hanoi_move.py

def hanoi_towers(start, via, target, n):
    # computes a list of discs steps to move a stack of n discs from
    # rod "start" to rod "target" employing intermidiate rod "via"
    if n == 0:
        return []
    else:
        return hanoi_towers(start, target, via, n-1) \
          + [str.format("disk {} from {} to {}", n, start, target)] \
          + hanoi_towers(via, start, target, n-1)


def hanoi_move(start, via, target,n , k):
    """ finds the k-th move in an Hanoi Towers instance with n discs """
    if n <= 0:
        return "zero or fewer disks"
    elif k <= 0 or k >= 2**n or type(k) != int:
        return "number of moves is illegal"
    elif k == 2**(n-1):
        return str.format("disk {} from {} to {}", n, start, target)
    elif k < 2**(n-1):
        return hanoi_move(start, target, via, n-1, k)
    else:
        return hanoi_move(via, start, target, n-1, k-2**(n-1))