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,Dest), (Dest, Aux1)}.
a) Design an algorithm and determine the time and spacecomplexities of moving n disks from start to Dest.
b) Implement this algorithm whereby your program prints out each ofthe 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 first100 and the last 100 moves.)