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.

Implement a solution for the Tower of Hanoi problem using an iterative approach.

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.

$($Optional$)$ Create a variation of the Tower of Hanoi problem where the user can specify the number of discs and the number of 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.

Should be done in python.