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01. Consider the following scenario: you have a machine hall containing three pegs named A, B, and C. Each peg can hold a number of discs, but a dise with a larger diameter can never be placed on top of a disc with a smaller diameter and all discs have different diameters. If there are n discs, then the discs are numbered from 1 to n, where 1 is the smallest disc and n is the largest disk. There exists a robot arm that can move exactly one disc at a time from peg A to B or B to A, or from B to C or C to B. The robot arm cannot do any other move. Inially, all n dises are on peg A stacked by increasing diameters from top to bottom, with the bottommost one of the largest diameter. The goal is to move all discs from peg A to C by using only the robot arm based on the rules and restrictions described above. You have to submit the following deliverables: a) Well documented pseudocode of a recursive algorithm that solves this problem and prints a protocol of all disc movements, e.g., disc 7 moved from A to B". b) A hand-run of your algorithm for n 4 c) Formulation and calculation of its complexity using the big-Oh notation. Justify your answers