Part A,

Provide a divide and conquer algorithm for determining the 3 largest values in a given unordered set of numbers. Provide a recurrence equation the time complexity of the algorithm and derive its exact solution (i.e. not the asymptotic solution). For simplicity, you may assume the size of the problem to be an exact power fo 2. [Give pseudocode, worst-case runtime] [explain in details]

Part B,

(True or False) Suppose you have 2 algorithms that solve the same problem, and both run in (theta)(log n) time. Then if both algorithms are implemented on the same machine, by the same programmer and in the same language, those algorithms will take the same amount of time to solve the problem on a given instance of the input.

[I know that the answer is false, but I am not sure about the answer. Please explain in details.]