Implement a solution for the Tower of Hanoi problem using recursion. Your solution should move the discs from the starting peg to the target peg using the auxiliary peg.

Compare the time and space complexity of both the recursive and iterative solutions and explain the differences.

Create a graphical user interface $($GUI$)$ that demonstrates the steps of the Tower of Hanoi problem as the discs are moved from the starting peg to the target peg. The GUI should allow the user to specify the number of discs and the speed at which the discs move.

Create a variation of the Tower of Hanoi problem where the user can specify more than three pegs. Your solution should still move all the discs from the starting peg to the target peg while adhering to the rules of the Tower of Hanoi problem.

I have a recursive solution but i need help with a gui when the play$()$ function is called $.$here is the code I have right now:

import time

class TOWER$\_$OF$\_$HANOI:

def $\_\_$init$\_\_($self$,$ num$\_$discs $=3,$ start$\_$peg $=\text{'}$A$\text{'},$ target$\_$peg $=\text{'}$B$\text{'},$ aux$\_$peg $=\text{'}$C$\text{'})$:

self.num$\_$discs $=$ num$\_$discs

self.moves $=[]$ # Store moves for visualization

self.start $=$ start$\_$peg

self.target $=$ target$\_$peg

self.aux $=$ aux$\_$peg

self.peg$\_$names $=($start$\_$peg, aux$\_$peg, target$\_$peg$)$

def solve$\_$via$\_$recursion$($self$)$: # base function is O$(1)$ but calls a O$(2^$n$)$ function

self.moves $=[]$ # populate moves

self.recursive$\_$solution$\_$cb$($self$.$num$\_$discs, self.peg$\_$names$[0],$ self.peg$\_$names$[1],$ self.peg$\_$names$[2])$

def recursive$\_$solution$\_$cb$($self$,$ n$,$ start, target, aux$)$: # O$(2^$n$)$

if $($n $==0)$:

return

self.recursive$\_$solution$\_$cb$($n $-1,$ start, aux, target$)$

self.moves.append$(($n$,$ start, target$))$

self.recursive$\_$solution$\_$cb$($n $-1,$ aux, target, start$)$

def play$($self$,$ speed$)$:

pass

toh $=$ TOWER$\_$OF$\_$HANOI$(3)$

#toh.solve$\_$via$\_$iteration$()$

#print$($toh$.$moves$)$

toh.solve$\_$via$\_$recursion$()$

#print$($toh$.$moves$)$

toh.play$(1)$