This download link is referred from the post: AKTU B-Tech Last 10 Years 2010-2020 Previous Question Papers || Dr. A.P.J. Abdul Kalam Technical University
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ECS-502
(Following Paper ID and Roll No. to be filled in your Answer Book)
Paper ID :110512 Roll No.
B.Tech.
(SEM. V) THEORY EXAM. 2015-16
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DESIGN AND ANALYSIS OF ALGORITHMS
[Time: 3 hours] [Maximum Marks: 100]
Section-A
- Attempt all parts. All parts carry equal marks. Write answer of each part in short. (10x2=20)
- Why should we do asymptotic analysis of algorithms? Explain.
- Order the following expressions by their asymptotic growth and justify your answer 2n, n!, (log n)!, n3, 2log2n, 22n, nlog log n, en
- How can you modify Quick sort algorithm to search an item in a list?
- What are all pairs shortest path?
- Define Convex Hull.
- Discuss various properties of Binomial Tree
- What are the steps to design an algorithm?
- Prove that red-black tree with n internal nodes has height at most 2log2(n+1)
- Prove that the maximum degree of n-node in a binomial tree is log2n.
- What do you understand by ‘stable' sort? Name two stable sort algorithms.
- Define Greedy Approach.
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Section-B
Attempt any five questions from this section. (5x10=50)
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- Explain insertion in Red Black Tree. Show steps for inserting 9,8,7,6,5,4,3,2, & 1 into empty RB tree.
- Show all the steps of Strassen's matrix Multiplication algorithm to multiply the following matrices X = and Y =
- Define Dynamic programming. How Dynamic Programming approach is used to find the shortest path? Illustrate with an example.
- Find optimal solution to the Fractional Knapsack instances n= 7 and Knapsack capacity M = 15 Where profits and weights are as follows (p1, p2, ......p7) = (10,5,15,7,6,18,3) & (w1, w2......w7) = (2,3,5,7,1,4,1) respectively
- Construct the string- matching automaton for the pattern P=aabab and illustrate its operation on the text string T=aaababaabaabaab.
- Illustrate the operation of heap sort on the array A=(6,1,2,4,3,5,7,9,8,0)
- Find an LCS for the sequences. X={x1, x2 ......Xm} and Y={y1,y2.....yn}. Also show that it requires O (m+n) time.
- Write short note on Fast Fourier Transform (FFT).
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Section-C
Attempt any two questions from this section. (2x15=30)
- Attempt both :
- Why the statement "The running time of algorithm A is at least O (n2) is meaningless"? Explain.
- What is the procedure of partition (A, p, r) in Quick Sort and also define the complexity of Quick Sort.
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- What do you mean by Branch & Bound? How TSP can be solve using this approach.
- Attempt both :
- Discuss the relationship between the class P, NP, NP- complete and NP- hard with suitable example of each class.
- Define Approximation algorithms. What is Approximation ratio? Give an Approximation algorithm for the Travelling Salesman
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This download link is referred from the post: AKTU B-Tech Last 10 Years 2010-2020 Previous Question Papers || Dr. A.P.J. Abdul Kalam Technical University
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