Solve the Towers of Hanoi game for the following graph G=(V,E) with V={Start, Aux 1, Aux2, Aux3, Dest} and E = {(Start,Aux1), (Aux1,Aux2), (Aux2,Aux3), (Aux3,Aux1), (Aux3,Dest)}.

1) Design an algorithm and determine the time and space complexities of moving n disks from Start to Dest.

2) 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.)

I would also like the code in java or c++ and please do not copy other codes in chegg or google because they are not what im looking for. It must have 5 pegs

(Start, A1,A2,A3,DEST) and move one peg per time . AKA "Move Disk 1 from A to B" Then "Move Disk 1 from B to C"