VTU CSE 4th Semester Analysis and Design of Algorithms Question Paper Aug 2004: To score better marks in the 4th semester, you should have depth knowledge in every subject. You can boost your preparation by solving previous year question papers. Every semester has an important role to shape the Computer Science & Engineering Career. It will give you information about the important chapters and concepts to be covered in all chapters.

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## VTU CSE 4th Semester Analysis and Design of Algorithms Question Paper Aug 2004

You must have Analysis and Design of Algorithms Question Paper along with the latest Computer Science 4th sem Syllabus to enhance your semester exam preparation.

Here you can check the 4th Sem Analysis and Design of Algorithms Paper

**Note: Answer any FIVE full questions.**

1. (a) Define 0,0), O notations.

(b) Prove : 3n^{3}-f 2n^{2} —0(n^{2}); 3^{n} ^ 0(2^{n})

(c) If ^(n) = 0(/(n)) and T2(rc) = 0(#(n)), then show that Ti(n-)-r T_{2}(n) ~ 0(max(f(n),ff(n))).

2. (a) Write the bubble sort algorithm and show that the worst case efficiency is quadratic.

(b) Outline an exhaustive search algorithm for travelling salesman problem. What is the efficiency class of this algorithm? Illustrate vyith an example.

3. (a) Describe a binary search algorithm. Show that the worst case efficiency is in $)(log 77,).

(b) Write algorithms for preorder, postorder, and inorder traversals of a tree. List the tree of Fig 3(b) in preorder, postorder and inorder.

4. (a) Write DFS algorithm and find its worst case efficiency.

(b) Write an algorithm to topologically sort a diagraph using DFS. Prove the correctness and find the time efficiency.

(c) Topologically sort the following graph shown in Fig.4(c)

5. (a) What is a 2-3 tree? Explain search, insertion and deletion operations and show that these operations are all in (log n) in both worst and average case, do

(b) What is a heap? Outline an algorithm to construct a heap. Derive the efficiency class of this algorithm.

6. (a) Describe an algorithm with an example to compute binomial coefficient and derive its time efficiency.

(b) Design a, @ (n^{2}) algorithm for finding an optimal binary search tree.

7. (a) Write the Kruskal’s algorithm to find minimum spanning tree in time

0(| E | log | E j); where j E | is the number of edges. Prove the correctness and derive the efficiency class of the algorithm.

(b) Apply Kruskars algorithm to find minimum spanning tree of the graph shown in Fig.7(b).

8 (a) Define P_{r} NP, and NP-complete problems.

(b) Write twice around the tree approximation algorithm for travelling salesman problem. Illustrate the working of the algorithm with an example.

(c) Show that the above algorithm is a 2 approximation algorithm.

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