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.

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.

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

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

.

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

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

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