
    }
}

4. Remove even integers from an array#

Implement a function removeEven( int[]Arr, int size ), which takes an array arr and its size and removes all the even elements from the given array.

For example:

// Input: Arr = [1,2,4,5,10,6,3]
// Output: Arr = [1,5,3]

using System; 
namespace chapter_2
{
    class Solution
    {
        static int [] removeEven(int[]Arr, int size)
        {
            int m = 0;
            for (int i = 0; i < size; i++)
            {
                if (Arr[i] % 2 != 0)  // if odd number found
                {
                    Arr[m] = Arr[i];   //inserting odd values in the array
                    ++m;
                }
            }
            int[] temp = new int[m];
            for (int i = 0; i < m; i++)
                temp[i] = Arr[i];
         
            Arr = temp;
            return Arr;  // returning the array after removing the odd numbers
        }
        //Remove Event Integers from an Array:
        static void Main(string[] args)
        {
            int[] arr = null;      // declaring array
            arr = new int[10];   // memory allocation
            Console.Write("Before remove even: ");
            for (int i = 0; i < 10; i++)
            {
                arr[i] = i;      // assigning values
                Console.Write(arr[i] + " ");
            }
            Console.WriteLine("");
            arr = removeEven(arr, 10);   // calling removeEven
            Console.Write("After remove even: ");
            for (int i = 0; i < 5; i++)
            {
                Console.Write( arr[i] + " ");    // prinitng array
            }
            Console.WriteLine(""); 
            return ;
        }
    }
}

Time Complexity: $O(n)$

This solution first checks if the first element of Arr is odd. Then it appends this element to the start of the array Arr; otherwise, it jumps to the next element. This repeats until the end of the array Arr is reached while keeping the count of total odd numbers m in Arr. Next, we make a temporary array, temp, to store all odd numbers.

From there, we delete the memory allocated to Arr, and point it to the temp array. Lastly, we return the array Arr that is, which now contains only odd elements.

5. Find the minimum value in an array#

Implement a function findMinimum(int arr[], int size), which takes an array arr and its size and returns the smallest number in the given array.

For example:

// Input: arr = [9,2,3,6]
// Output: 2

using System;
namespace chapter_2
{
    class Solution
    {
        // Find Minimum Value in an Array
        static int findMinimum(int []arr, int size)
        {
            int minimum = arr[0];
            //At every index compare its value with the minimum and if it is less 
            //then make that index value the new minimum value”
            for (int i = 0; i < size; i++)
            {
                if (arr[i] < minimum)
                {
                    minimum = arr[i];
                }
            }
            return minimum;
        }
        static void Main(string[] args)
        {
            int size = 4;
            int []arr = { 9, 2, 3, 6 };
            Console.Write("Array : ");
            for (int i = 0; i < size; i++)
                Console.Write(arr[i] + " ");
            Console.WriteLine("");
            int min = findMinimum(arr, size);
            Console.WriteLine("Minimum in the Array: " + min );
           
            return ;
        }
    }
}

using System;
namespace chapter_2
{
    class Solution
    {
        //Maximum Sum Subarray
        static int maxSumArr(int []arr, int arrSize)
        {
            if (arrSize < 1)
            {
                return 0;
            }
            int currMax = arr[0];
            int globalMax = arr[0];
            for (int i = 1; i < arrSize; i++)
            {
                if (currMax < 0)
                {
                    currMax = arr[i];
                }
                else
                {
                    currMax += arr[i];
                }
                if (globalMax < currMax)
                {
                    globalMax = currMax;
                }
            }
            return globalMax;
        }
        static void Main(string[] args)
        {
            int []arr = { -4, 2, -5, 1, 2, 3, 6, -5, 1 };
            int arrSize = arr.Length;
            int maxSum = maxSumArr(arr, arrSize);
            Console.WriteLine("Maximum contiguous sum is " + maxSum);
            return;
        }
    }
}

Time Complexity: $O(n)$

This solution uses Kadane’s algorithm to scan the entire array.

Take a look at Kadane’s algorithm in pseudocode:

currMax = A[0]
globalMax = A[0]
for i = 1 -> size of A
    if currMax is less than 0
        then currMax = A[i]
    otherwise 
        currMax = currMax + A[i]
    if globalMax is less than currMax 
        then globalMax = currMax

At each position in the array, we find the maximum sum of the subarray ending there. This is achieved by keeping a currMax for the current array index and a globalMax. By the end, we know that the value of globalMax will be the highest subarray, regardless of the value of currMax.

C# Linked Lists#

Below are the Node and LinkedList classes available for you to use throughout this section:

using System;

public class LinkedList
{
    public class Node
    {
        internal int data; //Data to store (could be int,string,object etc)
        internal Node nextElement; //Pointer to next element

        public Node()
        {
            //Constructor to initialize nextElement of newlyCreated Node
            nextElement = null;
        }
    };
    Node head;

    public LinkedList()
    {
        head = null;
    }
    public bool IsEmpty()
    {
        if (head == null) //Check whether the head points to null
            return true;
        else
            return false;
    }
    //Function inserts a value/new Node as the first Element of list
    public void InsertAtHead(int value)
    {
        Node newNode = new Node(); //creating a new node
        newNode.data = value;
        newNode.nextElement = head; //Linking newNode to head's pointer
        head = newNode; //head pointing to the start of the list
        Console.Write(value + " Inserted !    ");
    }
    public bool PrintList()
    {        // Printing the list
        if (IsEmpty())
        {
            Console.Write("List is Empty!");
            return false;
        }
        Node temp = head;        // starting from head node
        Console.Write("List : ");

        while (temp != null)
        {     // traveresing through the List
            Console.Write(temp.data + "->");
            temp = temp.nextElement;    // moving on to the temp's nextElement
        }
        Console.WriteLine("null ");    // printing null at the end
        return true;
    }
}

7. Insertion at Tail#

Create a function insertAtTail() that takes an integer, adds the integer to the end of a linked list, and returns the updated linked list. The new node will point to null.

Solution and Explanation

main.cs

LinkedList.cs

using System;
namespace chapter_3
{
    public class LinkedList
    {
        public class Node
        {
            internal int data; //Data to store (could be int,string,object etc)
            internal Node nextElement; //Pointer to next element

            public Node()
            {
                //Constructor to initialize nextElement of newlyCreated Node
                nextElement = null;
            }
        };
        Node head;

        public LinkedList()
        {
            head = null;
        }
        public Node GetHead()
        {
            return head;
        }
        bool IsEmpty()
        {
            if (head == null) //Check whether the head points to null
                return true;
            else
                return false;
        }
        public bool PrintList()
        {
            if (IsEmpty())
            {
                Console.Write("List is Empty!");
                return false;
            }
            Node temp = head;
            Console.Write("List : ");

            while (temp != null)
            {
                Console.Write(temp.data + "->");
                temp = temp.nextElement;
            }
            Console.WriteLine("null ");
            return true;
        }
        public void InsertAtHead(int value)
        {
            Node newNode = new Node();
            newNode.data = value;
            newNode.nextElement = head; //Linking newNode to head's nextNode
            head = newNode;
            
        }
        public string Elements()
        {
            string elementsList = "";
            Node start = head;

            while (start != null)
            {
                elementsList += start.data.ToString();
                elementsList += "->";
                start = start.nextElement;
            }
            elementsList += "null";
            return elementsList;
        }
        public void InsertAtTail(int value)
        {
            if (IsEmpty())
            { // inserting first element in list
                InsertAtHead(value); // head will point to first element of the list      
            }
            else
            {
                Node newNode = new Node(); // creating new node
                Node last = head; // last pointing at the head of the list

                while (last.nextElement != null)
                { // traversing through the list
                    last = last.nextElement;
                }

                newNode.data = value;
                Console.Write(value + " Inserted!    ");
                newNode.nextElement = null; // point last's nextElement to nullptr
                last.nextElement = newNode; // adding the newNode at the end of the list
            }
        }
    }
}

main.cs

LinkedList.cs

using System;
namespace chapter_3
{
    public class LinkedList
    {
        public class Node
        {
            internal int data; //Data to store (could be int,string,object etc)
            internal Node nextElement; //Pointer to next element

            public Node()
            {
                //Constructor to initialize nextElement of newlyCreated Node
                nextElement = null;
            }
        };
        Node head;

        public LinkedList()
        {
            head = null;
        }
        public Node GetHead()
        {
            return head;
        }
        bool IsEmpty()
        {
            if (head == null) //Check whether the head points to null
                return true;
            else
                return false;
        }
        public bool PrintList()
        {
            if (IsEmpty())
            {
                Console.Write("List is Empty!");
                return false;
            }
            Node temp = head;
            Console.Write("List : ");

            while (temp != null)
            {
                Console.Write(temp.data + "->");
                temp = temp.nextElement;
            }
            Console.WriteLine("null ");
            return true;
        }
        public void InsertAtHead(int value)
        {
            Node newNode = new Node();
            newNode.data = value;
            newNode.nextElement = head; //Linking newNode to head's nextNode
            head = newNode;
            Console.Write(value + " Inserted!");
        }
       public string Elements()
        { // this function will return all values of linked List
            string elementsList = "";
            Node start = head;
            Node check = head;

            elementsList += start.data.ToString();
            elementsList += "->";
            start = start.nextElement;

            while (start != null && start.data != check.data)
            {
                elementsList += start.data.ToString();
                elementsList += "->";
                start = start.nextElement;
            }

            if (start == null)
                return elementsList + "null";

            elementsList += check.data.ToString();
            return elementsList;
        }
       
        public string RemoveDuplicates()
        {
            Node start, startNext = null;
            start = head;

            /* Pick elements one by one */
            while ((start != null) && (start.nextElement != null))
            {
                startNext = start;

                /* Compare the picked element with rest 
                   of the elements */
                while (startNext.nextElement != null)
                {
                    /* If duplicate then delete it */
                    if (start.data == startNext.nextElement.data)
                    {
                        
                        // skipping elements from the list to be deleted
                        startNext.nextElement = startNext.nextElement.nextElement;
                       
                    }
                    else
                        startNext = startNext.nextElement; // pointing to next of startNext
                }
                start = start.nextElement;
            }
            return Elements();
        }     
    }
}

main.cs

LinkedList.cs

using System;
namespace chapter_3
{
    public class LinkedList
    {
        public class Node
        {
            internal int data; //Data to store (could be int,string,object etc)
            internal Node nextElement; //Pointer to next element

            public Node()
            {
                //Constructor to initialize nextElement of newlyCreated Node
                nextElement = null;
            }
        };
        Node head;

        public LinkedList()
        {
            head = null;
        }
        public Node GetHead()
        {
            return head;
        }
        bool IsEmpty()
        {
            if (head == null) //Check whether the head points to null
                return true;
            else
                return false;
        }
        public bool PrintList()
        {
            if (IsEmpty())
            {
                Console.Write("List is Empty!");
                return false;
            }
            Node temp = head;
            Console.Write("List : ");

            while (temp != null)
            {
                Console.Write(temp.data + "->");
                temp = temp.nextElement;
            }
            Console.WriteLine("null ");
            return true;
        }
        public void InsertAtHead(int value)
        {
            Node newNode = new Node();
            newNode.data = value;
            newNode.nextElement = head; //Linking newNode to head's nextNode
            head = newNode;
           
        }
       public string Elements()
        { // this function will return all values of linked List
            string elementsList = "";
            Node start = head;
            Node check = head;

            elementsList += start.data.ToString();
            elementsList += "->";
            start = start.nextElement;

            while (start != null && start.data != check.data)
            {
                elementsList += start.data.ToString();
                elementsList += "->";
                start = start.nextElement;
            }

            if (start == null)
                return elementsList + "null";

            elementsList += check.data.ToString();
            return elementsList;
        }
        
        public string RemoveDuplicates()
        {
            Node start, startNext = null;
            start = head;

            /* Pick elements one by one */
            while ((start != null) && (start.nextElement != null))
            {
                startNext = start;

                /* Compare the picked element with rest 
                   of the elements */
                while (startNext.nextElement != null)
                {
                    /* If duplicate then delete it */
                    if (start.data == startNext.nextElement.data)
                    {
                        
                        // skipping elements from the list to be deleted
                        startNext.nextElement = startNext.nextElement.nextElement;
                       
                    }
                    else
                        startNext = startNext.nextElement; // pointing to next of startNext
                }
                start = start.nextElement;
            }
            return Elements();

        }
        public string Union(LinkedList list1, LinkedList list2)
        {
            //Return other List if one of them is empty
            if (list1.IsEmpty())
                return list2.Elements();
            else if (list2.IsEmpty())
                return list1.Elements();

            Node start = list1.head; // starting from head of list 1

            //Traverse first list till the last element
            while (start.nextElement != null)
            {
                start = start.nextElement;
            }

            //Link last element of first list to the first element of second list
            start.nextElement = list2.head; // appendinf list2 with list 1
            return list1.RemoveDuplicates(); // removing duplicates from list and return list
        }
    }
}


using System;
using System.Diagnostics;
class myStack
{
    int[] stackArr;
    int capacity;
    int numElements;
    public myStack(int size)
    {
        capacity = size;
        stackArr = new int[size];
        Debug.Assert(stackArr != null);
        numElements = 0;
    }
    public bool isEmpty()
    {
        return (numElements == 0);
    }
    public int getTop()
    {
        return (numElements == 0 ? -1 : stackArr[numElements - 1]);
    }
    public bool push(int value)
    {
        if (numElements < capacity)
        {
            stackArr[numElements] = value;
            numElements++;
            return true;
        }
        else
        {
            Console.WriteLine("Stack Full.");
            return false;
        }
    }
    public int pop()
    {
        if (numElements == 0)
        {
            Console.WriteLine("Stack Empty");
            return -1;
        }
        else
        {
            numElements--;
            return stackArr[numElements];
        }
    }
    public int getSize()
    {
        return numElements;
    }
    public void showStack()
    {
        int i = 0;
        while (i < numElements)
        {
            Console.Write("\t" + stackArr[numElements - 1 - i]);
            i++;
        }
        Console.WriteLine("");
    }
}

using System;
using System.Collections;
namespace chapter_4
{
    class Challenge_1
    {
        //Start with Enqueuing 1.
        //Dequeue a number from queue and append 0 to it and enqueue it back to queue.
        //Perform step 2 but with appending 1 to the original number and enqueue back to queue.
        //Queue takes integer values so before enqueueing it make sure to convert string to integer.
        //Size of Queue should be 1 more than number because for a single number we're enqueuing two
        //variations of it , one with appended 0 while other with 1 being appended.
        static string [] findBin(int n)
        {
            string [] result = new string[n];
            Queue queue = new Queue();
            queue.Enqueue(1);
            string s1, s2;
            for (int i = 0; i < n; i++)
            {
                result[i] = queue.Dequeue().ToString();
                s1 = result[i] + "0";
                s2 = result[i] + "1";
                queue.Enqueue(Convert.ToInt32(s1));
                queue.Enqueue(Convert.ToInt32(s2));
            }
            return result;
        }
        static void Main(string[] args)
        {
            var output = findBin(4);
            for (int i = 0; i < 4; i++)
                Console.Write(output[i] + " ");
           
            return;
        }
    }
}

Time Complexity: $O(n)$

On line 17, 1 is enqueued as a starting point. Then, a number is dequeued from the queue and stored in the result array to generate a binary number sequence.

On lines 22-23, 0 and 1 are appended to it to produce the next numbers, which are then also enqueued to the queue on lines 24-25. The queue takes integer values. Before enqueueing, the solution makes sure to convert the string to an integer.

The size of the queue should be one more than n because you are enqueuing two variations of each number; one is appended with 0, and one with 1.

using System;
using System.Collections.Generic;
namespace chapter_4
{
    //Create Stack => myStack stack = new myStack(5);
    //where 5 is size of stack
    //Push Function => stack.push(int);
    //Pop Function => stack.pop();
    //TopFunction => stack.getTop();
    //Helper Functions => stack.isEmpty();
    class newQueue
    {
        
        Stack <int> mainStack;
        Stack <int> tempStack;
    
        public newQueue()
        {
            //Can use size from argument to create stack
            mainStack = new Stack<int> ();
            tempStack = new Stack<int> ();
        }
       
        void EnQueue(int value)
        {
            //Traverse elements from mainStack to tempStack
            //Push given value to mainStack
            //Traverse back the elements from tempStack to mainStack
            while (mainStack.Count != 0)
            {
                tempStack.Push(mainStack.Pop());
            }
            mainStack.Push(value);
            while (tempStack.Count != 0)
            {
                mainStack.Push(tempStack.Pop());
            }
        }
        int DeQueue()
        {
            //If mainStack is empty then we have no elements.
            //else return top element of mainStack as we always put oldest entered
            //element at the top of mainStack
            if (mainStack.Count == 0)
                return -1;
            else
                return mainStack.Pop();
        }
        static void Main(string[] args)
        {
            newQueue queue = new newQueue();
            queue.EnQueue(1);
            queue.EnQueue(2);
            queue.EnQueue(3);
            queue.EnQueue(4);
            queue.EnQueue(5);
            Console.WriteLine( queue.DeQueue());
            Console.WriteLine( queue.DeQueue());
            Console.WriteLine( queue.DeQueue());
            Console.WriteLine(queue.DeQueue());
            Console.WriteLine( queue.DeQueue());
            Console.WriteLine(queue.DeQueue());
            return ;
        }
    };
   
}

Time Complexity: $O(n)$

This approach, uses two stacks. The mainStack stores the queue elements and the tempStack acts as a temporary buffer to provide queue functionality.

Make sure that after every enqueue operation, the newly inserted value is at the bottom of the main stack.

Before insertion, all the other elements are transferred to tempStack and naturally, their order is reversed. The new element is added into the empty mainStack. Finally, all the elements are pushed back into mainStack and tempStack becomes empty.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace chapter_4
{
    class newStack
    {
        //We will use two stacks mainStack to hold origional values
        //and minStack to hold minimum values. Top of minStack will always
        //be the minimum value from mainStack
        Stack <int> mainStack;
        Stack<int> minStack;
        public newStack(int size)
        {
            mainStack = new Stack<int>(size);
            minStack = new Stack<int>(size);
        }
        //Removes and returns value from newStack
        //1. Pop element from minStack to make it sync with mainStack.
        //2. Pop element from mainStack and return that value.
        int pop()
        {
            minStack.Pop();
            return mainStack.Pop();
        }
        //Pushes values into newStack
        //1. Push value in mainStack and check value with the top value of minStack
        //2. If value is greater than top, then push top in minStack
        //else push value in minStack.
        void push(int value)
        {
            mainStack.Push(value);
            if ( (minStack.Count != 0) && (value > minStack.Peek()) )
            {
                minStack.Push(minStack.Peek());
            }
            else
                minStack.Push(value);
        }
        //Returns minimum value from newStack in O(1) Time
        int min()
        {
            return minStack.Peek();
        }
        static void Main(string[] args)
        {
            newStack stack = new newStack(6);
            stack.push(5);
            stack.push(2);
            stack.push(4);
            stack.push(1);
            stack.push(3);
            stack.push(9);
            Console.WriteLine(stack.min());
            stack.pop();
            stack.pop();
            stack.pop();
            Console.WriteLine(stack.min());
            return ;
        }
    }
}

Time Complexity: $O(1)$

The whole implementation relies on the existence of two stacks: minStack and mainStack.

mainStack holds the actual stack with all the elements, whereas minStack is a stack whose top always contains the current minimum value in the stack.

Whenever push is called, mainStack simply inserts the new value at the top.

However, minStack checks the value being pushed. If minStack is empty, this value is pushed into it and becomes the current minimum. If minStack already has elements in it, the value is compared with the top element.

If the value is lower than the top of minStack, it is pushed in and becomes the new minimum. Otherwise, the top remains the same.

Due to all these safeguards put in place, the min function only needs to return the value at the top of minStack.

main.cs

Graph.cs

LinkedList.cs

using System;

namespace chapter_5
{
    public class LinkedList
    {
        public class Node
        {
            internal int data; //Data to store (could be int,string,object etc)
            internal Node nextElement; //Pointer to next element

            public Node()
            {
                //Constructor to initialize nextElement of newlyCreated Node
                nextElement = null;
            }
        };
        Node head;

        public LinkedList()
        {
            head = null;
        }
        public Node GetHead()
        {
            return head;
        }
        bool IsEmpty()
        {
            if (head == null) //Check whether the head points to null
                return true;
            else
                return false;
        }
        public bool PrintList()
        {
            if (IsEmpty())
            {
                Console.Write("List is Empty!");
                return false;
            }
            Node temp = head;
            Console.Write("List : ");

            while (temp != null)
            {
                Console.Write(temp.data + "->");
                temp = temp.nextElement;
            }
            Console.WriteLine("null ");
            return true;
        }
        public void InsertAtHead(int value)
        {
            Node newNode = new Node();
            newNode.data = value;
            newNode.nextElement = head; //Linking newNode to head's nextNode
            head = newNode;

        }
        public string Elements()
        { // this function will return all values of linked List
            string elementsList = "";
            Node start = head;
            Node check = head;

            elementsList += start.data.ToString();
            elementsList += "->";
            start = start.nextElement;

            while (start != null && start.data != check.data)
            {
                elementsList += start.data.ToString();
                elementsList += "->";
                start = start.nextElement;
            }

            if (start == null)
                return elementsList + "null";

            elementsList += check.data.ToString();
            return elementsList;
        }
        public void InsertAtTail(int value)
        {
            if (IsEmpty())
            { // inserting first element in list
                InsertAtHead(value); // head will point to first element of the list      
            }
            else
            {
                Node newNode = new Node(); // creating new node
                Node last = head; // last pointing at the head of the list

                while (last.nextElement != null)
                { // traversing through the list
                    last = last.nextElement;
                }

                newNode.data = value;
                Console.Write(value + " Inserted!    ");
                newNode.nextElement = null; // point last's nextElement to nullptr
                last.nextElement = newNode; // adding the newNode at the end of the list
            }
        }

        // function to check if element exists in the list
        public bool Search(int value)
        {
            Node temp = head; // pointing temp to the head

            while (temp != null)
            {
                if (temp.data == value)
                { // if passed value matches with temp's data
                    return true;
                }
                temp = temp.nextElement; // pointig to temp's nextElement
            }
            return false; // if not found
        }
  
        public bool Delete(int value)
        {
            bool deleted = false; //returns true if the node is deleted, false otherwise

            if (IsEmpty())
            { //check if the list is empty
                Console.WriteLine("List is Empty");
                return deleted; //deleted will be false
            }

            //if list is not empty, start traversing it from the head
            Node currentNode = head; //currentNode to traverse the list
            Node previousNode = null; //previousNode starts from null

            if (currentNode.data == value)
            { // deleting value of head
                deleted = DeleteAtHead();
                Console.WriteLine(value + " deleted!");
                deleted = true; // true because value found and deleted
                return deleted; //returns true if the node is deleted
            }
            previousNode = currentNode;
            currentNode = currentNode.nextElement; // pointing current to current's nextElement
                                                   //Traversing/Searching for Node to Delete
            while (currentNode != null)
            {

                //Node to delete is found
                if (value == currentNode.data)
                {
                    // pointing previousNode's nextElement to currentNode's nextElement
                    previousNode.nextElement = currentNode.nextElement;
                    // delete currentNode;
                    currentNode = previousNode.nextElement;
                    deleted = true;
                    break;
                }
                previousNode = currentNode;
                currentNode = currentNode.nextElement; // pointing current to current's nextElement
            }
            //deleted is true only when value is found and deleted
            if (deleted == false)
            {
                Console.WriteLine(value + " does not exist!");
            }
            else
            {
                Console.WriteLine(value + " deleted!");
            }
            return deleted;
        } //end of delete()
        bool DeleteAtHead()
        {
            if (IsEmpty())
            { // check if list is empty
                Console.WriteLine("List is Empty");
                return false;
            }
           
            head = head.nextElement; //nextNode points to head's nextElement

            
            return true;
        }
    
        public int Length()
        {
            Node current = head; // Start from the first element
            int count = 0; // in start count is 0

            while (current != null)
            { // Traverse the list and count the number of nodes
                count++; // increment everytime as element is found
                current = current.nextElement; // pointing to current's nextElement
            }
            return count;
        }
  

        public string Reverse()
        {
            Node previous = null; //To keep track of the previous element, will be used in swapping links
            Node current = head; //firstElement
            Node next = null;

            //While Traversing the list, swap links
            while (current != null)
            {
                next = current.nextElement;
                current.nextElement = previous;
                previous = current;
                current = next;
            }

            head = previous; // pointing head to start of the list
            return Elements(); // calling elements to return a string of values in list
        }
      
        public bool DetectLoop()
        {
            Node slow = head, fast = head; //starting from head of the list

            while ((slow != null) && (fast != null) && (fast.nextElement != null)) //checking if all elements exist 
            {
                slow = slow.nextElement;
                fast = fast.nextElement.nextElement;

                /* If slow and fast meet at some point then there
                    is a loop */
                if (slow == fast)
                {
                    // Return 1 to indicate that loop is found */
                    return true;
                }
            }
            // Return 0 to indicate that ther is no loop*/
            return false;
        }
        public void InsertLoop()
        {
            Node temp = head;
            // traversing to get to last element of the list
            while (temp.nextElement != null)
            {
                temp = temp.nextElement;
            }
            temp.nextElement = head; // pointing last element to head of the list
        }
    
        public int FindMid()
        {
            //list is empty
            if (IsEmpty())
                return 0;

            //currentNode starts at the head
            Node currentNode = head;

            if (currentNode.nextElement == null)
            {
                //Only 1 element exist in array so return its value.
                return currentNode.data;
            }

            Node midNode = currentNode; //midNode starts at head
            currentNode = currentNode.nextElement.nextElement; //currentNode moves two steps forward

            //Move midNode (Slower) one step at a time
            //Move currentNode (Faster) two steps at a time
            //When currentNode reaches at end, midNode will be at the middle of List
            while (currentNode != null)
            {       // traversing from head to end

                midNode = midNode.nextElement;

                currentNode = currentNode.nextElement;     // pointing to current's next
                if (currentNode != null)
                    currentNode = currentNode.nextElement;     // pointing to current's next

            }
            if (midNode != null)     // pointing at middle of the list
                return midNode.data;
            return 0;
        }
    
        public string RemoveDuplicates()
        {
            Node start, startNext = null;
            start = head;

            /* Pick elements one by one */
            while ((start != null) && (start.nextElement != null))
            {
                startNext = start;

                /* Compare the picked element with rest 
                   of the elements */
                while (startNext.nextElement != null)
                {
                    /* If duplicate then delete it */
                    if (start.data == startNext.nextElement.data)
                    {

                        // skipping elements from the list to be deleted
                        startNext.nextElement = startNext.nextElement.nextElement;

                    }
                    else
                        startNext = startNext.nextElement; // pointing to next of startNext
                }
                start = start.nextElement;
            }
            return Elements();

        }

       
        public string Union(LinkedList list1, LinkedList list2)
        {
            //Return other List if one of them is empty
            if (list1.IsEmpty())
                return list2.Elements();
            else if (list2.IsEmpty())
                return list1.Elements();

            Node start = list1.head; // starting from head of list 1

            //Traverse first list till the last element
            while (start.nextElement != null)
            {
                start = start.nextElement;
            }

            //Link last element of first list to the first element of second list
            start.nextElement = list2.head; // appendinf list2 with list 1
            return list1.RemoveDuplicates(); // removing duplicates from list and return list
        }

      
        //To Find nth node from end of list
        public int FindNth(int n)
        {

            if (IsEmpty()) // if list is empty return -1
                return -1;

            int length = 0;
            Node currentNode = head; // pointing to head of the list

            // finding the length of the list
            while (currentNode != null)
            {
                currentNode = currentNode.nextElement;
                length++;
            }

            //Find the Node which is at (len - n) position from start
            currentNode = head;
            int position = length - n;

            if (position < 0 || position > length) // check if out of the range of the list
                return -1;

            int count = 0;
            // traversing till the nth Element of the list
            while (count != position)
            { // finding the position of the element
                currentNode = currentNode.nextElement;
                count++;
            }

            if (currentNode != null) // if node exists
                return currentNode.data;

            return -1;

        }
    }

}

main.cs

Graph.cs

LinkedList.cs

using System;
using System.Collections.Generic;
namespace chapter_5
{
    class Challenge_2
    {
        static void dfs_helper(Graph g, int source, bool [] visited, ref string result)
        {
            if (g.getVertices() < 1)
            {
                return;
            }
            //Create Stack(Implemented in previous chapters) for Depth First Traversal and Push source in it
            Stack<int> stack = new Stack<int> { };
            stack.Push(source);
            visited[source] = true;
            int current_node;
            LinkedList.Node temp;
            //Traverse while stack is not empty
            while (stack.Count != 0)
            {
                //Pop a vertex/node from stack and add it to the result
                current_node = stack.Pop();
                result += current_node.ToString() ;
                //Get adjacent vertices to the current_node from the array,
                //and if they are not already visited then push them in the stack
                temp = (g.getArray())[current_node].GetHead();
                while (temp != null)
                {
                    if (!visited[temp.data])
                    {
                        stack.Push(temp.data);
                        //Visit the node
                        visited[temp.data] = true;
                    }
                    temp = temp.nextElement;
                }
            } //end of while
        }
        static string dfsTraversal(Graph g)
        {
            string result = "";
            //Bool Array to hold the history of visited nodes
            //Make a node visited whenever you push it into stack
            bool [] visited = new bool[g.getVertices()];
            for (int i = 0; i < g.getVertices(); i++)
            {
                visited[i] = false;
            }
            for (int i = 0; i < g.getVertices(); i++)
            {
                if (!visited[i])
                    dfs_helper(g, i, visited, ref result);
            }
            //delete[] visited;
            visited = null;
            return result;
        }
        static void Main(string[] args)
        {
            Graph g = new Graph(7);
            g.addEdge(1, 2);
            g.addEdge(1, 3);
            g.addEdge(2, 4);
            g.addEdge(2, 5);
            Console.WriteLine (dfsTraversal(g));
           
        }
    }
}

Time Complexity: $O(V + N)$

The approach is very similar to that of the BFS solution. However, instead of a queue, use a stack since it follows the Last In First Out (LIFO) approach. You will see how that is useful in this situation.

dfsTraversal calls the helper function dfs_helper on every vertex, which is not visited. dfs_helper starts from source and each node is pushed into the stack. Whenever a node is popped, it is marked “visited” in the visited array, and its adjacent nodes are pushed into the stack.

The stack is helpful because it pops out the new adjacent nodes instead of returning the previous nodes that you pushed in.

main.cs

Graph.cs

LinkedList.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Runtime.Remoting.Messaging;
using System.Text;
using System.Threading.Tasks;

namespace chapter_5
{
    class Graph
    {
        int vertices;
        LinkedList [] array;

      
       public Graph(int v)
       {
            array = new LinkedList[v];
            vertices = v;
            for(int i = 0; i < v; i++)
            {
                array[i] = new LinkedList();
            }
        }

        public void addEdge(int source, int destination)
        {
            if (source < vertices && destination < vertices)
                array[source].InsertAtHead(destination);
        }

        public void printGraph()
        {
            Console.WriteLine("Adjacency List of Directed Graph");
            LinkedList.Node temp;
            for (int i = 0; i < vertices; i++)
            {
                Console.Write( "|" + i + "| => ");
                temp = (array[i]).GetHead();

                while (temp != null)
                {
                    Console.Write("[" + temp.data + "] -> ");
                    temp = temp.nextElement;
                }
                Console.WriteLine("NULL");
            }
        }

        public LinkedList [] getArray()
        {
            return array;
        }

        public int getVertices()
        {
            return vertices;
        }
    }
}

Time Complexity: $O(V + E)$

This solution is based in Kosaraju’s Strongly Connected Component Algorithm.

Initially, we run the Depth First Search on the whole graph in a loop on line 17. The DFS ensures that all the nodes in the graph are visited. If the graph is disconnected, the visited array will still have some vertices, which haven’t been set to true.

The theory is that the last vertex visited in the recursive DFS will be the mother vertex because at the last vertex, all slots in visited would be true (DFS only stops when all nodes are visited); hence, keeping track of this last vertex using lastV.

Then reset the visited array, and run the DFS only on lastV. If it visits all nodes, it is a mother vertex. If not, a mother vertex does not exist.

The only limitation in this algorithm is that it can only detect one mother vertex even if others exist.

main.cs

LinkedList.cs

Graph.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace chapter_5
{
    public class LinkedList
    {
        public class Node
        {
            internal int data; //Data to store (could be int,string,object etc)
            internal Node nextElement; //Pointer to next element

            public Node()
            {
                //Constructor to initialize nextElement of newlyCreated Node
                nextElement = null;
            }
        };
        Node head;

        public LinkedList()
        {
            head = null;
        }
        public Node GetHead()
        {
            return head;
        }
        bool IsEmpty()
        {
            if (head == null) //Check whether the head points to null
                return true;
            else
                return false;
        }
        public bool PrintList()
        {
            if (IsEmpty())
            {
                Console.Write("List is Empty!");
                return false;
            }
            Node temp = head;
            Console.Write("List : ");

            while (temp != null)
            {
                Console.Write(temp.data + "->");
                temp = temp.nextElement;
            }
            Console.WriteLine("null ");
            return true;
        }
        public void InsertAtHead(int value)
        {
            Node newNode = new Node();
            newNode.data = value;
            newNode.nextElement = head; //Linking newNode to head's nextNode
            head = newNode;

        }
        public string Elements()
        { // this function will return all values of linked List
            string elementsList = "";
            Node start = head;
            Node check = head;

            elementsList += start.data.ToString();
            elementsList += "->";
            start = start.nextElement;

            while (start != null && start.data != check.data)
            {
                elementsList += start.data.ToString();
                elementsList += "->";
                start = start.nextElement;
            }

            if (start == null)
                return elementsList + "null";

            elementsList += check.data.ToString();
            return elementsList;
        }
        public void InsertAtTail(int value)
        {
            if (IsEmpty())
            { // inserting first element in list
                InsertAtHead(value); // head will point to first element of the list      
            }
            else
            {
                Node newNode = new Node(); // creating new node
                Node last = head; // last pointing at the head of the list

                while (last.nextElement != null)
                { // traversing through the list
                    last = last.nextElement;
                }

                newNode.data = value;
                Console.Write(value + " Inserted!    ");
                newNode.nextElement = null; // point last's nextElement to nullptr
                last.nextElement = newNode; // adding the newNode at the end of the list
            }
        }
  
        // function to check if element exists in the list
        public bool Search(int value)
        {
            Node temp = head; // pointing temp to the head

            while (temp != null)
            {
                if (temp.data == value)
                { // if passed value matches with temp's data
                    return true;
                }
                temp = temp.nextElement; // pointig to temp's nextElement
            }
            return false; // if not found
        }
        
        public bool Delete(int value)
        {
            bool deleted = false; //returns true if the node is deleted, false otherwise

            if (IsEmpty())
            { //check if the list is empty
                Console.WriteLine("List is Empty");
                return deleted; //deleted will be false
            }

            //if list is not empty, start traversing it from the head
            Node currentNode = head; //currentNode to traverse the list
            Node previousNode = null; //previousNode starts from null

            if (currentNode.data == value)
            { // deleting value of head
                deleted = DeleteAtHead();
                Console.WriteLine(value + " deleted!");
                deleted = true; // true because value found and deleted
                return deleted; //returns true if the node is deleted
            }
            previousNode = currentNode;
            currentNode = currentNode.nextElement; // pointing current to current's nextElement
                                                   //Traversing/Searching for Node to Delete
            while (currentNode != null)
            {

                //Node to delete is found
                if (value == currentNode.data)
                {
                    // pointing previousNode's nextElement to currentNode's nextElement
                    previousNode.nextElement = currentNode.nextElement;
                    // delete currentNode;
                    currentNode = previousNode.nextElement;
                    deleted = true;
                    break;
                }
                previousNode = currentNode;
                currentNode = currentNode.nextElement; // pointing current to current's nextElement
            }
            //deleted is true only when value is found and deleted
            if (deleted == false)
            {
                Console.WriteLine(value + " does not exist!");
            }
            else
            {
                Console.WriteLine(value + " deleted!");
            }
            return deleted;
        } //end of delete()
        bool DeleteAtHead()
        {
            if (IsEmpty())
            { // check if list is empty
                Console.WriteLine("List is Empty");
                return false;
            }
           
            head = head.nextElement; //nextNode points to head's nextElement

            
            return true;
        }
 
        public int Length()
        {
            Node current = head; // Start from the first element
            int count = 0; // in start count is 0

            while (current != null)
            { // Traverse the list and count the number of nodes
                count++; // increment everytime as element is found
                current = current.nextElement; // pointing to current's nextElement
            }
            return count;
        }
      

        public string Reverse()
        {
            Node previous = null; //To keep track of the previous element, will be used in swapping links
            Node current = head; //firstElement
            Node next = null;

            //While Traversing the list, swap links
            while (current != null)
            {
                next = current.nextElement;
                current.nextElement = previous;
                previous = current;
                current = next;
            }

            head = previous; // pointing head to start of the list
            return Elements(); // calling elements to return a string of values in list
        }
      
        public bool DetectLoop()
        {
            Node slow = head, fast = head; //starting from head of the list

            while ((slow != null) && (fast != null) && (fast.nextElement != null)) //checking if all elements exist 
            {
                slow = slow.nextElement;
                fast = fast.nextElement.nextElement;

                /* If slow and fast meet at some point then there
                    is a loop */
                if (slow == fast)
                {
                    // Return 1 to indicate that loop is found */
                    return true;
                }
            }
            // Return 0 to indeciate that ther is no loop*/
            return false;
        }
        public void InsertLoop()
        {
            Node temp = head;
            // traversing to get to last element of the list
            while (temp.nextElement != null)
            {
                temp = temp.nextElement;
            }
            temp.nextElement = head; // pointing last element to head of the list
        }
      
        public int FindMid()
        {
            //list is empty
            if (IsEmpty())
                return 0;

            //currentNode starts at the head
            Node currentNode = head;

            if (currentNode.nextElement == null)
            {
                //Only 1 element exist in array so return its value.
                return currentNode.data;
            }

            Node midNode = currentNode; //midNode starts at head
            currentNode = currentNode.nextElement.nextElement; //currentNode moves two steps forward

            //Move midNode (Slower) one step at a time
            //Move currentNode (Faster) two steps at a time
            //When currentNode reaches at end, midNode will be at the middle of List
            while (currentNode != null)
            {       // traversing from head to end

                midNode = midNode.nextElement;

                currentNode = currentNode.nextElement;     // pointing to current's next
                if (currentNode != null)
                    currentNode = currentNode.nextElement;     // pointing to current's next

            }
            if (midNode != null)     // pointing at middle of the list
                return midNode.data;
            return 0;
        }
       
        public string RemoveDuplicates()
        {
            Node start, startNext = null;
            start = head;

            /* Pick elements one by one */
            while ((start != null) && (start.nextElement != null))
            {
                startNext = start;

                /* Compare the picked element with rest 
                   of the elements */
                while (startNext.nextElement != null)
                {
                    /* If duplicate then delete it */
                    if (start.data == startNext.nextElement.data)
                    {

                        // skipping elements from the list to be deleted
                        startNext.nextElement = startNext.nextElement.nextElement;

                    }
                    else
                        startNext = startNext.nextElement; // pointing to next of startNext
                }
                start = start.nextElement;
            }
            return Elements();

        }

      
        public string Union(LinkedList list1, LinkedList list2)
        {
            //Return other List if one of them is empty
            if (list1.IsEmpty())
                return list2.Elements();
            else if (list2.IsEmpty())
                return list1.Elements();

            Node start = list1.head; // starting from head of list 1

            //Traverse first list till the last element
            while (start.nextElement != null)
            {
                start = start.nextElement;
            }

            //Link last element of first list to the first element of second list
            start.nextElement = list2.head; // appendinf list2 with list 1
            return list1.RemoveDuplicates(); // removing duplicates from list and return list
        }

        //To Find nth node from end of list
        public int FindNth(int n)
        {

            if (IsEmpty()) // if list is empty return -1
                return -1;

            int length = 0;
            Node currentNode = head; // pointing to head of the list

            // finding the length of the list
            while (currentNode != null)
            {
                currentNode = currentNode.nextElement;
                length++;
            }

            //Find the Node which is at (len - n) position from start
            currentNode = head;
            int position = length - n;

            if (position < 0 || position > length) // check if out of the range of the list
                return -1;

            int count = 0;
            // traversing till the nth Element of the list
            while (count != position)
            { // finding the position of the element
                currentNode = currentNode.nextElement;
                count++;
            }

            if (currentNode != null) // if node exists
                return currentNode.data;

            return -1;

        }
    }
}

main.cs

BST.cs

namespace chapter_6
{
    // Node class with a value, left child node, and the rithe child node
    class Node
    {
       public int value;
        public Node leftChild;
       public Node rightChild;
        public Node()
        {
            value = 0;
            leftChild = null;
            rightChild = null;
        }

        public Node(int val)
        {
            value = val;
            leftChild = null;
            rightChild = null;
        }
    };
    //BinarySearchTree class that contains the root node.
    class BinarySearchTree
    {
        Node root;
        public BinarySearchTree(int rootValue)
        {
            root = new Node(rootValue);
        }
        public BinarySearchTree()
        {
            root = null;
        }
        public Node getRoot()
        {
            return root;
        }
    };
}

main.cs

BST.cs

using System;

namespace chapter_6
{
    class Node
    {
        public int value;
        public Node leftChild;
        public Node rightChild;
        public Node()
        {
            value = 0;
            leftChild = null;
            rightChild = null;
        }

        public Node(int val)
        {
            value = val;
            leftChild = null;
            rightChild = null;
        }
    }
    class BinarySearchTree
    {
        Node root;
        public BinarySearchTree(int rootValue)
        {
            root = new Node(rootValue);
        }
        public BinarySearchTree()
        {
            root = null;
        }
        public Node getRoot()
        {
            return root;
        }
        public Node insert(Node currentNode, int val)
        {
            if (currentNode == null)
            {
                return new Node(val);
            }
            else if (currentNode.value > val)
            {

                currentNode.leftChild = insert(currentNode.leftChild, val);

            }
            else
            {
                currentNode.rightChild = insert(currentNode.rightChild, val);
            }

            return currentNode;

        }

        public void insertBST(int value)
        {

            if (getRoot() == null)
            {
                root = new Node(value);
                return;
            }
            insert(this.getRoot(), value);
        }

        public void inOrderPrint(Node currentNode)
        {
            if (currentNode != null)
            {
                inOrderPrint(currentNode.leftChild);
                Console.WriteLine(currentNode.value);
                inOrderPrint(currentNode.rightChild);
            }
        }
        Node searchBST(int value)
        {

            //let's start with the root 
            Node currentNode = root;
            while ((currentNode != null) && (currentNode.value != value))
            {
                //the loop will run until the currentNode IS NOT null
                //and until we get to our value
                if (value < currentNode.value)
                {
                    //traverse to the left subtree
                    currentNode = currentNode.leftChild;
                }
                else
                { //traverse to the right subtree
                    currentNode = currentNode.rightChild;

                }

            }
            //after the loop, we'll have either the searched value
            //or null in case the value was not found
            return currentNode;
        }
        public Node search(Node currentNode, int value)
        {
            if (currentNode == null)
                return null;
            else if (currentNode.value == value)
                return currentNode;
            else if (currentNode.value > value)
                return search(currentNode.leftChild, value);
            else
                return search(currentNode.rightChild, value);
        }
       
        public bool deleteBST(int value)
        {
            return Delete(root, value);
        }
        public bool Delete(Node currentNode, int value)
        {

            if (root == null)
            {
                return false;
            }

            Node parent = root; //To Store parent of currentNode
            while ((currentNode != null) && (currentNode.value != value))
            {
                parent = currentNode;
                if (currentNode.value > value)
                    currentNode = currentNode.leftChild;
                else
                    currentNode = currentNode.rightChild;

            }

            if (currentNode == null)
                return false;
            else if ((currentNode.leftChild == null) && (currentNode.rightChild == null))
            {
                //1. Node is Leaf Node
                //if that leaf node is the root (a tree with just root)
                if (root.value == currentNode.value)
                {
                    
                    root = null;
                    return true;
                }
                else if (currentNode.value < parent.value)
                {
                  
                    parent.leftChild = null;
                    return true;
                }
                else
                {
                    
                    parent.rightChild = null;
                    return true;
                }

            }
            else if (currentNode.rightChild == null)
            {

                if (root.value == currentNode.value)
                {
                   
                    root = currentNode.leftChild;
                    return true;
                }
                else if (currentNode.value < parent.value)
                {
                    
                    parent.leftChild = currentNode.leftChild;
                    return true;
                }
                else
                {
                   
                    parent.rightChild = currentNode.leftChild;
                    return true;
                }

            }
            else if (currentNode.leftChild == null)
            {
                if (root.value == currentNode.value)
                {
                  
                    root = currentNode.rightChild;
                    return true;
                }
                else if (currentNode.value < parent.value)
                {
                   
                    parent.leftChild = currentNode.rightChild;
                    return true;
                }
                else
                {
                  
                    parent.rightChild = currentNode.rightChild;
                    return true;
                }

            }
            else
            {
                //Find Least Value Node in right-subtree of current Node
                Node leastNode = findLeastNode(currentNode.rightChild);
                //Set CurrentNode's Data to the least value in its right-subtree
                int tmp = leastNode.value;
                Delete(root, tmp);
                currentNode.value = leastNode.value;
                //Delete the leafNode which had the least value


                return true;
            }

        }

        //Helper function to find least value node in right-subtree of currentNode
        public Node findLeastNode(Node currentNode)
        {

            Node temp = currentNode;

            while (temp.leftChild != null)
            {
                temp = temp.leftChild;
            }

            return temp;

        }
        public void preOrderPrint(Node currentNode)
        {
            if (currentNode != null)
            {
                Console.WriteLine(currentNode.value);
                preOrderPrint(currentNode.leftChild);
                preOrderPrint(currentNode.rightChild);
            }

        }
      
    }
}

Time Complexity: $O(h)$

This solution is recursive to increase efficiency. The sorted structure of a BST makes this solution easier because we just have to find the left-most node.

First, we check if the root is null. If it is, we return -1(lines 10-11). Otherwise, we check to see if the left child of the current node is null. If it is, then this root is the leftmost node, and you return the value there (lines 12-13).

If a left node exists, call the findMin() function on it (lines 14-15).

main.cs

BST.cs

using System;

namespace chapter_6
{
    class Node
    {
        public int value;
        public Node leftChild;
        public Node rightChild;
        public Node()
        {
            value = 0;
            leftChild = null;
            rightChild = null;
        }

        public Node(int val)
        {
            value = val;
            leftChild = null;
            rightChild = null;
        }
    }
    class BinarySearchTree
    {
        Node root;
        public BinarySearchTree(int rootValue)
        {
            root = new Node(rootValue);
        }
        public BinarySearchTree()
        {
            root = null;
        }
        public Node getRoot()
        {
            return root;
        }
        public Node insert(Node currentNode, int val)
        {
            if (currentNode == null)
            {
                return new Node(val);
            }
            else if (currentNode.value > val)
            {

                currentNode.leftChild = insert(currentNode.leftChild, val);

            }
            else
            {
                currentNode.rightChild = insert(currentNode.rightChild, val);
            }

            return currentNode;

        }

        public void insertBST(int value)
        {

            if (getRoot() == null)
            {
                root = new Node(value);
                return;
            }
            insert(this.getRoot(), value);
        }

        public void inOrderPrint(Node currentNode)
        {
            if (currentNode != null)
            {
                inOrderPrint(currentNode.leftChild);
                Console.WriteLine(currentNode.value);
                inOrderPrint(currentNode.rightChild);
            }
        }
        Node searchBST(int value)
        {

            //let's start with the root 
            Node currentNode = root;
            while ((currentNode != null) && (currentNode.value != value))
            {
                //the loop will run until the currentNode IS NOT null
                //and until we get to our value
                if (value < currentNode.value)
                {
                    //traverse to the left subtree
                    currentNode = currentNode.leftChild;
                }
                else
                { //traverse to the right subtree
                    currentNode = currentNode.rightChild;

                }

            }
            //after the loop, we'll have either the searched value
            //or null in case the value was not found
            return currentNode;
        }
        public Node search(Node currentNode, int value)
        {
            if (currentNode == null)
                return null;
            else if (currentNode.value == value)
                return currentNode;
            else if (currentNode.value > value)
                return search(currentNode.leftChild, value);
            else
                return search(currentNode.rightChild, value);
        }
       
        public bool deleteBST(int value)
        {
            return Delete(root, value);
        }
        public bool Delete(Node currentNode, int value)
        {

            if (root == null)
            {
                return false;
            }

            Node parent = root; //To Store parent of currentNode
            while ((currentNode != null) && (currentNode.value != value))
            {
                parent = currentNode;
                if (currentNode.value > value)
                    currentNode = currentNode.leftChild;
                else
                    currentNode = currentNode.rightChild;

            }

            if (currentNode == null)
                return false;
            else if ((currentNode.leftChild == null) && (currentNode.rightChild == null))
            {
                //1. Node is Leaf Node
                //if that leaf node is the root (a tree with just root)
                if (root.value == currentNode.value)
                {
                    
                    root = null;
                    return true;
                }
                else if (currentNode.value < parent.value)
                {
                  
                    parent.leftChild = null;
                    return true;
                }
                else
                {
                    
                    parent.rightChild = null;
                    return true;
                }

            }
            else if (currentNode.rightChild == null)
            {

                if (root.value == currentNode.value)
                {
                   
                    root = currentNode.leftChild;
                    return true;
                }
                else if (currentNode.value < parent.value)
                {
                    
                    parent.leftChild = currentNode.leftChild;
                    return true;
                }
                else
                {
                   
                    parent.rightChild = currentNode.leftChild;
                    return true;
                }

            }
            else if (currentNode.leftChild == null)
            {
                if (root.value == currentNode.value)
                {
                  
                    root = currentNode.rightChild;
                    return true;
                }
                else if (currentNode.value < parent.value)
                {
                   
                    parent.leftChild = currentNode.rightChild;
                    return true;
                }
                else
                {
                  
                    parent.rightChild = currentNode.rightChild;
                    return true;
                }

            }
            else
            {
                //Find Least Value Node in right-subtree of current Node
                Node leastNode = findLeastNode(currentNode.rightChild);
                //Set CurrentNode's Data to the least value in its right-subtree
                int tmp = leastNode.value;
                Delete(root, tmp);
                currentNode.value = leastNode.value;
                //Delete the leafNode which had the least value


                return true;
            }

        }

        //Helper function to find least value node in right-subtree of currentNode
        public Node findLeastNode(Node currentNode)
        {

            Node temp = currentNode;

            while (temp.leftChild != null)
            {
                temp = temp.leftChild;
            }

            return temp;

        }
        public void preOrderPrint(Node currentNode)
        {
            if (currentNode != null)
            {
                Console.WriteLine(currentNode.value);
                preOrderPrint(currentNode.leftChild);
                preOrderPrint(currentNode.rightChild);
            }

        }
        int findMin(Node rootNode)
        {
            // So keep traversing (in order) towards left till you reach leaf node,
            //and then return leaf node's value
            if (rootNode == null)
                return -1;
            else if (rootNode.leftChild == null)
                return rootNode.value;
            else
                return findMin(rootNode.leftChild);
        }
    }
}

main.cs

Trie.cs

using System;

namespace chapter_7
{
    class TrieNode
    {
        const int ALPHABET_SIZE = 26;

        public TrieNode[] children = new TrieNode[ALPHABET_SIZE];
        public bool isEndWord;

        public TrieNode()
        {
            this.isEndWord = false;
            for (int i = 0; i < ALPHABET_SIZE; i++)
            {
                this.children[i] = null; ;
            }
        }
        //Function to unMark the currentNode as Leaf
        public void markAsLeaf()
        {
            this.isEndWord = true;
        }
        //Function to unMark the currentNode as Leaf
        public void unMarkAsLeaf()
        {
            this.isEndWord = false;
        }

    }
    class Trie
    {
        TrieNode root;

        public Trie()
        {
            root = new TrieNode();
        }
        //Function to get the index of a character 't'
        public int getIndex(char t)
        {
            return t - 'a';
        }
        //Function to insert a key,value pair in the Trie
        public void insertNode(string key)
        {
            //Empty string is not allowed
            if (key == string.Empty)
                return;

            //using transform() function and ::tolower in STL to convert 'key' to lowercase
            //transform(key.begin(), key.end(), key.begin(), ::tolower);
            key = key.ToLower();
            TrieNode currentNode = root;
            int index = 0;

            //Iterate the trie with the given character index,
            //If the index points to NULL
            //simply create a TrieNode and go down a level
            for (int level = 0; level < key.Length; level++)
            {
                index = getIndex(key[level]);

                if (currentNode.children[index] == null)
                {
                    currentNode.children[index] = new TrieNode();
                   Console.WriteLine( key[level] + " inserted" );
                }
                currentNode = currentNode.children[index];
            }

            //Mark the end character as leaf node
            currentNode.markAsLeaf();
            Console.WriteLine( "'" + key + "' inserted" );
        }
        //Function to search given key in Trie
        public bool searchNode(string key)
        {
            return false;
        }
        //Function to delete given key from Trie
        public bool deleteNode(string key)
        {
            return false;
        }
    } 
}

main.cs

Trie.cs

using System;

namespace chapter_7
{
    class TrieNode
    {
        const int ALPHABET_SIZE = 26;

        public TrieNode[] children = new TrieNode[ALPHABET_SIZE];
        public bool isEndWord;

        public TrieNode()
        {
            this.isEndWord = false;
            for (int i = 0; i < ALPHABET_SIZE; i++)
            {
                this.children[i] = null; ;
            }
        }
        //Function to unMark the currentNode as Leaf
        public void markAsLeaf()
        {
            this.isEndWord = true;
        }
        //Function to unMark the currentNode as Leaf
        public void unMarkAsLeaf()
        {
            this.isEndWord = false;
        }

    }
    class Trie
    {
        const int ALPHABET_SIZE = 26;
        TrieNode root;

        public Trie()
        {
            root = new TrieNode();
        }
        public TrieNode getRoot()
        {
            return root;
        }
        //Function to get the index of a character 't'
        public int getIndex(char t)
        {
            return t - 'a';
        }
        //Function to insert a key,value pair in the Trie
        public void insertNode(string key)
        {
            //Empty string is not allowed
            if (key == string.Empty)
                return;

            //using transform() function and ::tolower in STL to convert 'key' to lowercase
            //transform(key.begin(), key.end(), key.begin(), ::tolower);
            key = key.ToLower();
            TrieNode currentNode = root;
            int index = 0;

            //Iterate the trie with the given character index,
            //If the index points to NULL
            //simply create a TrieNode and go down a level
            for (int level = 0; level < key.Length; level++)
            {
                index = getIndex(key[level]);

                if (currentNode.children[index] == null)
                {
                    currentNode.children[index] = new TrieNode();
                   Console.WriteLine( key[level] + " inserted" );
                }
                currentNode = currentNode.children[index];
            }

            //Mark the end character as leaf node
            currentNode.markAsLeaf();
            Console.WriteLine( "'" + key + "' inserted" );
        }
        //Function to search given key in Trie
        public bool searchNode(string key)
        {
            if (key == string.Empty)
                return false;

            key = key.ToLower();
            TrieNode currentNode = root;
            int index = 0;

            //Iterate the Trie with given character index,
            //If it is NULL at any point then we stop and return false
            //We will return true only if we reach leafNode and have traversed the
            //Trie based on the length of the key
            for (int level = 0; level < key.Length; level++)
            {
                index = getIndex(key[level]);

                if (currentNode.children[index] == null)
                    return false;
                currentNode = currentNode.children[index];
            }
            if ((currentNode != null) & (currentNode.isEndWord))
            {
                return true;
            }
    
            return false;
        }
        //Helper Function to return true if currentNode does not have any children
        public bool hasNoChildren(TrieNode currentNode)
        {
            for (int i = 0; i < ALPHABET_SIZE; i++)
            {
                if ((currentNode.children[i]) != null)
                    return false;
            }
            return true;
        }
        //Recursive function to delete given key
        public bool deleteHelper(string key, TrieNode currentNode, int length, int level)
        {
            bool deletedSelf = false;

            if (currentNode == null)
            {
                Console.WriteLine("Key does not exist");
                return deletedSelf;
            }

            //Base Case: If we have reached at the node which points to the alphabet at the end of the key.
            if (level == length)
            {
                //If there are no nodes ahead of this node in this path
                //Then we can delete this node
                if (hasNoChildren(currentNode))
                {
                   
                    currentNode = null; //clear the pointer by pointing it to NULL
                    deletedSelf = true;
                }
                //If there are nodes ahead of currentNode in this path 
                //Then we cannot delete currentNode. We simply unmark this as leaf
                else
                {
                    currentNode.unMarkAsLeaf();
                    deletedSelf = false;
                }
            }
            else
            {
                TrieNode childNode = currentNode.children[getIndex(key[level])];
                bool childDeleted = deleteHelper(key, childNode, length, level + 1);
                if (childDeleted)
                {
                    //Making children pointer also null: since child is deleted
                    currentNode.children[getIndex(key[level])] = null;
                    //If currentNode is leaf node that means currntNode is part of another key
                    //and hence we can not delete this node and it's parent path nodes
                    if (currentNode.isEndWord)
                    {
                        deletedSelf = false;
                    }
                    //If childNode is deleted but if currentNode has more children then currentNode must be part of another key.
                    //So, we cannot delete currenNode
                    else if (!hasNoChildren(currentNode))
                    {
                        deletedSelf = false;
                    }
                    //Else we can delete currentNode
                    else
                    {
                        currentNode = null;
                        deletedSelf = true;
                    }
                }
                else
                {
                    deletedSelf = false;
                }
            }
            return deletedSelf;
        }

        //Function to delete given key from Trie
        public void deleteNode(string key)
        {
            if ((root == null) || (key == string.Empty))
            {
               Console.WriteLine("Null key or Empty trie error");
                return;
            }
            deleteHelper(key, root, key.Length, 0);
        }
    } 
}

main.cs

MaxHeap.cs

using System;
using System.Collections.Generic;

namespace chapter_8
{
    class MaxHeap<T> where T: IComparable<T>
    {

        void percolateUp(int i)
        {
            if (i <= 0)
                return;
            else if (h[parent(i)].CompareTo ( h[i]) < 0)
            {
                // Swaps the value of two variables
                T temp = h[i];
                h[i] = h[parent(i)];
                h[parent(i)] = temp;
                percolateUp(parent(i));
            }
        }
        public void maxHeapify(int i) 
        {
            int lc = lchild(i);
            int rc = rchild(i);
            int imax = i;

            if (lc < size() && (h[lc].CompareTo(h[imax]) > 0))
                imax = lc;
            if (rc < size() && (h[rc].CompareTo(h[imax]) > 0))
                imax = rc;
            if (i != imax)
            {
                T temp = h[i];
                h[i] = h[imax];
                h[imax] = temp;
                maxHeapify(imax);
            }
        }

        List<T> h = null;
        public MaxHeap() {
            h = new List<T>();
        }
        public int size() {
            return h.Count;
        }
        public T getMax() 
        {
            if (size() <= 0)
            {
                return (T)Convert.ChangeType(-1, typeof(T));
            }
            else
                return h[0];           
        }
        public void insert(T  key) 
        {
            // Push elements into vector from the back
            h.Add(key);
            // Store index of last value of vector in  variable i
            int i = size() - 1;
            // Restore heap property
            percolateUp(i);
        }
        public void printHeap()
        {
            for (int i = 0; i <= size() - 1; i++)
            {
                Console.Write( h[i] + " ") ;
            }
            Console.WriteLine("");
        }
        public void buildHeap(T [] arr, int size)
        {
            // Copy elements of array into the List h 
            h.AddRange(arr);
            for (int i = (size - 1) / 2; i >= 0; i--)
            {
                maxHeapify(i);
            }
        }   
        public int parent(int i)
        {
            return (i - 1) / 2;
        }
        public int lchild(int i)
        {
            return i * 2 + 1;
        }
        public int rchild(int i)
        {
            return i * 2 + 2;
        }
        public void removeMax()
        {
            if (size() == 1)
            {
                // Remove the last item from the list
                h.RemoveAt(h.Count - 1);
            }
            else if (size() > 1)
            {
                // Swaps the value of two variables
                T temp = h[0];
                h[0] = h[size() - 1];
                h[size() - 1] = temp;
                // Deletes the last element
                h.RemoveAt(h.Count - 1);
                // Restore heap property
                maxHeapify(0);
            }
            
        }

    }
}

Time Complexity: $O(n)$

Notice that you start from the bottom of the heap, i.e., i = size-1 (line 78). If the height of the heap is h, then the levels go from “0” (at the root node) to “h” at the deepest leaf nodes. By calling maxHeapify() at the leaf nodes, you will have a constant time operation.

At level h - 1h−1, for every node, maxHeapify() makes one comparison and swap operation at most. At level h−2, , it makes two at most comparisons and swaps for every node. This continues until the root node, where it makes h comparisons at most, swaps operations.

main.cs

MinHeap.cs

using System;
using System.Collections.Generic;


namespace chapter_8
{
    class MinHeap<T> where T : IComparable<T>
    {
        List<T> h = null;
        public int parent(int i)
        {
            return (i - 1) / 2;
        }
        public int lchild(int i)
        {
            return i * 2 + 1;
        }
        public int rchild(int i)
        {
            return i * 2 + 2;
        }

        void minHeapify(int i)
        {
            int lc = lchild(i);
            int rc = rchild(i);
            int imin = i;
            if (lc < size() && (h[lc].CompareTo(h[imin]) < 0))
                imin = lc;
            if (rc < size() && (h[rc].CompareTo(h[imin]) < 0))
                imin = rc;
            if (i != imin)
            {
                T temp = h[i];
                h[i] = h[imin];
                h[imin] = temp;
                minHeapify(imin);
            }
        }

        //percolateUp(): It is meant to restore the 
        //heap property going up from a node to the root.
        void percolateUp(int i)
        {
            if (i <= 0)
                return;
            else if (h[parent(i)].CompareTo(h[i]) > 0)
            {
                // Swaps the value of two variables
                T temp = h[i];
                h[i] = h[parent(i)];
                h[parent(i)] = temp;
                percolateUp(parent(i));
            }
        }

        public MinHeap()
        {
            h = new List<T>();
        }

        public int size()
        {
            return h.Count;
        }

        public T getMin()
        {
            if (size() <= 0)
            {
                return (T)Convert.ChangeType(-1, typeof(T));
            }
            else
            {
                return h[0];
            }
        }
        public void insert(T key)
        {
            // Push elements into vector from the back
            h.Add(key);
            // Store index of last value of vector in  variable i
            int i = size() - 1;
            // Restore heap property
            percolateUp(i);
        }
        public void removeMin()
        {
            if (size() == 1)
            {
                // Remove the last item from the list
                h.RemoveAt(h.Count - 1);
            }
            else if (size() > 1)
            {
                // Swaps the value of two variables
                T temp = h[0];
                h[0] = h[size() - 1];
                h[size() - 1] = temp;
                // Deletes the last element
                h.RemoveAt(h.Count - 1);
                // Restore heap property
                minHeapify(0);
            }

        }
        public void buildHeap(T[] arr, int size)
        {
            // Copy elements of array into the List h 
            h.AddRange(arr);
            for (int i = (size - 1) / 2; i >= 0; i--)
            {
                minHeapify(i);
            }
        }

        //Bonus function: printHeap()
        public void printHeap()
        {
            for (int i = 0; i <= size() - 1; i++)
            {
                Console.Write( h[i] + " ");
            }
            Console.WriteLine("");

        }
    }
}

using System;
using System.Collections.Generic;
namespace chapter_9
{
    class Program
    {
        static bool isSubset(int [] arr1, int [] arr2, int size1, int size2)
        {
            if (size2 > size1)
            {
                return false;
            }
            HashSet<int> ht = new HashSet<int>();
            // ht stores all the values of arr1
            for (int i = 0; i < size1; i++)
            { 
                // following the last element of the container
                // If key is not present in the unordered_set then insert it
                if (!ht.Contains(arr1[i]))
                    ht.Add(arr1[i]);
            }
            // loop to check if all elements of arr2 are also in arr1
            for (int i = 0; i < size2; i++)
            {
                // If key is not found condition will return false
                // If found it will return iterator to that key
                if (!ht.Contains(arr2[i]))
                    return false;
            }
            return true;
        }
        static void Main(string[] args)
        {
            int []arr1 = { 9, 4, 7, 1, -2, 6, 5 };
            int []arr2 = { 7, 1, -2 };
            Console.WriteLine(isSubset(arr1, arr2, 7, 3));
            return;
        }
    }
}

Time Complexity: $O(m+n)$ where m is the number of elements in arr1 and n is the number of elements in arr2.

C# built-in HashSet makes this solution much simpler. First, we iterate over arr1 on line 16. If the value at the current index is not present in the HashSet, we insert that value in the HashSet on lines 20-21. Then, we iterate through arr2 to see whether their elements are present in HashSet.

If all the elements of arr2 are present in HashSet, then your function will return true lines 25-32.

using System;
using System.Collections.Generic;
namespace chapter_9
{
    class challenge_5
    {
        static string findPair(int[] arr, int size)
        {
            string result = "";
            // Create HashMap with Key being sum and value being a pair i.e key = 3 , value = {1,2}
            // Traverse all possible pairs in given arr and store sums in map
            // If sum already exist then print out the two pairs.
            Dictionary<int, int[]> hMap = new Dictionary<int, int[]>();
            int sum;
            int[] prev_pair = null;
            for (int i = 0; i < size; ++i)
            {
                for (int j = i + 1; j < size; ++j)
                {
                    sum = arr[i] + arr[j]; //calculate sum
                    if (!hMap.ContainsKey(sum))
                    {
                        // If the sum is not present in Map then insert it along with pair
                        int[] temp_Arr = new int[2];
                        temp_Arr[0] = arr[i];
                        temp_Arr[1] = arr[j];
                        hMap[sum] = temp_Arr;
                    }
                    else
                    {
                        //Sum already present in Map
                        prev_pair = hMap[sum];
                        // Since array elements are distinct, we don't
                        // need to check if any element is common among pairs
                        result += "{" + prev_pair[0].ToString() + "," + prev_pair[1].ToString() + "}{" + arr[i].ToString() + "," + arr[j].ToString() + "}";
                        return result;
                    }
                }
            }//end of for
            return result;
        }
        static void Main(string[] args)
        {
            int[] arr = { 3, 4, 7, 1, 12, 9 };
            Console.WriteLine(findPair(arr, 6));
        }
    }
}

Time Complexity: $O(n^2)$

This solution uses C#'s built-in Dictionary class for simplicity.

On lines 23-33, each element in arr is summed with all other elements. The sum becomes the key in the hMap. At every key, store the integer pair whose sum generated that key.

Whenever a sum is found such that its key in the hMap already has an integer pair stored in it, you can conclude that this sum can be made by two different pairs in the array. These two pairs are then returned in the result array on lines 36-46.

Reverse a string in C#
Check if a given string is a palindrome
Rotate an array
Find the second largest integer within an array using one loop
Convert a 2D Array to a 1D Array
Explain and implement the MergeSort algorithm
Find out if a linked list is circular
Balance a binary search tree
Search a sorted array with lowest time complexity possible
0-1 Knapsack problem
Reverse a linked list

Match beginning and ending parenthesis in a string
Shuffle an array of integers in place
Find the ancestors of a given node in a BST
Find the shortest path between two vertices in a graph
Count the number of edges in an undirected graph
Check balanced parenthesis using a stack
Sort values in a stack
Reverse first k elements in a queue
Find the middle node of a linked list

What to learn next#

Great work on those questions! The best way to prepare for your next interview is to keep getting hands-on practice with common data structure questions like these.

To help your prepare for your interview right, Educative has created the course Data Structures for Coding Interviews in C#. This course lets you hone your data structure skills with hundreds of practice questions, each with live coding environments and in-depth explanations.

By the end of the course, you’ll be an expert on identifying and solving all the most-asked interview question patterns.

Happy learning!

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Crack the top 45 C# data structure questions

Ace your C# interview the first time
Practice hundreds of common interview questions with hands-on code environments and instant feedback.

Data Structures for Coding Interviews in C#

Complexity Measures Questions#

1. Big O complexity: Nested Addition#

2. Big O complexity: Nested Multiplication#

3. Big O with nested multiplication (advanced)#

C# Arrays#

4. Remove even integers from an array#

5. Find the minimum value in an array#

6. Maximum subarray sum#

C# Linked Lists#

7. Insertion at Tail#

8. Remove Duplicates from a Linked List#

9. Join two linked lists#

C# Stacks and Queues#

10. Generate binary numbers from 1 to N#

11. Implement a queue using stacks#

12. Find the lowest value in a stack#

C# Graphs#

13. Implement Depth First Search (DFS)#

14. Find a “Mother Vertex” in a graph#

15. Remove edge#

Keep practicing C#.#

C# Trees and Tries#

16. Find the lowest value in a Binary Search Tree#

17. Find the height of a BST#

18. 2-3 Trees vs. BST#

19. Insertion in a Trie#

20. Total words in a Trie#

C# Heaps and Hashing#

21. Implement a Max-Heap#

22. Find k smallest elements in an array#

23. Trie vs. Hash Table#

24. Subset Array Checker#

25. Find two pairs with an equal sum#

20 more questions for a C# coding interview#

What to learn next#

Continue reading about C##

Crack the top 45 C# data structure questions

Ace your C# interview the first time Practice hundreds of common interview questions with hands-on code environments and instant feedback. Data Structures for Coding Interviews in C#

Complexity Measures Questions#

1. Big O complexity: Nested Addition#

2. Big O complexity: Nested Multiplication#

3. Big O with nested multiplication (advanced)#

C# Arrays#

4. Remove even integers from an array#

5. Find the minimum value in an array#

6. Maximum subarray sum#

C# Linked Lists#

7. Insertion at Tail#

8. Remove Duplicates from a Linked List#

9. Join two linked lists#

C# Stacks and Queues#

10. Generate binary numbers from 1 to N#

11. Implement a queue using stacks#

12. Find the lowest value in a stack#

C# Graphs#

13. Implement Depth First Search (DFS)#

14. Find a “Mother Vertex” in a graph#

15. Remove edge#

Keep practicing C#.#

C# Trees and Tries#

16. Find the lowest value in a Binary Search Tree#

17. Find the height of a BST#

18. 2-3 Trees vs. BST#

19. Insertion in a Trie#

20. Total words in a Trie#

C# Heaps and Hashing#

21. Implement a Max-Heap#

22. Find k smallest elements in an array#

23. Trie vs. Hash Table#

24. Subset Array Checker#

25. Find two pairs with an equal sum#

20 more questions for a C# coding interview#

What to learn next#

Continue reading about C##

Ace your C# interview the first time
Practice hundreds of common interview questions with hands-on code environments and instant feedback.

Data Structures for Coding Interviews in C#