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Advanced Data Structures are concepts are dealt in detailed fashion

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- 3. f 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 complexity15. 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

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