MLR Institute of Technology

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1 MLR Institute of Technology Laxma Reddy Avenue, Dundigal, Quthbullapur (M), Hyderabad Phone Nos: / , Fax : TUTORIAL QUESTION BANK Course Name : DATA STRUCTURES Course Code : A30502 Class : II B.Tech I Semester Branch : Computer Science and Engineering Year : Course Faculty : Mrs. L. Lakshmi, Assoc.Professor Mr. Gouse Sheik, Associate Professor Mr. Madhuravani, Assistant Professor Mr. K. Praveen Kumar, Asst.Prof OBJECTIVES: 1. To understand the basic concepts such as Abstract Data Types, Linear and Non Linear Data structures. 2. To understand the notations used to analyze the Performance of algorithms. 3. To understand the behavior of data structures such as stacks, queues, trees, hash tables, search trees, Graphs and their representations. 4. To choose the appropriate data structure for a specified application. 5. To understand and analyze various searching and sorting algorithms. 6. To write programs in C to solve problems using data structures such as arrays, linked lists, stacks, queues, trees, graphs, hash tables, search trees.

2 PART-A (Short Answer Questions) S.No Question Blooms Taxonomy Level Course Outcome UNIT - I 1 Define an Algorithm? Remember 5 2 List the basic asymptotic efficiency Remember 5 classes 3 Define O-notation? Remember 5 4 Define worst-case efficiency? Remember 5 5 Define best-case efficiency? Remember 5 6 Define Data Structure? Remember 5 7 List different types of linked lists Remember 5 8 List out the applications of a linked list Remember 5 9 Differentiate between arrays and linked lists 10 List out the advantages of using a linked Remember 5 list UNIT II 1 Define Stack? Remember 5 2 Define Queue? Remember 5 3 List out the applications of Stack? Remember 5 4 List out the applications of Queue? Remember 5 5 List out the basic operations of stack? Remember 5 6 Translate the given infix expression into its equivalent postfix expression? (A + B) (C * D) / (F + G) 7 Write the name of the principle followed by Queue? 8 Evaluate the value of the following Postfix expression? * 9 Translate the given infix expression into its equivalent postfix expression? (A+ B)*(C*D E)*F / G is Remember 5 Evaluate 3 10 List out the basic operations of Queue? Remember 5 UNIT - III 1 Define Tree? Remember 5 2 Define Binary Tree? Remember 5 3 Define Threaded Binary Tree? Remember 5 4 List out the types of Binary Tree? Remember 5 5 Define Graph? Remember 5 6 List different ways of representing Graph. Remember 5 7 Define Heap? Remember 5 8 List different types of Heap? Remember 5 9 Define Height of a Tree? Remember 5 10 List out the basic operations of Heap? Remember 5

3 UNIT - IV 1 List out the sorting techniques which use Remember 5 Divide and Conquer policy? 2 Tell the name of the data structure which Remember 5 is used in Recursion internally? 3 Tell the basic requirement to search an Remember 5 element using Binary Search? 4 Discuss the key comparisons an insertion sort makes in its worst case? 5 Discuss the limitations of Binary Search 6 Discuss the conditions under which sequential search of a list is preferred over binary search? 7 Define Heap? 8 Which of the data structure is used in Remember 5 BFS? Why? 9 Which of the data structure is used in Remember 5 DFS? Why? 10 List different types of Hashing? UNIT - V 1 Define BST? Remember 5 2 Define AVL? Remember 5 3 Analyze the complexity of BST and AVL? 4 List out the applications of BTree? 5 List out the different pattern matching algorithms? 6 List out the different types of Tries? 7 List out the different applications of Tries? 8 Analyze the complexity of AVL and RedBlack Tree? 9 List out the basic operations of AVL? 10 List out the basic operations of SplayTree?

4 PART B (LONG ANSWER QUESTIONS) S.No Question UNIT - I 1 Write a recursive which converts any integer value to its equivalent binary value. 2 How do you find the complexity of an algorithm? What is the relation between the time and space complexities of an algorithm? Justify your answer with an example. 3 Compare two functions n 2 and 2 n/4 for various values of n. Determine when second becomes larger than first. 4 Explain an efficient way of storing a sparse matrix in memory. Write a module to find the transpose of a sparse matrix stored in this way. 5 Compare and Contrast singly linked list and doubly linked list with suitable examples. 6 Write a C program to check whether a given matrix is sparse matrix or not.the size of the matrix must be minimum 2x2. 7 Explain linear and non linear data structures with examples. 8 Write the importance of frequency count in the analysis of an algorithm. Blooms Taxonomy Level Course Outcome Evaluate 4 9 Write a program to print Fibonacci sequence. 10 Define Recursion? Explain design methodology and Remember 5 implementation of recursive algorithms. UNIT - II 1 Write a C program to implement the following operations using Singly linked list. a. Create a single linked list with N number of nodes. b. Insert a new node at the end. c. Delete a node from the beginning. d. Insert a node at the middle. 2 Write a C program to evaluate the following postfix expression? * Write a program to implement the basic operations of a Queue using arrays. 4 Write a program to implement the basic operations of a Stack using arrays. 5 Write a C program to reverse the elements stored in a single linked list. 6 Write a C program to convert infix to polish notation.

5 7 Write a C program to implement the following operations using doubly linked list. a. Create a double linked list with N number of nodes. b. Insert a new node at the end. c. Delete a node from the beginning. d. Insert a node at the middle. 8 Write a C program to implement the DEQUE using doubly linked list. 9 Show how to implement a Queue using two stacks. Analyze the run time of Queue operations. 10 Show how to implement a Stack using two queues. Analyze the run time of Stack operations. UNIT - III 1 Explain different methods of binary tree representation. 2 Given a set of input representing the nodes of a binary tree, write a non recursive algorithm that must be able to output the three traversal orders. Write an algorithm for checking validity of the input, i.e., the program must know if the input is disjoint, duplicated and has a loop 3 Explain how a general tree can be represented as a Binary Tree. 4 Explain the representations of graph with an examples. Apply 4 Apply 4 5 Write the non-recursive algorithm to traverse a tree in preorder 6 Translate the following infix expressions into its equivalent postfix expressions; (i) (A + B D)/(E F)+ G (ii) A*(B+ D)/ E F*(G + H/ K) 7 Which are the two standard ways of traversing a graph? Explain them with an example of each. 8 How will you represent a max-heap sequentially? Explain with an example. 9 Write an algorithm to insert an element to a maxheap that is represented sequentially. 10 Construct a binary tree whose nodes in inorder and preorder are given as follows: Inorder : 10, 15, 17, 18, 20, 25, 30, 35, 38, 40, 50 Preorder: 20, 15, 10, 18, 17, 30, 25, 40, 35, 38, 50 UNIT - IV Apply 4 Apply 4

6 1 The following values are to be stored in a hash table 25, 42, 96, 101, 102, 162, 197 Describe how the values are hashed by using division method of hashing with a table size of 7. Use chaining as the method of collision resolution. 2 Compare the time complexities of linear search and binary search with suitable examples? 3 Write a C program that searches a particular value in a stored array of integers using Binary Search technique. 4 An Array contains a list of integers 3, 13, 7, 26, 44, 23, 98, 57, 65, 24, 84, 37. Design a C program to sort the array elements using quick sort and trace the steps? 5 Compare the time complexities of various sorting techniques? 6 Define Hashing. How do collisions happen during hashing? Explain the different techniques resolving of collision. 7 Show the various passes of insertion sort on an Apply 4 unsorted list 11, 15, 2, 13, 6 8 Write a C program to sort the given elements using Quick Sort. 9 Write a C program to sort the given elements using Heap Sort. 10 Explain how priority queues can be implemented using Heap. UNIT - V 1 Write a C program to perform the following BST operations i) Creation ii) Traversal 2 Write a C program to perform the following AVL operations Creation ii) Traversal 3 What is a height balanced tree? Explain how the height is balanced after addition/deletion of nodes in it? 4 Given a Binary Search Tree. Write an algorithm to Tree check whether the tree is an AVL tree or not and discuss the run time complexity. 5 Explain the concept of tries with suitable examples. 6 Describe Red-Black trees with suitable example. 7 Construct a B-tree of order 5 for the following data. Apply 4 3,14,7,1,8,5,11,17,13,6,23,12,20,26,4,16,18,24,25,19 8 Show the result of inserting 2,5,1,4,6,7,3,9 into an empty AVL tree. Apply 4

7 9 Write recursive function to find the mirror image of Apply 4 a given binary tree. Show the contents of stack stepwise. 10 Write a C program to find the depth of an AVL tree. PART-C (Critical Thinking Questions) S.No Question UNIT - I 1 Analyze the function and find the output of following function for start pointing to first node of following linked list? 1->2->3->4->5->6 void fun(struct node* start) { if(start == NULL) return; printf("%d ", start->data); if(start->next!= NULL ) fun(start->next->next); printf("%d ", start->data); 2 The following C function takes a singlelinked list of integers as a parameter and rearranges the elements of the list. The function is called with the list containing the integers 1, 2, 3, 4, 5, 6, 7 in the given order. Analyze the code and find the contents of the list after the function completes execution? struct node { int value; struct node *next; ; void rearrange(struct node *list) { struct node *p, * q; int temp; if ((!list)!list->next) return; p = list; q = list->next; while(q) { temp = p->value; Blooms Taxonomy Level Course Outcome Analyze 3 Analyze 3

8 p->value = q->value; q->value = temp; p = q->next; q = p? p->next:0; 3 Consider the following algorithm Algorithm fun3 (x, y) if (x>y) return -1 elseif (x equal y) return 1 else return (x * fun3 (x+1, y)) end if end fun3 Show what would be returned if fun3 is called as a)fun3(10,4) b) fun3(4,3) c) fun3(4,7) d) fun3(0,0) 4 Write a function with the following prototype that returns the sum of the digits of an integer. int sumofdigits(int x); If x is 234, the function should return , that is, 9. If x is negative, ignore the minus sign. For example, -12 and 12 both return 3. Use recursion. 5 You wish to create a database of stars. For each star, the database will store several megabytes of data. Considering that your database will store billions of stars, choose the data structure that will provide the best performance. With this data structure you should be able to find, insert, and delete stars. Justify your choice. UNIT - II 1 Suppose a circular queue of capacity (n 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables, respectively. Initially, REAR = FRONT = 0. Write the conditions to Evaluate 3 Remember 5

9 detect queue full and queue empty? 2 Assume that the operators +, -, are left associative and ^ is right associative. The order of precedence (from highest to lowest) is ^, x, +, -. Produce the postfix expression corresponding to the infix expression a + b c - d ^ e ^ f? 3 You are in front of a stack of pancakes of different diameter. Unfortunately, you cannot eat them unless they are sorted according to their size, with the biggest one at the bottom. To sort them, you are given a spatula that you can use to split the stack in two parts and then flip the top part of the stack. Write the pseudo-code of a function sortpancakes that sorts the stack. The i-th element of array pancakes contains the diameter of the i-th pancake, counting from the bottom. The sortpancakes algorithm can modify the stack only through the spatulaflip function whose interface is specified below. (Hint: Notice that you can move a pancake at position x to position y, without modifying the positions of the order of the other pancakes, using a sequence of spatula flips.) /* Flips over the stack of pancakes from position pos and returns the result */ int[] spatulaflip(int pos, int[] pancakes); int[] sortpancakes(int[] pancakes) { 4 The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. What is the postorder traversal sequence of the same tree? 5 Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter Understand 4 MultiDequeue(Q){ m = k while (Q is not empty and m > 0) { Dequeue(Q) m = m - 1 What is the worst case time complexity of

10 a sequence of n MultiDequeue() operations on an initially empty queue? UNIT - III 1 You are given a set of persons P and their friendship relation R. That is, (a, b) R iff a is a friend of b. You must find a way to introduce person x to person y through a chain of friends. Model this problem with a graph and describe a strategy to solve the problem. 2 Consider the following array: A = h4, 33, 6, 90, 33, 32, 31, 91, 90, 89, 50, 33 (a) Is A a min-heap? Justify your answer by briefly explaining the min-heap property. time: 10 (b) If A is a min-heap, then extract the minim value and then rearrange the array with the min-heapify procedure. In doing that, show the array at every iteration of min-heapify. If A is not a min-heap, then rearrange it to satisfy the min-heap property. 3 Consider the pseudocode given below. The function DoSomething() takes as argument a pointer to the root of an arbitrary tree represented by the leftmostchild-rightsibling representation. Each node of the tree is of type treenode. typedef struct treenode* treeptr; struct treenode { treeptr leftmostchild, rightsibling; ; int DoSomething (treeptr tree) { int value = 0; if (tree!= NULL) { if (tree->leftmostchild == NULL) value = 1; else value = DoSomething(tree- >leftmostchild); value = value + DoSomething(tree- >rightsibling); return(value);

11 When the pointer to the root of a tree is passed as the argument to DoSomething, what is the function return value. 4 A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. What is the level-order traversal of the heap after the insertion of the elements is: 5 Consider a rooted Binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having having exactly 4 nodes O(n a Logn b ). What is the value of a + 10b is UNIT - IV 1 After two passes of a sorting algorithm, the following array: , has been rearranged as follows: Which sorting algorithm is being used (selection, bubble or insertion) defined your answer 2 Consider the elements stored in queue X={25,29,38,36,32,54,44,40, apply radix sort 3 You need a picture frame, so you walk down to the local photo store to examine their collection. They have all of their frames lined up against the wall. Apply the linear search algorithm to this problem, and describe how you would find the frame you wanted. 4 After two passes of a sorting algorithm, the following array: , has been rearranged as follows: Which sorting algorithm is being used (selection, bubble or insertion) defined your answer 5 What is the running time for insertion sort when: 1. the array is already sorted in ascending order? 2. the array is already sorted in descending order? Understand 4 Understand 4

12 On each iteration of its outer loop, insertion sort finds the correct place to insert the next item, relative to the ones that are already in sorted order. It does this by searching back through those items, one at a time. Would insertion sort be speeded up if instead it used binary search to find the correct place to insert the next item? UNIT - V 1 Consider an initially empty B-Tree with minimum degree t = 3. Draw the B-Tree after the insertion of the keys 27, 33, 39, 1, 3, 10, 7, 200, 23, 21, 20, and then after the additional insertion of the keys 15, 18, 19, 13, 34, 200, 100, 50, Draw the binary search tree obtained when the keys 1, 2, 3, 4, 5, 6, 7 are inserted in the given order into an initially empty tree. What is the problem of the tree you get? Why is it a problem? How could you modify the insertion algorithm to solve this problem. Justify your answer. 3 Consider a B+-tree in which the maximum number of keys in a node is 5. What is the minimum number of keys in any non-root node? 4 What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0 5 In delete operation of BST, we need inorder successor (or predecessor) of a node when the node to be deleted has both left and right child as non-empty. Which of the inorder successor is needed in delete operation? Evaluate 4