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| Questions |
| Develop an efficient algorithm to find a list of all the prime numbers up to a number n (say 100). |
| Explain the following types of problems in Computer Science with the help of an example problem for each: i) Searching ii) String Processing iii) Geometric Problems iv) Numerical Problems |
| What is the purpose of asymptotic analysis? What are the drawbacks of asymptotic analysis? Explain the Big-O notation with the help of an example. |
| Write the linear search algorithm and discuss its best case, worst case and average case time complexity. Show the best case, worst case and the average case of linear search in the following data: 13, 15, 2, 6, 14, 10, 8, 7, 3, 5, 19, 4, 17 |
| Make an optimal Huffman tree and design the Huffman code for the following set of frequencies:a:7, e:6, s:20, d:2, f:1, g:3, h:4, t:7. |
| Write and explain the recursive binary search algorithm. Use this algorithm for searching an element in a sorted array of 7 elements. |
| Analyse the Quick sort algorithm using Master Method. Also draw the relevant recursion tree |
| Write the algorithm for the divide and conquer strategy for Matrix multiplication. Also, analyse this algorithm. |
| Write and explain the algorithm of Topological sorting. How can you compute time complexity for topological sorting? |
| Explain the working of Prim’s algorithm for finding the minimum cost spanning tree with the help of an example. Also find the time complexity of Prim’salgorithm. |
| Explain the working of Bellman-Ford algorithm for finding the shortest path from a single source to all destinations with the help of an example. Also find the time complexity of this algorithm. |
| Explain the process of creating a optimal binary search with the help of an example. |
| Using the Rabin Karp algorithm, find the pattern string in the given text. Pattern: “ten”, Text: “attainthtenbetan”. Write all the steps involved. |
| Differentiate between Knuth Morris Pratt and Naïve String matching Algorithm. |
| Differentiate between the following with the help of an example of each: (i) Optimization and Decision Problems (ii) P and NP problems |
| What are NP Hard and NP complete problems? Explain any one problem of each type. |
| Explain backtracking; and Branch and Bound techniques with the help of an example each. |
| What are the desirable characteristics of an algorithm? Find the GCD of p = 144 and q = 55 using Euclid’s algorithm. |
| Differentiate between Greedy Technique and Dynamic Programming approach of problem solving. Name few problems which are solved using these techniques. |
| What are asymptotic notations? Explain the significance of Big- O, Omega and theta notations with suitable example |
| Sort the given sequence of numbers using Bubble sort. Write all the steps involved. 13, 15, 2, 6, 14, 10, 8, 7, 3, 5, 19, 4. |
| Write the Huffman code for the following set of frequencies of given symbols. A:1, B:1, K:2, D:3, F:5, G:8 , H:13, E:21. |
| Write the steps involved in searching an element in a given array of sorted elements using Binary search algorithm. Assume the searched element if not present in the sequence. |
| Analyse the merge sort algorithm Master Method. Also draw the relevant recursion tree |
| Explain divide and conquer strategy with an example of Matrix multiplication. |
| What is a minimum cost spanning tree? Explain the working of Kruskal’s Algorithm with example. |
| While dealing with the negative edge weights, the Dijkstra’s algorithm is not considered best. Explain the alternate suitable algorithm for single source shortest path with an example. |
| Explain the principle of optimality with respect to binary search. |
| Using the Rabin Karp algorithm, find the pattern string in the given text. Pattern: “fed”, Text: “acfeddadfdec”. Write all the steps involved |
| Differentiate between Knuth Morris Pratt and Rabin Karp Algorithm. |
| Differentiate between NP, NP-Hard and NP-Complete problems with suitable example of each |
| Discuss about the techniques to show the NP- Hardness in brief. |
| What is a vertex cover problem? Discuss Graham’s algorithm in detail. |
| Write a brute force method and Horner’s algorithm to evaluate a polynomial expression and compute their complexities |
| Define a recurrence relation using Divide and Conquer technique and describe its elements |
| Differentiate between the followings with the help of examples: (2+2 marks) (a) Deterministic and Stochastic Algorithms (b) Local and Global optima. |
| Formulate the Knapsack problem and write the pseudo code for solving a fractional Knapsack problem. Also calculate its time complexity |
| Find an optimal solution for the knapsack instance n (number of objects) =7 and W ( totalweight) =15. Profits and weights of each object are shown below: (p1, p2………..p7) = (10, 5, 15, 7, 6, 18, 3) (w1, w2………w7) = (2, 3, 5, 7, 6, 4, 1) Show all the steps. |
| Which is the most suitable graph representation scheme for a dense graph? Draw its representation with the help of an example. What is the space complexity of a such graph representation scheme? |
| How does DFS graph traversal scheme work? Explain |
| Define and write some applications of Topological Ordering. Write its pseudo code and calculate its time complexity. |
| State the principle of optimality? What are the steps to be followed in solving a problem using Dynamic Programming technique? What kinds of problems can be solved through dynamic programming technique? Elaborate. |
| Suppose T(n) and f(n) and two functions. Write asymptotic notations (Ο, Ω, Θ) using these two functions and explain the growth rate of these functions in each notation. |
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