1. NP-hard problems are at least as hard as the problems in NP, and NP-complete problems are NP-hard problems that are also in NP. NP-hard problems are the hardest problems in NP based on known evidence. 2. The document discusses various data structures and algorithms including splay trees, red-black trees, binomial heaps, Fibonacci heaps, divide and conquer algorithms, randomized algorithms, k-d trees, segment trees, and their properties and operations. 3. Key operations like insertion, deletion, querying, balancing are explained for different data structures through examples to illustrate their working and analyze time complexities. Properties like self-balancing, lazy updates, amortized analysis

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REG NO:
University Departments: Anna Universify, Chennai
M.E (FT) Degree Examination, Muy Z0IZ -ZA
Semester I - (Regulation 2009)
Branch : Computer Science and Engineering
CP 91T2 ADVANCED DATA STRUCTURES AND ALGORITHMS
Time : 3 hrs Answer all questions Max Marlis:l00
PartA(10x2=2Dmarks)
1. Define NP hard and NP complete problems and provide relation between
them.
2. Prove by contradiction: log(3) is irrational.
..'!. ..
'tt'
'1
3. Solve the recurrence relation : T(n) :3 T(n/2)+ c.n, given n is a power of 2
and c is a positive constant.
4. what is an AVL tree? what is its maximum height for n nodes ?
5. Define Trie data structure
6. What is special about Leftist tree?
7. Write down the properties of Deap data structure
8. State an application of counting binary tree
9. Draw a k-D tree where k:l
10. Explain stabbing query
Part B ( 5x 16 = 80 marks)
17' a. Perform detailed amortized analysis over the sequence of operations for l0
generating the first 9 subsets ov€r a binary set of elements.
6
b. State the properties of Big Oh notation
12. a. i) State if Splay tree is amortized data structure
Explain procedure for insertion and deletion of nodes in the splay tree with
ii) an example.
10
(oR)
b.'i) State the properties of Red black tree

4. ii) Wirl * example, perform the operations of an insertion and a deletion
on a
red black tree that makes the tree unbalanced and resolve the
imbalance. 10
13' a' i) Define binomial heap and explain the operations of insertion deletion
with
an example
10
ii) Explain why lazy binomial heap is called so?
6
(oR)
b. ii) Explain melding ofpriority queues
ii) Write algorithms for insertion and deletion operations in a Fibonacci
Heap
and explain with an example
l0
14' a' i) Explain a divide and conquer based algorithm for finding the
convex hull
over a set of n points. What is the time complexity of tf,g
algorithm? 12
ii)
Define deterministic and non deterministic algorithms
4 €:)
(oR)
b. i) What is a randomized algorithm?
4
ii) State the tree Vertex splitting problem and explain the
algorithm to solve t2
the problem and analyze its time complexity
15. a. f)efine ID( - quad lree and explain the basic operations of insertion,
deletion and querying
t6
(oR)
b. Define segment tree with n points and explain the querying
operation with
an example and evaluate the query time
t6