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

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

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

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

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

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

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

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