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

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

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.

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

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

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

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

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