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					                               Fourth Semester B.E Degree Examination
                                 (Common to CS and IS)
                                 Model Question Paper I

                       06CS43 Analysis and Design of Algorithms
Note: Answer any FIVE Full questions, selecting at least TWO Questions from each

    Time: 3 Hours                                                Maximum marks : 100
                                         PART -A
1. a. With the help of a flowchart, explain the various stages of algorithm design
      process.                                                                (08 marks)
   b. Explain any three fundamental problem types.                            (06 marks)
   c. Let A be the adjacency matrix of an undirected graph. Explain what properties of the
       matrix indicate that
                   i. The graph is complete
                  ii. The graph has a loop
                 iii. The graph has an isolated vertex                        (06 marks)

2. a. Explain the worst-case , best-case and average case efficiencies of an algorithm
       with help of an example.                                                (08 marks)
   b. Explain the general plan for analyzing the efficiency of a recursive algorithm.
                                                                               (08 marks)
   c. Solve the following recurrence relations.
       i. x(n) = x(n-1) + 5 for n >1 , x(1)=0
       ii. x(n) = 3x(n-1) for n > 1, x(1) =4                                   (04 marks)

3. a. What is brute-force method? Write a brute-force string matching algorithm.
      Analyze its complexity.                                                   (08 marks)
   b. Write the quick sort algorithm. Analyze its efficiency. Apply the algorithm to sort the
      list { 4, 1, 6, 3, 9, 2, 7, 5}.                                           (12 marks)

4. a. Explain how the Divide-and-Conquer strategy is used to multiply large integers.
      Apply the same to compute 2101 * 1130.                                 (10 marks)
   b. Explain the Johnson Trotter algorithm for generating permutations.
      Generate the permutations for the given set {1, 2, 3, 4} by
              i. Bottom-up minimal change algorithm
             ii. The Johnson Trotter algorithm
            iii. The lexicographic order algorithm                            (10 marks)

                                         PART -B
5. a. Explain Transform-and-Conquer technique. What are the major variations of this
      technique.                                                                (06 marks)
   b. Explain the different rotations of AVL tree. Construct an AVL tree for the input
      sequence 3,6,5,1,2,4                                                      (10 marks)
   c. Construct a 2-3 tree for the data of 5 (b) above.                         (04 marks)

                                                                                  Page 1 of 4
 6. a. Explain the different types of hashing. For the input 30,20,56,75,31,19 and hash
         function h(K) = 2K mod 11 , construct the open hash table.                (08 marks)
     b. What are memory functions? Explain how they are used to solve the knapsack
          problem . Solve the instance of the knapsack problem below. Capacity W= 5
                                     Item Weight Value
                                     1      2       $12
                                     2      1       $10
                                     3      3       $20
                                     4      2       $15
                                                                                   (12 marks)
7. a. i. Construct a Huffman code for the following data
                            Character A B C D                  -
                            Probability 0.4 0.1 0.2 0.15 0.15
         ii. Encode the text ABACABAD using the code of (i) above.
        iii. Decode the text whose encoding is 10001011100101 with the code of (i) above.
                                                                                   (10 marks)
    b. What are decision trees? Explain the concept of decision trees for sorting algorithms.
                                                                                   (10 marks)

8. a. Distinguish between P, NP and NP-complete problems. Give examples for each
      category.                                                                  (10 marks)
   b. Apply backtracking to solve the following instance of the subset sum problem
                     S={5,1,4,3} and d=11.                                       (10 marks)

                                                                                  Page 2 of 4
                         Fourth Semester B.E Degree Examination
                                 (Common to CS and IS)
                                 Model Question Paper II

                     06CS43 Analysis and Design of Algorithms
Note: Answer any FIVE Full questions, selecting at least TWO Questions from each

     Time: 3 Hours                                               Maximum marks : 100
                                         PART -A

1.    a)     Explain the notion of algorithm and its important characteristics with the
             help of an algorithm.                                           (06 Marks)
      b)     Write an algorithm to check whether the given number is an Armstrong
             number or not.(Ex: 13+53+33=153)                                (06 Marks)
      c)     Briefly explain the following terms-                            (08 Marks)
             i) Dictionary           ii) Stable algorithm
             iii) ADT                iv) First child next sibling representation of trees
2.    a)     Explain the various asymptotic notations with examples. (08 Marks)
      b)     Use the informal definitions of O, O, ? to determine whether
             the following assertions are true or false.                     (06 Marks)
             i) n(n+1)/2 € O(n3)             ii)n(n+1)/2 € O(n2)
             iii) n(n+1)/2 € ? (n3)          iv) n(n+1)/2€ O (n)
      c)     Discuss the algorithm for element uniqueness problem for its
             efficiency.                                                     (06 Marks)
3.    a)     Explain selection sort algorithm and its efficiency.            (08 Marks)
      b)     Discuss the merge sort algorithm with recursive tree and discuss its
             efficiency. Apply the same algorithm to sort the list {4,6,1,3,9,5,2,7}.
                                                                             (12 Marks)
4.    a)     Briefly explain Strassen’s matrix multiplication. Obtain its (12 Marks)
             complexity. Apply the algorithm to multiply the given 2 matrices.

                     1       2              5       6
                     3       4      X       7       8

      b)     Differentiate between DFS and BFS tree traversals. Explain, with an example,
             how DFS algorithm can be used to obtain the topological sorting
                                                        (08 Marks)
                                      PART -B

5.    a)     Write and explain the Heap sort algorithm using top-down approach.
             Using this algorithm, sort the elements {M,O,R,N,I,N,G} in alphabetical
             order.                                                    (10 Marks)
      b)     Explain the Boyer-Moore algorithm for string matching with
             an example.                                               (10 Marks)

                                                                                   Page 3 of 4
6    a)   Construct the open hash table and closed hash table for the input:
          30,20,56,75,31,19 using the hash function h(k)=k mod 11. (08 Marks)
     b)   State all-pairs shortest path algorithm. Using it, solve the (12 Marks)

                 0           2       8     1        8
                 6           0       3     2        8
                 8           8       0     4        8
                 8           8       2     0        3
                 3           8       8     8        0

7.   a)   What is Greedy technique? Explain how the different steps of this
          technique are taken care in generating a minimum spanning tree
          through a sequence of expanding sub trees. Apply this algorithm
          to the following graph:                                    (10 Marks)

                             b                                  c
                             a                                  a

                     5           3                      4

                         a       6              d           2           e
                         a                      a                       a

     b)   Explain the concept of Decision tree for searching the sorted
          array.                                                       (10 Marks)
8.   a)   Distinguish between P,NP and NP complete problems. Give examples
           for each category.                                          (10 Marks)
     b)   Solve the following instance of Assignment problem using
          Branch-Bound technique                                       (10 Mraks)

                     Job1                Job2               Job3            Job4
                       9                   2                  7               8
                       6                   4                  3               7
                       5                   8                  1               8
                       7                   6                  9               4

                                                                                   Page 4 of 4

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