Chapter 26. Arrays

#!/bin/bash


area[11]=23
area[13]=37
area[51]=UFOs

#  Array members need not be consecutive or contiguous.

#  Some members of the array can be left uninitialized.
#  Gaps in the array are okay.
#  In fact, arrays with sparse data ("sparse arrays")
#+ are useful in spreadsheet-processing software.


echo -n "area[11] = "
echo ${area[11]}    #  {curly brackets} needed.

echo -n "area[13] = "
echo ${area[13]}

echo "Contents of area[51] are ${area[51]}."

# Contents of uninitialized array variable print blank (null variable).
echo -n "area[43] = "
echo ${area[43]}
echo "(area[43] unassigned)"

echo

# Sum of two array variables assigned to third
area[5]=`expr ${area[11]} + ${area[13]}`
echo "area[5] = area[11] + area[13]"
echo -n "area[5] = "
echo ${area[5]}

area[6]=`expr ${area[11]} + ${area[51]}`
echo "area[6] = area[11] + area[51]"
echo -n "area[6] = "
echo ${area[6]}
# This fails because adding an integer to a string is not permitted.

echo; echo; echo

# -----------------------------------------------------------------
# Another array, "area2".
# Another way of assigning array variables...
# array_name=( XXX YYY ZZZ ... )

area2=( zero one two three four )

echo -n "area2[0] = "
echo ${area2[0]}
# Aha, zero-based indexing (first element of array is [0], not [1]).

echo -n "area2[1] = "
echo ${area2[1]}    # [1] is second element of array.
# -----------------------------------------------------------------

echo; echo; echo

# -----------------------------------------------
# Yet another array, "area3".
# Yet another way of assigning array variables...
# array_name=([xx]=XXX [yy]=YYY ...)

area3=([17]=seventeen [24]=twenty-four)

echo -n "area3[17] = "
echo ${area3[17]}

echo -n "area3[24] = "
echo ${area3[24]}
# -----------------------------------------------

exit 0

#!/bin/bash
# poem.sh: Pretty-prints one of the document author's favorite poems.

# Lines of the poem (single stanza).
Line[1]="I do not know which to prefer,"
Line[2]="The beauty of inflections"
Line[3]="Or the beauty of innuendoes,"
Line[4]="The blackbird whistling"
Line[5]="Or just after."

# Attribution.
Attrib[1]=" Wallace Stevens"
Attrib[2]="\"Thirteen Ways of Looking at a Blackbird\""
# This poem is in the Public Domain (copyright expired).

echo

for index in 1 2 3 4 5    # Five lines.
do
  printf "     %s\n" "${Line[index]}"
done

for index in 1 2          # Two attribution lines.
do
  printf "          %s\n" "${Attrib[index]}"
done

echo

exit 0

# Exercise:
# --------
# Modify this script to pretty-print a poem from a text data file.

#!/bin/bash
# array-ops.sh: More fun with arrays.


array=( zero one two three four five )
# Element 0   1   2    3     4    5

echo ${array[0]}       #  zero
echo ${array:0}        #  zero
                       #  Parameter expansion of first element,
                       #+ starting at position # 0 (1st character).
echo ${array:1}        #  ero
                       #  Parameter expansion of first element,
                       #+ starting at position # 1 (2nd character).

echo "--------------"

echo ${#array[0]}      #  4
                       #  Length of first element of array.
echo ${#array}         #  4
                       #  Length of first element of array.
                       #  (Alternate notation)

echo ${#array[1]}      #  3
                       #  Length of second element of array.
                       #  Arrays in Bash have zero-based indexing.

echo ${#array[*]}      #  6
                       #  Number of elements in array.
echo ${#array[@]}      #  6
                       #  Number of elements in array.

echo "--------------"

array2=( [0]="first element" [1]="second element" [3]="fourth element" )

echo ${array2[0]}      # first element
echo ${array2[1]}      # second element
echo ${array2[2]}      #
                       # Skipped in initialization, and therefore null.
echo ${array2[3]}      # fourth element


exit 0

#!/bin/bash
# array-strops.sh: String operations on arrays.
# Script by Michael Zick.
# Used with permission.

#  In general, any string operation in the ${name ... } notation
#+ can be applied to all string elements in an array
#+ with the ${name[@] ... } or ${name[*] ...} notation.


arrayZ=( one two three four five five )

echo

# Trailing Substring Extraction
echo ${arrayZ[@]:0}     # one two three four five five
                        # All elements.

echo ${arrayZ[@]:1}     # two three four five five
                        # All elements following element[0].

echo ${arrayZ[@]:1:2}   # two three
                        # Only the two elements after element[0].

echo "-----------------------"

#  Substring Removal
#  Removes shortest match from front of string(s),
#+ where the substring is a regular expression.

echo ${arrayZ[@]#f*r}   # one two three five five
                        # Applied to all elements of the array.
                        # Matches "four" and removes it.

# Longest match from front of string(s)
echo ${arrayZ[@]##t*e}  # one two four five five
                        # Applied to all elements of the array.
                        # Matches "three" and removes it.

# Shortest match from back of string(s)
echo ${arrayZ[@]%h*e}   # one two t four five five
                        # Applied to all elements of the array.
                        # Matches "hree" and removes it.

# Longest match from back of string(s)
echo ${arrayZ[@]%%t*e}  # one two four five five
                        # Applied to all elements of the array.
                        # Matches "three" and removes it.

echo "-----------------------"

# Substring Replacement

# Replace first occurance of substring with replacement
echo ${arrayZ[@]/fiv/XYZ}   # one two three four XYZe XYZe
                            # Applied to all elements of the array.

# Replace all occurances of substring
echo ${arrayZ[@]//iv/YY}    # one two three four fYYe fYYe
                            # Applied to all elements of the array.

# Delete all occurances of substring
# Not specifing a replacement means 'delete'
echo ${arrayZ[@]//fi/}      # one two three four ve ve
                            # Applied to all elements of the array.

# Replace front-end occurances of substring
echo ${arrayZ[@]/#fi/XY}    # one two three four XYve XYve
                            # Applied to all elements of the array.

# Replace back-end occurances of substring
echo ${arrayZ[@]/%ve/ZZ}    # one two three four fiZZ fiZZ
                            # Applied to all elements of the array.

echo ${arrayZ[@]/%o/XX}     # one twXX three four five five
                            # Why?

echo "-----------------------"


# Before reaching for awk (or anything else) --
# Recall:
#   $( ... ) is command substitution.
#   Functions run as a sub-process.
#   Functions write their output to stdout.
#   Assignment reads the function's stdout.
#   The name[@] notation specifies a "for-each" operation.

newstr() {
    echo -n "!!!"
}

echo ${arrayZ[@]/%e/$(newstr)}
# on!!! two thre!!! four fiv!!! fiv!!!
# Q.E.D: The replacement action is an 'assignment.'

#  Accessing the "For-Each"
echo ${arrayZ[@]//*/$(newstr optional_arguments)}
#  Now, if Bash would just pass the matched string as $0
#+ to the function being called . . .

echo

exit 0

#!/bin/bash
# script-array.sh: Loads this script into an array.
# Inspired by an e-mail from Chris Martin (thanks!).

script_contents=( $(cat "$0") )  #  Stores contents of this script ($0)
                                 #+ in an array.

for element in $(seq 0 $((${#script_contents[@]} - 1)))
  do                #  ${#script_contents[@]}
                    #+ gives number of elements in the array.
                    #
                    #  Question:
                    #  Why is  seq 0  necessary?
                    #  Try changing it to seq 1.
  echo -n "${script_contents[$element]}"
                    # List each field of this script on a single line.
  echo -n " -- "    # Use " -- " as a field separator.
done

echo

exit 0

# Exercise:
# --------
#  Modify this script so it lists itself
#+ in its original format,
#+ complete with whitespace, line breaks, etc.

#!/bin/bash

declare -a colors
#  All subsequent commands in this script will treat
#+ the variable "colors" as an array.

echo "Enter your favorite colors (separated from each other by a space)."

read -a colors    # Enter at least 3 colors to demonstrate features below.
#  Special option to 'read' command,
#+ allowing assignment of elements in an array.

echo

element_count=${#colors[@]}
# Special syntax to extract number of elements in array.
#     element_count=${#colors[*]} works also.
#
#  The "@" variable allows word splitting within quotes
#+ (extracts variables separated by whitespace).
#
#  This corresponds to the behavior of "$@" and "$*"
#+ in positional parameters. 

index=0

while [ "$index" -lt "$element_count" ]
do    # List all the elements in the array.
  echo ${colors[$index]}
  let "index = $index + 1"
done
# Each array element listed on a separate line.
# If this is not desired, use  echo -n "${colors[$index]} "
#
# Doing it with a "for" loop instead:
#   for i in "${colors[@]}"
#   do
#     echo "$i"
#   done
# (Thanks, S.C.)

echo

# Again, list all the elements in the array, but using a more elegant method.
  echo ${colors[@]}          # echo ${colors[*]} also works.

echo

# The "unset" command deletes elements of an array, or entire array.
unset colors[1]              # Remove 2nd element of array.
                             # Same effect as   colors[1]=
echo  ${colors[@]}           # List array again, missing 2nd element.

unset colors                 # Delete entire array.
                             #  unset colors[*] and
                             #+ unset colors[@] also work.
echo; echo -n "Colors gone."			   
echo ${colors[@]}            # List array again, now empty.

exit 0

#!/bin/bash
# empty-array.sh

#  Thanks to Stephane Chazelas for the original example,
#+ and to Michael Zick for extending it.


# An empty array is not the same as an array with empty elements.

array0=( first second third )
array1=( '' )   # "array1" consists of one empty element.
array2=( )      # No elements . . . "array2" is empty.

echo
ListArray()
{
echo
echo "Elements in array0:  ${array0[@]}"
echo "Elements in array1:  ${array1[@]}"
echo "Elements in array2:  ${array2[@]}"
echo
echo "Length of first element in array0 = ${#array0}"
echo "Length of first element in array1 = ${#array1}"
echo "Length of first element in array2 = ${#array2}"
echo
echo "Number of elements in array0 = ${#array0[*]}"  # 3
echo "Number of elements in array1 = ${#array1[*]}"  # 1  (Surprise!)
echo "Number of elements in array2 = ${#array2[*]}"  # 0
}

# ===================================================================

ListArray

# Try extending those arrays.

# Adding an element to an array.
array0=( "${array0[@]}" "new1" )
array1=( "${array1[@]}" "new1" )
array2=( "${array2[@]}" "new1" )

ListArray

# or
array0[${#array0[*]}]="new2"
array1[${#array1[*]}]="new2"
array2[${#array2[*]}]="new2"

ListArray

# When extended as above; arrays are 'stacks'
# The above is the 'push'
# The stack 'height' is:
height=${#array2[@]}
echo
echo "Stack height for array2 = $height"

# The 'pop' is:
unset array2[${#array2[@]}-1]	#  Arrays are zero-based,
height=${#array2[@]}            #+ which means first element has index 0.
echo
echo "POP"
echo "New stack height for array2 = $height"

ListArray

# List only 2nd and 3rd elements of array0.
from=1		# Zero-based numbering.
to=2		#
array3=( ${array0[@]:1:2} )
echo
echo "Elements in array3:  ${array3[@]}"

# Works like a string (array of characters).
# Try some other "string" forms.

# Replacement:
array4=( ${array0[@]/second/2nd} )
echo
echo "Elements in array4:  ${array4[@]}"

# Replace all matching wildcarded string.
array5=( ${array0[@]//new?/old} )
echo
echo "Elements in array5:  ${array5[@]}"

# Just when you are getting the feel for this . . .
array6=( ${array0[@]#*new} )
echo # This one might surprise you.
echo "Elements in array6:  ${array6[@]}"

array7=( ${array0[@]#new1} )
echo # After array6 this should not be a surprise.
echo "Elements in array7:  ${array7[@]}"

# Which looks a lot like . . .
array8=( ${array0[@]/new1/} )
echo
echo "Elements in array8:  ${array8[@]}"

#  So what can one say about this?

#  The string operations are performed on
#+ each of the elements in var[@] in succession.
#  Therefore : Bash supports string vector operations
#+ if the result is a zero length string,
#+ that element disappears in the resulting assignment.

#  Question, are those strings hard or soft quotes?

zap='new*'
array9=( ${array0[@]/$zap/} )
echo
echo "Elements in array9:  ${array9[@]}"

# Just when you thought you where still in Kansas . . .
array10=( ${array0[@]#$zap} )
echo
echo "Elements in array10:  ${array10[@]}"

# Compare array7 with array10.
# Compare array8 with array9.

# Answer: must be soft quotes.

exit 0

#! /bin/bash
# array-assign.bash

#  Array operations are Bash specific,
#+ hence the ".bash" in the script name.

# Copyright (c) Michael S. Zick, 2003, All rights reserved.
# License: Unrestricted reuse in any form, for any purpose.
# Version: $ID$
#
# Clarification and additional comments by William Park.

#  Based on an example provided by Stephane Chazelas
#+ which appeared in the book: Advanced Bash Scripting Guide.

# Output format of the 'times' command:
# User CPU <space> System CPU
# User CPU of dead children <space> System CPU of dead children

#  Bash has two versions of assigning all elements of an array
#+ to a new array variable.
#  Both drop 'null reference' elements
#+ in Bash versions 2.04, 2.05a and 2.05b.
#  An additional array assignment that maintains the relationship of
#+ [subscript]=value for arrays may be added to newer versions.

#  Constructs a large array using an internal command,
#+ but anything creating an array of several thousand elements
#+ will do just fine.

declare -a bigOne=( /dev/* )
echo
echo 'Conditions: Unquoted, default IFS, All-Elements-Of'
echo "Number of elements in array is ${#bigOne[@]}"

# set -vx



echo
echo '- - testing: =( ${array[@]} ) - -'
times
declare -a bigTwo=( ${bigOne[@]} )
#                 ^              ^
times

echo
echo '- - testing: =${array[@]} - -'
times
declare -a bigThree=${bigOne[@]}
# No parentheses this time.
times

#  Comparing the numbers shows that the second form, pointed out
#+ by Stephane Chazelas, is from three to four times faster.
#
#  William Park explains:
#+ The bigTwo array assigned as single string, whereas
#+ bigThree assigned element by element.
#  So, in essence, you have:
#                   bigTwo=( [0]="... ... ..." )
#                   bigThree=( [0]="..." [1]="..." [2]="..." ... )


#  I will continue to use the first form in my example descriptions
#+ because I think it is a better illustration of what is happening.

#  The reusable portions of my examples will actual contain
#+ the second form where appropriate because of the speedup.

# MSZ: Sorry about that earlier oversight folks.


#  Note:
#  ----
#  The "declare -a" statements in lines 31 and 43
#+ are not strictly necessary, since it is implicit
#+ in the  Array=( ... )  assignment form.
#  However, eliminating these declarations slows down
#+ the execution of the following sections of the script.
#  Try it, and see what happens.

exit 0

#! /bin/bash
# CopyArray.sh
#
# This script written by Michael Zick.
# Used here with permission.

#  How-To "Pass by Name & Return by Name"
#+ or "Building your own assignment statement".


CpArray_Mac() {

# Assignment Command Statement Builder

    echo -n 'eval '
    echo -n "$2"                    # Destination name
    echo -n '=( ${'
    echo -n "$1"                    # Source name
    echo -n '[@]} )'

# That could all be a single command.
# Matter of style only.
}

declare -f CopyArray                # Function "Pointer"
CopyArray=CpArray_Mac               # Statement Builder

Hype()
{

# Hype the array named $1.
# (Splice it together with array containing "Really Rocks".)
# Return in array named $2.

    local -a TMP
    local -a hype=( Really Rocks )

    $($CopyArray $1 TMP)
    TMP=( ${TMP[@]} ${hype[@]} )
    $($CopyArray TMP $2)
}

declare -a before=( Advanced Bash Scripting )
declare -a after

echo "Array Before = ${before[@]}"

Hype before after

echo "Array After = ${after[@]}"

# Too much hype?

echo "What ${after[@]:3:2}?"

declare -a modest=( ${after[@]:2:1} ${after[@]:3:2} )
#                    ---- substring extraction ----

echo "Array Modest = ${modest[@]}"

# What happened to 'before' ?

echo "Array Before = ${before[@]}"

exit 0

#! /bin/bash
# array-append.bash

# Copyright (c) Michael S. Zick, 2003, All rights reserved.
# License: Unrestricted reuse in any form, for any purpose.
# Version: $ID$
#
# Slightly modified in formatting by M.C.


# Array operations are Bash-specific.
# Legacy UNIX /bin/sh lacks equivalents.


#  Pipe the output of this script to 'more'
#+ so it doesn't scroll off the terminal.


# Subscript packed.
declare -a array1=( zero1 one1 two1 )
# Subscript sparse ([1] is not defined).
declare -a array2=( [0]=zero2 [2]=two2 [3]=three2 )

echo
echo '- Confirm that the array is really subscript sparse. -'
echo "Number of elements: 4"        # Hard-coded for illustration.
for (( i = 0 ; i < 4 ; i++ ))
do
    echo "Element [$i]: ${array2[$i]}"
done
# See also the more general code example in basics-reviewed.bash.


declare -a dest

# Combine (append) two arrays into a third array.
echo
echo 'Conditions: Unquoted, default IFS, All-Elements-Of operator'
echo '- Undefined elements not present, subscripts not maintained. -'
# # The undefined elements do not exist; they are not being dropped.

dest=( ${array1[@]} ${array2[@]} )
# dest=${array1[@]}${array2[@]}     # Strange results, possibly a bug.

# Now, list the result.
echo
echo '- - Testing Array Append - -'
cnt=${#dest[@]}

echo "Number of elements: $cnt"
for (( i = 0 ; i < cnt ; i++ ))
do
    echo "Element [$i]: ${dest[$i]}"
done

# Assign an array to a single array element (twice).
dest[0]=${array1[@]}
dest[1]=${array2[@]}

# List the result.
echo
echo '- - Testing modified array - -'
cnt=${#dest[@]}

echo "Number of elements: $cnt"
for (( i = 0 ; i < cnt ; i++ ))
do
    echo "Element [$i]: ${dest[$i]}"
done

# Examine the modified second element.
echo
echo '- - Reassign and list second element - -'

declare -a subArray=${dest[1]}
cnt=${#subArray[@]}

echo "Number of elements: $cnt"
for (( i = 0 ; i < cnt ; i++ ))
do
    echo "Element [$i]: ${subArray[$i]}"
done

#  The assignment of an entire array to a single element
#+ of another array using the '=${ ... }' array assignment
#+ has converted the array being assigned into a string,
#+ with the elements separated by a space (the first character of IFS).

# If the original elements didn't contain whitespace . . .
# If the original array isn't subscript sparse . . .
# Then we could get the original array structure back again.

# Restore from the modified second element.
echo
echo '- - Listing restored element - -'

declare -a subArray=( ${dest[1]} )
cnt=${#subArray[@]}

echo "Number of elements: $cnt"
for (( i = 0 ; i < cnt ; i++ ))
do
    echo "Element [$i]: ${subArray[$i]}"
done
echo '- - Do not depend on this behavior. - -'
echo '- - This behavior is subject to change - -'
echo '- - in versions of Bash newer than version 2.05b - -'

# MSZ: Sorry about any earlier confusion folks.

exit 0

#!/bin/bash
# bubble.sh: Bubble sort, of sorts.

# Recall the algorithm for a bubble sort. In this particular version...

#  With each successive pass through the array to be sorted,
#+ compare two adjacent elements, and swap them if out of order.
#  At the end of the first pass, the "heaviest" element has sunk to bottom.
#  At the end of the second pass, the next "heaviest" one has sunk next to bottom.
#  And so forth.
#  This means that each successive pass needs to traverse less of the array.
#  You will therefore notice a speeding up in the printing of the later passes.


exchange()
{
  # Swaps two members of the array.
  local temp=${Countries[$1]} #  Temporary storage
                              #+ for element getting swapped out.
  Countries[$1]=${Countries[$2]}
  Countries[$2]=$temp
  
  return
}  

declare -a Countries  #  Declare array,
                      #+ optional here since it's initialized below.

#  Is it permissable to split an array variable over multiple lines
#+ using an escape (\)?
#  Yes.

Countries=(Netherlands Ukraine Zaire Turkey Russia Yemen Syria \
Brazil Argentina Nicaragua Japan Mexico Venezuela Greece England \
Israel Peru Canada Oman Denmark Wales France Kenya \
Xanadu Qatar Liechtenstein Hungary)

# "Xanadu" is the mythical place where, according to Coleridge,
#+ Kubla Khan did a pleasure dome decree.


clear                      # Clear the screen to start with. 

echo "0: ${Countries[*]}"  # List entire array at pass 0.

number_of_elements=${#Countries[@]}
let "comparisons = $number_of_elements - 1"

count=1 # Pass number.

while [ "$comparisons" -gt 0 ]          # Beginning of outer loop
do

  index=0  # Reset index to start of array after each pass.

  while [ "$index" -lt "$comparisons" ] # Beginning of inner loop
  do
    if [ ${Countries[$index]} \> ${Countries[`expr $index + 1`]} ]
    #  If out of order...
    #  Recalling that \> is ASCII comparison operator
    #+ within single brackets.

    #  if [[ ${Countries[$index]} > ${Countries[`expr $index + 1`]} ]]
    #+ also works.
    then
      exchange $index `expr $index + 1`  # Swap.
    fi  
    let "index += 1"
  done # End of inner loop

# ----------------------------------------------------------------------
# Paulo Marcel Coelho Aragao suggests for-loops as a simpler altenative.
#
# for (( last = $number_of_elements - 1 ; last > 1 ; last-- ))
# do
#     for (( i = 0 ; i < last ; i++ ))
#     do
#         [[ "${Countries[$i]}" > "${Countries[$((i+1))]}" ]] \
#             && exchange $i $((i+1))
#     done
# done
# ----------------------------------------------------------------------
  

let "comparisons -= 1" #  Since "heaviest" element bubbles to bottom,
                       #+ we need do one less comparison each pass.

echo
echo "$count: ${Countries[@]}"  # Print resultant array at end of each pass.
echo
let "count += 1"                # Increment pass count.

done                            # End of outer loop
                                # All done.

exit 0

#!/bin/bash
# embedded-arrays.sh
# Embedded arrays and indirect references.

# This script by Dennis Leeuw.
# Used with permission.
# Modified by document author.


ARRAY1=(
        VAR1_1=value11
        VAR1_2=value12
        VAR1_3=value13
)

ARRAY2=(
        VARIABLE="test"
        STRING="VAR1=value1 VAR2=value2 VAR3=value3"
        ARRAY21=${ARRAY1[*]}
)       # Embed ARRAY1 within this second array.

function print () {
        OLD_IFS="$IFS"
        IFS=$'\n'       #  To print each array element
                        #+ on a separate line.
        TEST1="ARRAY2[*]"
        local ${!TEST1} # See what happens if you delete this line.
        #  Indirect reference.
	#  This makes the components of $TEST1
	#+ accessible to this function.


        #  Let's see what we've got so far.
        echo
        echo "\$TEST1 = $TEST1"       #  Just the name of the variable.
        echo; echo
        echo "{\$TEST1} = ${!TEST1}"  #  Contents of the variable.
                                      #  That's what an indirect
                                      #+ reference does.
        echo
        echo "-------------------------------------------"; echo
        echo


        # Print variable
        echo "Variable VARIABLE: $VARIABLE"
	
        # Print a string element
        IFS="$OLD_IFS"
        TEST2="STRING[*]"
        local ${!TEST2}      # Indirect reference (as above).
        echo "String element VAR2: $VAR2 from STRING"

        # Print an array element
        TEST2="ARRAY21[*]"
        local ${!TEST2}      # Indirect reference (as above).
        echo "Array element VAR1_1: $VAR1_1 from ARRAY21"
}

print
echo

exit 0

#   As the author of the script notes,
#+ "you can easily expand it to create named-hashes in bash."
#   (Difficult) exercise for the reader: implement this.

#!/bin/bash
# sieve.sh (ex68.sh)

# Sieve of Eratosthenes
# Ancient algorithm for finding prime numbers.

#  This runs a couple of orders of magnitude slower
#+ than the equivalent program written in C.

LOWER_LIMIT=1       # Starting with 1.
UPPER_LIMIT=1000    # Up to 1000.
# (You may set this higher . . . if you have time on your hands.)

PRIME=1
NON_PRIME=0

let SPLIT=UPPER_LIMIT/2
# Optimization:
# Need to test numbers only halfway to upper limit (why?).


declare -a Primes
# Primes[] is an array.


initialize ()
{
# Initialize the array.

i=$LOWER_LIMIT
until [ "$i" -gt "$UPPER_LIMIT" ]
do
  Primes[i]=$PRIME
  let "i += 1"
done
#  Assume all array members guilty (prime)
#+ until proven innocent.
}

print_primes ()
{
# Print out the members of the Primes[] array tagged as prime.

i=$LOWER_LIMIT

until [ "$i" -gt "$UPPER_LIMIT" ]
do

  if [ "${Primes[i]}" -eq "$PRIME" ]
  then
    printf "%8d" $i
    # 8 spaces per number gives nice, even columns.
  fi
  
  let "i += 1"
  
done

}

sift () # Sift out the non-primes.
{

let i=$LOWER_LIMIT+1
# We know 1 is prime, so let's start with 2.

until [ "$i" -gt "$UPPER_LIMIT" ]
do

if [ "${Primes[i]}" -eq "$PRIME" ]
# Don't bother sieving numbers already sieved (tagged as non-prime).
then

  t=$i

  while [ "$t" -le "$UPPER_LIMIT" ]
  do
    let "t += $i "
    Primes[t]=$NON_PRIME
    # Tag as non-prime all multiples.
  done

fi  

  let "i += 1"
done  


}


# ==============================================
# main ()
# Invoke the functions sequentially.
initialize
sift
print_primes
# This is what they call structured programming.
# ==============================================

echo

exit 0



# -------------------------------------------------------- #
# Code below line will not execute, because of 'exit.'

#  This improved version of the Sieve, by Stephane Chazelas,
#+ executes somewhat faster.

# Must invoke with command-line argument (limit of primes).

UPPER_LIMIT=$1                  # From command line.
let SPLIT=UPPER_LIMIT/2         # Halfway to max number.

Primes=( '' $(seq $UPPER_LIMIT) )

i=1
until (( ( i += 1 ) > SPLIT ))  # Need check only halfway.
do
  if [[ -n $Primes[i] ]]
  then
    t=$i
    until (( ( t += i ) > UPPER_LIMIT ))
    do
      Primes[t]=
    done
  fi  
done  
echo ${Primes[*]}

exit 0

#!/bin/bash
# stack.sh: push-down stack simulation

#  Similar to the CPU stack, a push-down stack stores data items
#+ sequentially, but releases them in reverse order, last-in first-out.

BP=100            #  Base Pointer of stack array.
                  #  Begin at element 100.

SP=$BP            #  Stack Pointer.
                  #  Initialize it to "base" (bottom) of stack.

Data=             #  Contents of stack location.  
                  #  Must use global variable,
                  #+ because of limitation on function return range.

declare -a stack


push()            # Push item on stack.
{
if [ -z "$1" ]    # Nothing to push?
then
  return
fi

let "SP -= 1"     # Bump stack pointer.
stack[$SP]=$1

return
}

pop()                    # Pop item off stack.
{
Data=                    # Empty out data item.

if [ "$SP" -eq "$BP" ]   # Stack empty?
then
  return
fi                       #  This also keeps SP from getting past 100,
                         #+ i.e., prevents a runaway stack.

Data=${stack[$SP]}
let "SP += 1"            # Bump stack pointer.
return
}

status_report()          # Find out what's happening.
{
echo "-------------------------------------"
echo "REPORT"
echo "Stack Pointer = $SP"
echo "Just popped \""$Data"\" off the stack."
echo "-------------------------------------"
echo
}


# =======================================================
# Now, for some fun.

echo

# See if you can pop anything off empty stack.
pop
status_report

echo

push garbage
pop
status_report     # Garbage in, garbage out.      

value1=23; push $value1
value2=skidoo; push $value2
value3=FINAL; push $value3

pop              # FINAL
status_report
pop              # skidoo
status_report
pop              # 23
status_report    # Last-in, first-out!

#  Notice how the stack pointer decrements with each push,
#+ and increments with each pop.

echo

exit 0

# =======================================================


# Exercises:
# ---------

# 1)  Modify the "push()" function to permit pushing
#   + multiple element on the stack with a single function call.

# 2)  Modify the "pop()" function to permit popping
#   + multiple element from the stack with a single function call.

# 3)  Add error checking to the critical functions.
#     That is, return an error code, depending on
#   + successful or unsuccessful completion of the operation,
#   + and take appropriate action.

# 4)  Using this script as a starting point,
#   + write a stack-based 4-function calculator.

#!/bin/bash

# Douglas Hofstadter's notorious "Q-series":

# Q(1) = Q(2) = 1
# Q(n) = Q(n - Q(n-1)) + Q(n - Q(n-2)), for n>2

# This is a "chaotic" integer series with strange and unpredictable behavior.
# The first 20 terms of the series are:
# 1 1 2 3 3 4 5 5 6 6 6 8 8 8 10 9 10 11 11 12 

#  See Hofstadter's book, "Goedel, Escher, Bach: An Eternal Golden Braid",
#+ p. 137, ff.


LIMIT=100     # Number of terms to calculate.
LINEWIDTH=20  # Number of terms printed per line.

Q[1]=1        # First two terms of series are 1.
Q[2]=1

echo
echo "Q-series [$LIMIT terms]:"
echo -n "${Q[1]} "             # Output first two terms.
echo -n "${Q[2]} "

for ((n=3; n <= $LIMIT; n++))  # C-like loop conditions.
do   # Q[n] = Q[n - Q[n-1]] + Q[n - Q[n-2]]  for n>2
#  Need to break the expression into intermediate terms,
#+ since Bash doesn't handle complex array arithmetic very well.

  let "n1 = $n - 1"        # n-1
  let "n2 = $n - 2"        # n-2
  
  t0=`expr $n - ${Q[n1]}`  # n - Q[n-1]
  t1=`expr $n - ${Q[n2]}`  # n - Q[n-2]
  
  T0=${Q[t0]}              # Q[n - Q[n-1]]
  T1=${Q[t1]}              # Q[n - Q[n-2]]

Q[n]=`expr $T0 + $T1`      # Q[n - Q[n-1]] + Q[n - Q[n-2]]
echo -n "${Q[n]} "

if [ `expr $n % $LINEWIDTH` -eq 0 ]    # Format output.
then   #      ^ Modula operator
  echo # Break lines into neat chunks.
fi

done

echo

exit 0

# This is an iterative implementation of the Q-series.
# The more intuitive recursive implementation is left as an exercise.
# Warning: calculating this series recursively takes a VERY long time.

#!/bin/bash
# twodim.sh: Simulating a two-dimensional array.

# A one-dimensional array consists of a single row.
# A two-dimensional array stores rows sequentially.

Rows=5
Columns=5
# 5 X 5 Array.

declare -a alpha     # char alpha [Rows] [Columns];
                     # Unnecessary declaration. Why?

load_alpha ()
{
local rc=0
local index

for i in A B C D E F G H I J K L M N O P Q R S T U V W X Y
do     # Use different symbols if you like.
  local row=`expr $rc / $Columns`
  local column=`expr $rc % $Rows`
  let "index = $row * $Rows + $column"
  alpha[$index]=$i
# alpha[$row][$column]
  let "rc += 1"
done  

#  Simpler would be
#+   declare -a alpha=( A B C D E F G H I J K L M N O P Q R S T U V W X Y )
#+ but this somehow lacks the "flavor" of a two-dimensional array.
}

print_alpha ()
{
local row=0
local index

echo

while [ "$row" -lt "$Rows" ]   #  Print out in "row major" order:
do                             #+ columns vary,
                               #+ while row (outer loop) remains the same.
  local column=0

  echo -n "       "            #  Lines up "square" array with rotated one.
  
  while [ "$column" -lt "$Columns" ]
  do
    let "index = $row * $Rows + $column"
    echo -n "${alpha[index]} "  # alpha[$row][$column]
    let "column += 1"
  done

  let "row += 1"
  echo

done  

# The simpler equivalent is
#     echo ${alpha[*]} | xargs -n $Columns

echo
}

filter ()     # Filter out negative array indices.
{

echo -n "  "  # Provides the tilt.
              # Explain how.

if [[ "$1" -ge 0 &&  "$1" -lt "$Rows" && "$2" -ge 0 && "$2" -lt "$Columns" ]]
then
    let "index = $1 * $Rows + $2"
    # Now, print it rotated.
    echo -n " ${alpha[index]}"
    #           alpha[$row][$column]
fi    

}
  



rotate ()  #  Rotate the array 45 degrees --
{          #+ "balance" it on its lower lefthand corner.
local row
local column

for (( row = Rows; row > -Rows; row-- ))
  do       # Step through the array backwards. Why?

  for (( column = 0; column < Columns; column++ ))
  do

    if [ "$row" -ge 0 ]
    then
      let "t1 = $column - $row"
      let "t2 = $column"
    else
      let "t1 = $column"
      let "t2 = $column + $row"
    fi  

    filter $t1 $t2   # Filter out negative array indices.
                     # What happens if you don't do this?
  done

  echo; echo

done 

#  Array rotation inspired by examples (pp. 143-146) in
#+ "Advanced C Programming on the IBM PC," by Herbert Mayer
#+ (see bibliography).
#  This just goes to show that much of what can be done in C
#+ can also be done in shell scripting.

}


#--------------- Now, let the show begin. ------------#
load_alpha     # Load the array.
print_alpha    # Print it out.  
rotate         # Rotate it 45 degrees counterclockwise.
#-----------------------------------------------------#

exit 0

# This is a rather contrived, not to mention inelegant simulation.

# Exercises:
# ---------
# 1)  Rewrite the array loading and printing functions
#     in a more intuitive and less kludgy fashion.
#
# 2)  Figure out how the array rotation functions work.
#     Hint: think about the implications of backwards-indexing an array.
#
# 3)  Rewrite this script to handle a non-square array,
#     such as a 6 X 4 one.
#     Try to minimize "distortion" when the array is rotated.