Advanced Bash-Scripting Guide:
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# 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

    #! /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.)

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