hanoi.py

"""
Write a recursive function that prints a solution to the classic Towers of
Hanoi puzzle. Your function should accept three integer parameters representing
the number of disks, the starting peg number, and ending peg number. Your
function should print the solution to the game to move from the given start peg
to the given end peg. For example, the call of `hanoi(3, 1, 3)` should print
the folowing output to move the three pegs from peg #1 to peg #3.

```
move disk 1 from peg 1 to peg 3
move disk 2 from peg 1 to peg 2
move disk 1 from peg 3 to peg 2
move disk 3 from peg 1 to peg 3
move disk 1 from peg 2 to peg 1
move disk 2 from peg 2 to peg 3
move disk 1 from peg 1 to peg 3
```
"""

def hanoi(
    number_of_disks: int,
    starting_peg: int,
    ending_peg: int,
):
    pegs = set((1, 2, 3))
    pegs.remove(starting_peg)
    pegs.remove(ending_peg)
    middle_peg = pegs.pop()

    if number_of_disks > 0:
        hanoi(
            number_of_disks=number_of_disks - 1,
            starting_peg=starting_peg,
            ending_peg=middle_peg,
        )

        print(
            f"move disk {number_of_disks} "
            f"from peg {starting_peg} "
            f"to peg {ending_peg}."
        )

        hanoi(
            number_of_disks=number_of_disks - 1,
            starting_peg=middle_peg,
            ending_peg=ending_peg,
        )


hanoi(
    number_of_disks=3,
    starting_peg=1,
    ending_peg=3,
)