Advanced Bash-Scripting Guide
24.3. Recursion Without Local Variables
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
Chapter 24. Functions 417
Advanced Bash-Scripting Guide
#! /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.
Chapter 24. Functions 418
Advanced Bash-Scripting Guide 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.)
Chapter 24. Functions 419
