Please give the algorithm with its complexity and the code also.

Thank you in advance.

1. Solve the Towers of Hanoi game for the following graph G-(VE) with V-Start, Auxl, Aux2. Aux3, Dest) and-E = {(Start,Aux 1), (Aux 1 ,Am2), (Aux2,Aux3), (Aux3,Aurl), (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.)