24.3. Recursion Without Local Variables (Revision #1)

A function may recursively call itself even without use of local variables.

Example 24-16. The Fibonacci Sequence

#!/bin/bash
# fibo.sh : Fibonacci sequence (recursive)
# Author: M. Cooper
# License: GPL3

# ----------algorithm--------------
# Fibo(0) = 0
# Fibo(1) = 1
# else
#   Fibo(j) = Fibo(j-1) + Fibo(j-2)
# ---------------------------------

MAXTERM=15       # Number of terms (+1) to generate.
MINIDX=2         # If idx is less than 2, then Fibo(idx) = idx.

Fibonacci ()
{
  idx=$1   # Doesn't need to be local. Why not?
  if [ "$idx" -lt "$MINIDX" ]
  then
    echo "$idx"  # First two terms are 0 1 ... see above.
  else
    (( --idx ))  # j-1
    term1=$( Fibonacci $idx )   #  Fibo(j-1)

    (( --idx ))  # j-2
    term2=$( Fibonacci $idx )   #  Fibo(j-2)

    echo $(( term1 + term2 ))
  fi
  #  An ugly, ugly kludge.
  #  The more elegant implementation of recursive fibo in C
  #+ is a straightforward translation of the algorithm in lines 7 - 10.
}

for i in $(seq 0 $MAXTERM)
do  # Calculate $MAXTERM+1 terms.
  FIBO=$(Fibonacci $i)
  echo -n "$FIBO "
done
# 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610
# Takes a while, doesn't it? Recursion in a script is slow.

echo

exit 0

Example 24-17. The Towers of Hanoi

#! /bin/bash
#
# The Towers Of Hanoi
# Bash script
# Copyright (C) 2000 Amit Singh. All Rights Reserved.
# http://hanoi.kernelthread.com
#
# Tested under Bash version 2.05b.0(13)-release.
# Also works under Bash version 3.x.
#
#  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 disks with a hole drilled out of the center,
#+ so they can slip over the posts and rest flat.
#  The rings have different diameters, and they stack in ascending
#+ 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 http://hanoi.kernelthread.com
#+ or pp. 186-92 of _The Armchair Universe_ by A.K. Dewdney.
#
#
#         ...                   ...                    ...
#         | |                   | |                    | |
#        _|_|_                  | |                    | |
#       |_____|                 | |                    | |
#      |_______|                | |                    | |
#     |_________|               | |                    | |
#    |___________|              | |                    | |
#   |             |             | |                    | |
# .--------------------------------------------------------------.
# |**************************************************************|
#          #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.
              # Modification to original script.

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

case $# in
    1) case $(($1>0)) in     # Must have at least one disk.
       1)  # Nested case statement.
           dohanoi $1 1 3 2
           echo "Total moves = $Moves"   # 2^n - 1, where n = # of disks.
           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 -- see the Dewdney reference, above.)