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

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

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

Write a Turing machine to recognize the language of all strings of even length over the alphabet {a, b}.

Show stepwise sorting of elements using Heapsort algorithm to the following max heap

.

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

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

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