Solve the following recurrence equations:
(i) T(n) = 2T(n/2) + 0(n)
(ii) T(n) = T(n - 1) + 0(n)

 

Define ambiguity in Context-Free Grammar (CFG). Prove that the following grammar is ambiguous.

Write a recursive function in C language to calculate the sum of all digits in a long integer provided as input.

Discuss the relationship between class P, NP, NP complete and NP Hard problems with suitable example of each class.

Use Prim's algorithm to construct a minimum spanning tree for the following graph. (use starting node A). 

For a problem P, two algorithms A and B have time complexities T1(n) = 5n² and T2 (n) = 100nlogn respectively. Find the range for n, the size of instance of the given problem P, for which A is more efficient than B.

Give an algorithm for topological sort. Obtain a topological ordering for the following graph:

Define fractional Knap-Sack problem, and give a greedy algorithm to solve this problem efficiently