Q.1: What are the rules of manipulate Big-Oh expressions and about the typical growth rates of algorithm? - Q.2: Discuss the steps in mathematical analysis for recursive algorithm. Do the same for finding the factorial of a number. - Q.3: Find the optimal binary merge tree (pattern) for ten files whose length are. 28, 32, 12,5,84,53,91, 35, 3 and 11 also find its weighted external path length. - Q.4: Explain the memory function method for the Knapsack problem and give the algorithm. - Q.5: Apply Warshall's algorithm to find the transitive closure of the digraph defined by the following adjacency matrix. - Q.6: Explain how branch and bound techniques can be used to solve travelling sales person problem. - Q.7: What is Hamiltonian cycle? Write an algorithm to find all Hamiltonian cycle in graph? - Q.8: Explain the relationship between class P, NP, NP-complete and NP hard problem with example of each class. - Q.9: Solve the recurrence relation: T(n) = 3 (n/4) + n -