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Frequently Asked Questions
Q. 1) Find the Kth Largest Element in an Array: Given an unsorted array of integers, write a function that returns the kth largest element in the array. For example, if the input array is [3, 2, 1, 5, 6, 4] and k = 2, the output should be 5. Implement the function using the quickselect algorithm and analyze its time complexity
Quickselect is an algorithm based on the partitioning step of QuickSort. It selects the kth largest element by partially sorting the array. It works by choosing a pivot and partitioning the array around it. If the pivot’s position is the kth largest, we return it. Otherwise, we continue searching in the appropriate partition. Time Complexity: O(n) on average, O(n²) in the worst case.
Q. 2) Merge Two Sorted Arrays: Given two sorted arrays, merge them into a single sorted array. The function should take two sorted arrays as input and return a new sorted array. For example, if the input arrays are [1, 3, 5] and [2, 4, 6], the output should be [1, 2, 3, 4, 5, 6]. Implement the solution in O(n) time complexity.
To merge two sorted arrays, we can use a two-pointer approach: one pointer for each array. We compare the elements at the pointers, add the smaller element to the merged array, and move the corresponding pointer forward. We continue until both arrays are fully merged. Time Complexity: O(n), where n is the total number of elements in both arrays.
Q. 3) Linked List Reversal: Write a function to reverse a singly linked list. The function should take the head of the list as input and return the new head after reversal. For example, if the original linked list is 1 -> 2 -> 3 -> 4 -> 5, the output should be 5 -> 4 -> 3 -> 2 -> 1. Provide the time and space complexity of your solution.
To reverse a singly linked list, we traverse the list while reversing the direction of the pointers. At each node, we update the next pointer to point to the previous node. Once the traversal is complete, the last node will be the new head. Time Complexity: O(n), where n is the number of nodes. Space Complexity: O(1), since we are not using any extra space.
Q. 4) Array Manipulation: Write a function that rotates an array of integers by a given number of positions. For example, if the array is [1, 2, 3, 4, 5] and the number of positions is 2, the rotated array should be [4, 5, 1, 2, 3]. Implement this function in such a way that the time complexity is O(n).
To rotate an array by k positions, we first reverse the entire array. Then, we reverse the first k elements and reverse the remaining n-k elements. This method ensures that the array is rotated in-place with O(n) time complexity. Time Complexity: O(n), where n is the number of elements in the array.
Q. 5) Given two singly linked lists, determine the point where they intersect. If the two linked lists do not intersect, return null. You can assume that the intersection point is the same for both lists, and you are required to find it. For example, if the two linked lists are: List 1: 1 → 3 → 5 → 7 → 9 → 11 List 2: 2 → 4 → 5 → 7 → 9 → 11 The intersection point is at the node with the value 5. Write a function that takes two linked lists as input. Return the node at which the two lists intersect. If they don't intersect, return null. Solve this problem with O(n) time complexity and O(1) space complexity.
To find the intersection point of two linked lists, we can use two pointers. We traverse both lists, and when a pointer reaches the end of its list, we redirect it to the head of the other list. This ensures that both pointers will travel the same distance by the time they meet at the intersection. Time Complexity: O(n), where n is the length of the longer list. Space Complexity: O(1), as we are using constant space.
Q. 6) What is an Abstract data type? How is it implemented in C++?
An Abstract Data Type is a model that defines a data structure with operations but does not specify the implementation details. In C++, ADTs can be implemented using classes, where the operations are defined as abstract methods (pure virtual functions). For example, a stack ADT defines operations like push, pop, and peek, but does not define how they are implemented internally.
Q. 7) What is a Queue Data Structure? How can it be implemented using an Array in C++?A Queue is a linear data structure that follows the First In, First Out (FIFO) principle. In a queue, the element added first will be the first one to be removed. The queue supports two main operations: Enqueue: Adds an element to the rear of the queue. Dequeue: Removes an element from the front of the queue.
A Queue is a linear data structure that follows the FIFO (First In, First Out) principle. It can be implemented using an array by keeping track of two pointers: one for the front of the queue and one for the rear. Enqueue: Add an element at the rear of the queue. Dequeue: Remove an element from the front of the queue. In an array implementation, the rear pointer keeps track of where to insert the next element, and the front pointer tracks the element to be removed. This implementation requires handling the array's circular behavior (wrapping around) when the queue is full or empty.
Q. 8) Find the Middle Element of a Linked List Problem: Write a function to find the middle element of a singly linked list. If there are two middle elements, return the second middle element. Input: A linked list: 1 → 2 → 3 → 4 → 5 Output: 3.
To find the middle element of a linked list, we can use the two-pointer technique. One pointer moves one step at a time, and the other moves two steps at a time. When the faster pointer reaches the end, the slower pointer will be at the middle. If there are two middle elements, we return the second one. Time Complexity: O(n), where n is the number of nodes.
Q. 9) Write a function to detect if a cycle exists in a singly linked list. Input: A linked list with or without a cycle. Output: Return true if there is a cycle, else return false.
To detect a cycle in a singly linked list, we can use Floyd’s Tortoise and Hare algorithm. Two pointers traverse the list: one moves one step at a time (slow pointer) and the other moves two steps at a time (fast pointer). If there is a cycle, the fast pointer will eventually meet the slow pointer. Time Complexity: O(n), where n is the number of nodes. Space Complexity: O(1).
Q. 10) What is a default constructor? What is the advantage of having one?
A default constructor is a constructor that takes no parameters. It is called automatically when an object is created without any arguments. Its advantage is that it allows for initialization of default values for an object when it is created. In C++, if no constructor is defined, the compiler provides a default constructor.
Q. 11) Use the STL queue (std:queue) container to implement a print queue that accepts incoming print jobs, named as PrintJob #1, PrintJob #2, etc. The print jobs arrive in random order in the sense that the first job might be PrintJob #4, the next one might be Printjob #1, etc. The print queue will look something like this: PrintJob #4 PrintJob #2 PrintJob #1 PrintJob #3 .. The program will generate the print job name strings (the digits are random numbers) and inserts these into the queue in the order received. After every second job inserted in the queue, the program will pop the job at the front of the queue displaying a message saying a particular job, identified by its name, is completed and the size of the queue. As each job is inserted in the queue, the program will display a message saying “Added PrintJob #n to the queue. Size of the queue is …”. Insert a total about 10 jobs to the queue. Please remember that the actions of adding jobs to the queue and every so often removing the job at the front of the queue should be interspersed. Submit the code and the output on Camvas.
The program can use the std::queue from the Standard Template Library (STL) to simulate a print queue. Jobs are added to the queue as they arrive. After every second job insertion, the job at the front of the queue is processed and removed. This demonstrates the FIFO principle of queues.
Q. 12) What is the matching number of the bipartite graph shown above (i.e., what is the number of edges in a maximum matching)?
The matching number of a bipartite graph refers to the maximum number of edges that can be selected such that no two edges share a common vertex. It can be found using algorithms like the Hungarian Algorithm or Maximum Bipartite Matching.
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