How to do a "Control Break" (Algorithm) | Unix Linux Forums | Tips and Tutorials

  Go Back    


Tips and Tutorials Helpful articles from our Users.

How to do a "Control Break" (Algorithm)

Tips and Tutorials


Closed Thread    
 
Thread Tools Search this Thread Display Modes
    #1  
Old 12-08-2012
bakunin bakunin is offline Forum Staff  
Bughunter Extraordinaire
 
Join Date: May 2005
Last Activity: 25 October 2014, 3:34 PM EDT
Location: In the leftmost byte of /dev/kmem
Posts: 4,286
Thanks: 45
Thanked 824 Times in 651 Posts
How to do a "Control Break" (Algorithm)

A vast amount of problems asked in "Shell Programming an Scripting" can be traced back to be an application of a basic algorithm called a Control Break. Every programmer - and script writers are programmers nonetheless - should immediately recognize problems of this sort and know how to deal with them. We will first discuss the problem in theory, then implement a shell script dealing with an example data set to show the ropes.


The Single Control Break

The most basic form is the single control break. It occurs when some record-oriented data is sortable by a key and all the records with an identical key value are to be processed somehow.

Too complicated? Perhaps, but in fact it is really easy: suppose you have a file of customers (the key) and their purchase values. The goal is to get the purchase totals for every customer. You build a sum (the processing) for all entries with the same customer ID (the identical key values). Lets see:


Code:
Alan      75
Bill      50
Charlie   75
Bill      40
Charlie   55
Alan      25
Bill      30

The first thing we have to do is to identify our key - the part we want to use to differentiate between customers, their names - and the data we need to do our processing - in this case the purchase values. This is easy in our example, but can be quite tricky in real-world applications

By the way: do not confuse "key" and "key value". Key is the part of the line we sort on. Here it is the first word. Key value is the value the key part holds in each record. The key value for line 1 is "Alan", while for line 5 it is "Charlie":


Code:
<Key>     <data>
Alan      75
Bill      50
Charlie   75
Bill      40
Charlie   55
Alan      25
Bill      30

The next step is really easy for shell programmers, because there is a genuine UNIX command for it: we need to sort our input data set for the key we have identified. In our case this simply means: sort , without any options.

Data after applying "sort"

Code:
Alan      25
Alan      75
Bill      30
Bill      40
Bill      50
Charlie   55
Charlie   75


Suppose we read this, line by line. Because it is sorted we can rely on all the identical key values coming right one after the other. That is, once we read a line with "Bill", there will be no "Alan"s any more. Keep this in mind while we set up a simple read-loop for the file:

Script.version1.sh:


Code:
#! /bin/ksh

typeset    customer=""
typeset -i value=0
typeset    infile="./input"

sort "$infile" |\
while read customer value ; do
     print - "Customer is: $customer\t\t Purchase is: $value"
done

exit 0

OK, we got the reading of the input correctly, as we have seen from the sample output. So let us come back on our last idea: every time the value of the key changes, one "group" (one certain customer) is finished and a new one begins.

Every time the key value changes from one to the next line we need to output the total. Let us see if we get the line where this happens correctly - we will just mark it, do nothing else:

Script.version2.sh:

Code:
#! /bin/ksh

typeset    customer=""
typeset -i value=0
typeset    infile="./input"
typeset    lastcustomer=""

sort "$infile" |\
while read customer value ; do
     if [ "$lastcustomer" != "$customer" ] ; then
          print - "Here needs to be a total."
     fi
     print - "Customer is: $customer\t\t Purchase is: $value"

     lastcustomer="$customer"
done

exit 0

Well - almost, yes? Two things which aren't quite right.

First, the first total is requested in the first line, which is nonsense. It happens because the value of "lastcustomer" is pre-set to "" which is of course different of the first customer name we actually read in. Still, there should be no total there.

Second, the last total, for "Charlie", is missing at all. The reason is that after the last record, which would end the group of "Charlie"s, the loop is simply left. So let us fix the code to take care of these two problems:

Script.version3.sh:

Code:
#! /bin/ksh

typeset    customer=""
typeset -i value=0
typeset    lastcustomer=""
typeset    infile="./input"

sort "$infile" |\
while read customer value ; do
     if [ "$lastcustomer" != "$customer" -a "$lastcustomer" != "" ] ; then
          print - "Here needs to be a total"
     fi
     print - "Customer is: $customer\t\t Purchase is: $value"

     lastcustomer="$customer"
done
print - "Here needs to be a total"

exit 0

Very well! Now let us implement the total: we already know, where we need to output it. We need to sum up every value read in in a sum variable. Upon the "control break" happening, when the key value changes, we have to output the sum, then reinitialize the sum variable with zero again and continue. Let's do it:


Code:
#! /bin/ksh

typeset    customer=""
typeset -i value=0
typeset    lastcustomer=""
typeset    infile="./input"
typeset -i sum=0

sort "$infile" |\
while read customer value ; do
     if [ "$lastcustomer" != "$customer" -a "$lastcustomer" != "" ] ; then
          print - "--- Total for $lastcustomer is $sum"
          (( sum = 0 ))
     fi
     print - "Customer is: $customer\t\t Purchase is: $value"
     (( sum = sum + value ))

     lastcustomer="$customer"
done
print - "--- Total for $lastcustomer is $sum"

exit 0

That was really easy, wasn't it? In fact, that was all - we solved the problem! But suppose we would have had to calculate the average of the purchases instead of the total for each customer. You sure know by now how this works, no?

OK, don't read any further! Instead, do it yourself and compare your solution to mine:


Code:
#! /bin/ksh

typeset    customer=""
typeset -i value=0
typeset    lastcustomer=""
typeset    infile="./input"
typeset -i sum=0             # total of the purchases
typeset -i avg=0             # average purchase 
typeset -i num=0             # number of purchases

sort "$infile" |\
while read customer value ; do
     if [ "$lastcustomer" != "$customer" -a "$lastcustomer" != "" ] ; then
          (( avg = sum / num ))        # calculate average
          print - "--- Average purchase of $lastcustomer is $avg"
          (( sum = 0 ))                # clear counters
          (( num = 0 ))
          (( avg = 0 ))
     fi
     print - "Customer is: $customer\t\t Purchase is: $value"
     (( sum = sum + value ))
     (( num = num + 1 ))

     lastcustomer="$customer"
done

(( avg = sum / num ))
print - "--- Average purchase of $lastcustomer is $avg"

exit 0

Very well! But you see, when the "end processing" gets more and more complicated there is more and more redundant code to be written: once inside the main loop, once after it. It is therefore a good idea - at least for anything less trivial than summation - to move the end processing of each group to a function you can call:



Code:
#! /bin/ksh

pEndProcessing ()
{
typeset    cust="$1"
typeset -i sum=$2
typeset -i num=$3
typeset -i avg=$(( sum / num ))

print - "--- Average purchase of $cust is $avg"
print - ""                   # insert extra line feed for easier reading

return 0
}



# main ()
typeset    customer=""
typeset -i value=0
typeset    lastcustomer=""
typeset    infile="./input"
typeset -i sum=0             # total of the purchases
typeset -i num=0             # number of purchases

sort "$infile" |\
while read customer value ; do
     if [ "$lastcustomer" != "$customer" -a "$lastcustomer" != "" ] ; then
          pEndProcessing "$lastcustomer" $sum $num
          (( sum = 0 ))                # clear counters
          (( num = 0 ))
     fi
     print - "Customer is: $customer\t\t Purchase is: $value"
     (( sum = sum + value ))
     (( num = num + 1 ))

     lastcustomer="$customer"
done

pEndProcessing "$lastcustomer" $sum $num

exit 0

Perfect! This was our final transformation and i promise you will be able to solve all kinds of simple control break type problems using this blueprint and adapting it. That's all!




The Multiple Control Break

You might already have sensed it from the innocent word "single": this wasn't really all there is. Where there is "single" there is "multiple" and the same is true here. So here is the multiple control break, which is of course more complex than the single one. But don't panic! The solution is really easy to grasp for experts of the single control break - you!

Suppose that every group you have to process consists of several subgroups you have to process too. Sounds complicated again? Well, an example will clear that up. This is a list of the cars our customers purchased:

file input2


Code:
Bell    Dodge   Charger
Craig   VW      Touareg
Graham  VW      Golf
Jones   Dodge   Dart
Leslie  Dodge   Dart
Myers   Dodge   Avenger
Rock    Dodge   Avenger
Loman   VW      Beetle
Smith   Dodge   Dart
Smyth   VW      Beetle

You see, we have several models as well as several manufacturers. In the end i not only want to know how many of every model we sold, but also, how the manufacturers fared. So we need a sum over all the "Dodge"s and the "VW"s, but also a sub-sum for the Dodge Charger, one for the Dodge Dart, etc..

At first we start again with identifying the key(s): now, every key consists of a main key and a sub-key. If the main key value changes, we have a "primary control break", if only the sub-key value changes we have a "secondary control break". Instead of the single-layer control break we had in our first example we have now a two-layer hierarchy. Having anything else than a single layer - instead of the 2 levels here there could be several - means executing a multiple control break.

This time the sorting process is way more complex. I suggest you consult the man page of sort if you are not absolutely sure what the following command does:


Code:
# sort -bk 2 input2  
Myers   Dodge   Avenger
Rock    Dodge   Avenger
Bell    Dodge   Charger
Jones   Dodge   Dart
Leslie  Dodge   Dart
Smith   Dodge   Dart
Loman   VW      Beetle
Smyth   VW      Beetle
Graham  VW      Golf
Craig   VW      Touareg

As you have already gotten that far, i am sure the following code will be obvious to you. I changed the totalling function a bit to do either a "big" total (for the manufacturers) or a "small" total (for the models). But beware: i have introduced a very subtle weakness in the program and you might want to try to find it. Spoilsports will find it below, but if you want to try your debugging expertise - be my guest.

And now, without further ado, here is the "double control break":


Code:
#! /bin/ksh

pEndProcessing ()
{
typeset    type="$1"
typeset    manu="$2"
typeset    mod="$3"
typeset -i num=$4

case "$type" in
     small)
          print - "Total sold $manu $mod's: $num"
          ;;

     big)
          print - "-------- Total sold $manu's: $num\n"
          ;;

     *)
          print -u2 - "Error: i cannot handle mode $type"
          ;;
esac

return 0
}




# main ()
typeset    customer=""
typeset    manufacturer=""
typeset    model=""
typeset -i nummanu=0
typeset -i nummodel=0
typeset    infile="./input2"

sort -bk 2 "$infile" |\
while read customer manufacturer model ; do
     if [ "$lastmodel" != "$model" -a "$lastmodel" != "" ] ; then
          pEndProcessing small "$lastmanufacturer" "$lastmodel" $nummodel
          if [ "$lastmanufacturer" != "$manufacturer" ] ; then
               pEndProcessing big "$lastmanufacturer" "$lastmodel" $nummanu
               (( nummanu = 0 ))
          fi
          (( nummodel = 0 ))
     fi

     (( nummanu = nummanu + 1 ))
     (( nummodel = nummodel + 1 ))
     lastmodel="$model"
     lastmanufacturer="$manufacturer"
done

pEndProcessing small "$lastmanufacturer" "$lastmodel" $nummodel
pEndProcessing big "$lastmanufacturer" "$lastmodel" $nummanu

exit 0

Have you found the weakness? You probably need a hint. OK, the problem is in this line:


Code:
     if [ "$lastmodel" != "$model" -a "$lastmodel" != "" ] ; then

Still not sure? OK, here is the last hint: replace the input file "input2" with the following "input3" and let it run again:


Code:
Bell    ManufacturerA     ModelA
Craig   ManufacturerB     ModelC
Graham  ManufacturerB     ModelD
Jones   ManufacturerA     ModelA
Leslie  ManufacturerA     ModelB
Myers   ManufacturerA     ModelC
Rock    ManufacturerA     ModelA
Loman   ManufacturerB     ModelD
Smith   ManufacturerA     ModelC
Smyth   ManufacturerB     ModelE

Solution follows:

When you look at the sorted file, you will notice that the "last" model of "ManufacturerA" has the same name as the "first" model of "ManufacturerB". Because of this the "big" control break for the manufacturer is not executed. The weakness in the line is, that it implies a "big" group change to contain a "small" group change too. This does not necessarily have to be the case. Modify the line therefore like this:


Code:
     if [ \( "$lastmodel" != "$model" \
             -o "$lastmanufacturer" != "$manufacturer" \
          \) -a "$lastmodel" != "" ] ; then

and you will see the program can even process the "input3" file.

Happy shell programming.




...on Second Thoughts, or: Instead of an Epilogue

Since i have written the first version of this article we had a few threads where its logic was applicable. Sometimes in a straightforward manner, sometimes only after adapting the basic algorithm to fit the problem at hand. I have to admit that in my striving to clarify the inner workings of this common algorithm i failed to show where it fits into a greater picture.

Some have mentioned that the control break can be (or even: is already) implemented in other languages: SQL, awk and others. This is true. I tried to explain the basic workings of this algorithm in a general-purpose language and while i recognize some (specialized) languages have such a functionality already built in little would be gained in terms of understanding if i would be to refer only to "this keyword" and be done. But now, that we have learned what exactly is done and how we do it, i want to make good for my neglect by explaining how it can be done in other languages:

The control break in SQL

In short: you do not need it, because it is part of the language. In fact it is what the "GROUP BY" clause does.


The control break in awk

In this thread i suggested to apply this article to the problem and DonCragun mentioned - rightfully - that it would be easier to do in awk. I suggest you read his very elegant solution there.

Basically it burns down to the following: construct an "associative array" (1) where the index is your key and the array element is your number you want to sum up on. Using the file from the first example this would look like:


Code:
customers["Alan"] = 100
customers["Bill"] = 120
customers["Charlie"] = 130

In the main part you just load this array, in the end part you cycle through it and print the sums. Suppose the first field to be the key and the second to be the value:


Code:
awk '
{       array[$1] += $2 }
END {   for(index in array)
                printf("%s  %f\n", index, array[index])
}' input1

The advantage of this is: you do not have to sort the input before processing it. Elements of the associative array are created as they are needed. On the downside, you process the output file in memory: until you have read the complete input you have to hold the output (the array itself) in memory, only then you can process (=output) it. This is a very small concern in the overwhelming majority of cases, but you should be aware of this.

Thanks, Acknowledgements

I should mention that - being the awk ignorant that i am - i borrowed DonCraguns awk script and my only addition was to "dumb it down" to the bare minimum. I am additionally thankful for his valuable suggestions regarding this article. I barely know SQL and if it had not been for fpmurphys alertness this wouldn't have come to me that "GROUP BY" in SQL does exactly what i wrote about. He also mentioned XSLT, but i haven't used this language in my life. I am sure that, generous as he is, he will explain to you what i do not know if you ask him.

Errors, omissions and misrepresentations are still my own fault and if you find any dubious passages, including typos: do not take them with you but report them to me. I'll be glad to weed them out.

bakunin


________________
(1) In case you do not know this term: it is an array where the indexes are not numerical but strings. So, instead of

Code:
cars[1]=25
cars[2]=10
cars[3]=21
...

you'd have


Code:
cars["yellow cars"]=25
cars["red cars"]=10
cars["blue cars"]=21
...


Last edited by bakunin; 07-20-2013 at 11:38 AM..
The Following 4 Users Say Thank You to bakunin For This Useful Post:
Don Cragun (12-08-2012), jim mcnamara (12-08-2012), Scott (07-20-2013), Yoda (06-08-2013)
Sponsored Links
    #2  
Old 12-09-2012
fpmurphy's Avatar
fpmurphy fpmurphy is offline Forum Staff  
who?
 
Join Date: Dec 2003
Last Activity: 25 October 2014, 1:14 AM EDT
Location: /dev/ph
Posts: 4,823
Thanks: 64
Thanked 431 Times in 399 Posts
I have to say that I have never heard this particular issue called the Control Break Algorithm before but a quick Internet search showed that the term is becoming somewhat common among educators. In SQL, this would be handled by the GROUP BY statement, in XSLT it is called grouping and is typically handled by the Muenchian Method.
Sponsored Links
Closed Thread

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

More UNIX and Linux Forum Topics You Might Find Helpful
Thread Thread Starter Forum Replies Last Post
Looking for Your Help on dijkstra algorithm ali2011 Programming 4 11-30-2011 04:19 PM
BASH: Break line, read, break again, read again... SilversleevesX Shell Programming and Scripting 2 05-06-2011 06:56 AM
Algorithm In Pseudocode delsega UNIX for Advanced & Expert Users 1 03-10-2008 11:10 AM
algorithm filthymonk Shell Programming and Scripting 5 07-20-2007 03:13 AM
FTP's algorithm toughguy2handle Programming 1 09-23-2005 02:52 PM



All times are GMT -4. The time now is 05:09 PM.