CS9212 DATA STRUCTURES AND ALGORITHM QUESTION PAPERS - JANUARY 2010

PART - A (10 x 2 = 20 MARKS)

ANSWER ALL THE QUESTIONS

1.	Consider the two functions f (n) =3n^2+5 and g (n) =n^2. Prove with graphical representation that asymptotic upper bound of f (n) is g (n)?
2.	Solve the recurrence equation of Merge sort to show that the worst-case complexity is O (nlogn)?
3.	Define Null Path length? What is the role of NPL in Leftist Heap?
4.	Is the height of every tree in a Binomial heap that has n elements O (log n)? If not what is the worst-case height as a function of n?
5.	What is the maximum and minimum height of a binary tree with 28 nodes? Mention the suitable tree traversal to sort the values in increasing order?
6.	Compare the worst case height of a red-black tree with n nodes and that of an AVL tree with the same number of nodes?
7.	Why it is necessary to have the auxiliary array billow: high in function Merge? Give an example that shows why-in-place merging is insufficient?
8.	Find an optimal placement for 13 programs on three tapes T0, T1 and T2. Where the programs are of lengths 12,5.8,3,2,7,5.1,8.2,4,3,11,10, and 6.
9.	Give an example of a set of knapsack instances for which |s^i| = 2^I, 0<i<n. Your set should include one instance for each n.
10.	Present a backtracking algorithm for solving the knapsack optimization problem using the variable tuple size formulation.

PART - B (5 x 16 = 80MARKS)

ANSWER ALL THE QUESTIONS

11.	(a) (i) Write algorithm to perform in order and preorder traversal of binary tree. (8) (ii) Explain about recurrence equation with an example. (8) (OR) (b) (i) Explain the principle of Amortized Analysis. (10) (ii) Write algorithm to insert a node in the beginning of a list. (6)
12.	12.       (a) Write algorithm to construct Fibonacci heap with suitable example. (16) (OR) (b) Write algorithm to construct Binomial heap with suitable example. (16)
13.	(a) (i) Construct a B-tree to insert the following (order of the tree is 3)     5,25,3,75,4,43,6,8,10     (ii)What are the properties of Red black trees? (4) (OR) (b) (i) What is the need for splay trees? Give an example. (8)
14.	(a) (i) Discuss Strassen’s matrix multiplication as well as classical O (n^2) one. Determine when Strassen’s method outperforms the classical one. (8)      (ii) Code the divide and conquer algorithm DCHull () in C++ and last it in appropriate data. (8) (OR) (b) Code and distinguish the JS and FJS functions for job sequencing with suitable data. Analyze the complexities of these two functions. (16)
15.	(a) Find the minimum cost path from S to T in the multistage graph of the given figure. Do this first using forward approach and then using backward approach. (16) (OR) (b) Give an n x n chess board, a knight is placed on an arbitrary square with coordinates (x, y). The problem is to determine (n^2-1) knight moves such that every square of the board is visited once if such a sequence of moves exists. Write a C++ program to solve this problem. (16)