Algorithms: Step by Step please.

Kindly, no handwriting please, and thanks a lot:

Problem 4. In year 2069 the eleventh hovercraft of the class MARK III came off the assembly lines of the Boeing Company's (misnamed) rotorcraft division. This hovercraft was called "Nebuchadnezzar." Unfortunately, the core libraries of Nebuchadnezzar were corrupted during installation, so the only uncorrupted data structure left was a simple stack. Boeing software engineers set out to reimplement all the other data structures in terms of stacks, and they started out with queues. a) The following are parts of their original implementation of a queue using two stacks (in.stack and out_stack). Analyze the worst-case running times of its enqueue and dequeue methods and express them using "Big-Oh" notation. Algorithm enqueue(o) in.stack.push(o) Algorithm dequeue) while (! in stack.isEmpty()) do out stack.push(in.stack.pop() if (out_stack.isEmpty()) then throw a QueueEmptyException return.obj + out stack.pop() while (! out_stack.isEmpty()) do in stack.push(out_stack.pop()) return return.obj; b) Sometime in the early twenty-first century a war erupted between the humans and the machines, which humans lost. 120 years after its creation, the hovercraft Nebuchadnez- zar ended up in the hands of the human resistance leader and hacker extraordinaire, Morpheus. Always on the run, the rebels needed much faster software to escape the machines, so Morpheus and his crew set out to optimize Neb's code. Thus a new implementation of a queue (still using two stacks) was born: Algorithm enqueue(o) in.stack.push(0) Algorithm dequeue() if (out_stack.isEmpty()) then while (! in stack.isEmpty() do out stack.push(in.stack.pop()) if (out_stack.isEmpty()) then throw a QueueEmpty Exception return out_stack.pop() What is the worst-case complexity of performing a series of 2n enqueue and n dequeue operations in an unspecified order? Express this using "Big-Oh" notation