2. Solve the Towers of Hanoi game for the following graph G=(V,E) with V={Start, Aux1, Aux2,

Aux3, Aux4, Dest} and E = {(Start,Aux1), (Aux1,Aux2), (Aux2,Aux3), (Aux3,Aux4),

(Aux4, Aux1), (Aux3,Dest)}.

(a) Design an algorithm and determine the time and space complexities of moving n disks from

Start to Dest.

(b) Implement this algorithm whereby your program prints out each of the moves of every disk.

Show the output for n=1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. (If the output is too long, print out only the

first 100 and the last 100 moves.)