23.3. Recursion Without Local Variables

#! /bin/bash
#
# The Towers Of Hanoi
# Bash script
# Copyright (C) 2000 Amit Singh. All Rights Reserved.
# https://hanoi.kernelthread.com
#
# Last tested under bash version 2.05b.0(13)-release
#
#  Used in "Advanced Bash Scripting Guide"
#+ with permission of script author.
#  Slightly modified and commented by ABS author.

#=================================================================#
#  The Tower of Hanoi is a mathematical puzzle attributed to
#+ Edouard Lucas, a nineteenth-century French mathematician.
#
#  There are three vertical posts set in a base.
#  The first post has a set of annular rings stacked on it.
#  These rings are flat disks with a hole drilled out of the center,
#+ so they can slip over the posts.
#  The rings have different diameters, and they stack in descending
#+ order, according to size.
#  The smallest ring is on top, and the largest on the bottom.
#
#  The task is to transfer the stack of rings
#+ to one of the other posts.
#  You can move only one ring at a time to another post.
#  You are permitted to move rings back to the original post.
#  You may place a smaller ring atop a larger one,
#+ but *not* vice versa.
#  Again, it is forbidden to place a larger ring atop a smaller one.
#
#  For a small number of rings, only a few moves are required.
#+ For each additional ring,
#+ the required number of moves approximately doubles,
#+ and the "strategy" becomes increasingly complicated.
#
#  For more information, see https://hanoi.kernelthread.com.
#
#
#         ...                   ...                    ...
#         | |                   | |                    | |
#        _|_|_                  | |                    | |
#       |_____|                 | |                    | |
#      |_______|                | |                    | |
#     |_________|               | |                    | |
#    |___________|              | |                    | |
#   |             |             | |                    | |
# .--------------------------------------------------------------.
# |**************************************************************|
#          #1                   #2                      #3
#
#=================================================================#


E_NOPARAM=66  # No parameter passed to script.
E_BADPARAM=67 # Illegal number of disks passed to script.
Moves=        # Global variable holding number of moves.
              # Modifications to original script.

dohanoi() {   # Recursive function.
    case $1 in
    0)
        ;;
    *)
        dohanoi "$(($1-1))" $2 $4 $3
        echo move $2 "-->" $3
	let "Moves += 1"  # Modification to original script.
        dohanoi "$(($1-1))" $4 $3 $2
        ;;
    esac
}

case $# in
1)
    case $(($1>0)) in     # Must have at least one disk.
    1)
        dohanoi $1 1 3 2
        echo "Total moves = $Moves"
        exit 0;
        ;;
    *)
        echo "$0: illegal value for number of disks";
        exit $E_BADPARAM;
        ;;
    esac
    ;;
*)
    echo "usage: $0 N"
    echo "       Where \"N\" is the number of disks."
    exit $E_NOPARAM;
    ;;
esac

# Exercises:
# ---------
# 1) Would commands beyond this point ever be executed?
#    Why not? (Easy)
# 2) Explain the workings of the workings of the "dohanoi" function.
#    (Difficult)