2. (a) Explain the concept of virtual functions in C++ with suitable examples. (b) Explain the concept of operator overloading in C++.

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1 Code No: R Set No (a) What is a friend function? Explain the advantages and disadvantages of it? (b) What is static member function? Explain it s limitations. [8+8] 2. (a) Explain the concept of virtual functions in C++ with suitable examples. (b) Explain the concept of operator overloading in C++. [8+8] 3. (a) Write a program to replace all the occurrences of a word with some other word in a given file. (b) Write a program to check whether the given string is palindrome or not. [8+8] 4. Write an algorithm for transposing a given matrix of n m size and determine the time complexity of the algorithm by using Asymptotic notation method. [16] 5. (a) What is the structure to represent node in a skip list. Write the constructor for skiplist. (b) Write a method in C++ to find a pair with key thekey in a dictionary using skip list representation? What is its complexity? [8+8] 6. What is an AVL Tree? Explain about the different rotation patterns in AVL trees for balancing with appropriate examples? [16] 7. (a) Find a necessary and sufficient condition for the root of a depth first search for a connected graph to be an articulation point. (b) Solve the following recurrence relation using substitution method [8+8] T(n) = 1 where n <= 4 = 2T ( n) +logn where n > 4 8. (a) If objects are selected in order of decreasing V i /W i then prove that the algorithm Knapsack finds an optimal solution. (b) Explain the Optimal binary search tree. [8+8]

2 Code No: R Set No (a) What do you mean by Data abstraction? (b) Difference between C structure and C++ structure. (c) Diffrence between a assignment operator and a copy constructor. (d) What is the difference between?overloading? and overridding? [ ] 2. (a) Explain the need for Virtual Destructor. (b) Can we have Virtual Constructors? [8+8] 3. (a) What does throw; (without an exception object after the throw keyword) mean? Where would we use it? (b) How do we throw polymorphically? (c) When we throw this object, how many times will it be copied? [5+5+6] 4. (a) Discuss briefly the asymptotic notations used for finding the complexity of Algorithms. (b) Write a C++ program to implement the sparse matrix. [8+8] 5. Define the abstract class for dictionary? Write the methods f ind, insert, erase used in dictionary? Explain the time complexities to perform above three operations? [16] 6. (a) Prove that the insertion of a new node in a red-black tree with n nodes in θ (logn) time in the worst case. (b) Derive the amortized complexity of a find, insert or delete operation performed on a splay tree with n elements. [8+8] 7. (a) Find a necessary and sufficient condition for the root of a depth first search for a connected graph to be an articulation point. (b) Solve the following recurrence relation using substitution method [8+8] T(n) = 1 where n <= 4 = 2T ( n) +logn where n > 4 8. (a) Show how Prim s algorithm can be implemented using heap. What would be the time complexity of the algorithm. (b) What is the time complexity of traveling sales person problem using dynamic programming. [10+6]

3 Code No: R Set No (a) Explain about the dynamic memory allocation and de-allocation in C++. (b) Explain about static inner classes with a program. [8+8] 2. Explain the difference between virtual function and virtual inheritance. [16] 3. (a) Why should we use iostream instead of the traditional cstdio? (b) Why does a program go into an infinite loop when someone enters an invalid input character? (c) How can we get std::cin to skip invalid input characters? [5+6+5] 4. (a) What is meat by Profiling? Explain it with an example. (b) Trace the heap sort algorithm to sort the following list of numbers 8, 20, 9, 4, 15, 10, 7, 22, 3, 12. [8+8] 5. Develop a class for hash table using linear probing and neverused concept to handle an erase operation. Write complete C++ code for all the methods. Include a method to reorganize the table when (say) 60% of the empty buckets have never used equal to false. The reorganization should move pairs around as necessary and leave a properly configured hash table in which neverused is true for every empty bucket. [16] 6. Define a Binary Search Tree? Write the procedures to perform insertion, deletion and searching in a binary search tree? [16] 7. (a) Show that depth first search can be used to find the connected components of an undirected graph. (b) Write the Quick sort algorithm Also analyze its time complexity in Best case. [6+10] 8. (a) Solve the following 0/1 Knapsack Problem using dynamic programming n=4, m=30, (w 1, w 2, w 3, w 4 ) = (10,15,6,9) and (p 1, p 2, p 3, p 4 ) = (2,5,8,1). (b) Differentiate between Greedy method and Dynamic Programming [8+8]

4 Code No: R Set No (a) Explain about the static variable? (b) Explain about the static functions and static classes in detail with a program. [8+8] 2. (a) What special considerations do we need to know about when I use Virtual Inheritance? (b) What special considerations do we need to know about when I inherit from a class that uses virtual inheritance? (c) What special considerations do I need to know about when I use a class that uses virtual inheritance? [5+5+6] 3. (a) What does throw; (without an exception object after the throw keyword) mean? Where would we use it? (b) How do we throw polymorphically? (c) When we throw this object, how many times will it be copied? [5+5+6] 4. (a) What is a heap? Differentiate between heap and binary search tree. (b) Show that log 3 n is O(n 1/3 ). (c) Briefly explain about Hashing. [5+5+6] 5. (a) Explain the linear probing method in Hashing? Explain its performance analysis? (b) What is hashing with Chains? Explain? Compare this with Linear Probing? [8+8] 6. (a) Prove that the insertion of a new node in a red-black tree with n nodes in θ (logn) time in the worst case. (b) Derive the amortized complexity of a find, insert or delete operation performed on a splay tree with n elements. [8+8] 7. Prove the equation T( N ) + a T ( N /b ) + θ(n k log p N) [16] Where a 1, b 1 and P 0 is T(N) = O(N log b a)ifa > bk O (N k log p+1 N) if a = b k O(N k log p N) if a < b k. 1 of 2

5 Code No: R Set No (a) Show how Prim s algorithm can be implemented using heap. What would be the time complexity of the algorithm. (b) What is the time complexity of traveling sales person problem using dynamic programming. [10+6] 2 of 2

Question Paper Code : 97044

Reg. No. : Question Paper Code : 97044 B.E./B.Tech. DEGREE EXAMINATION NOVEMBER/DECEMBER 2014 Third Semester Computer Science and Engineering CS 6301 PROGRAMMING AND DATA STRUCTURES-II (Regulation 2013)