TweetFollow Us on Twitter

Oct 00 Challenge

Volume Number: 16 (2000)
Issue Number: 10
Column Tag: Programmer's Challenge

Programmer's Challenge

by Bob Boonstra, Westford, MA

What Bills did they Pay?

This month we are helping the accounting department of a small business with a problem. Our little business is a daily newspaper that survives on its advertising revenue. Each day they print a newspaper, and each newspaper contains a number of ads. Whenever the accounting staff can find the time, they send out invoices to their advertising customers. Sometimes they bill daily, sometimes weekly, sometimes irregularly during a week or longer period. Most of the customers pay promptly, and most of them reference the invoice being paid along with their Payment. That's good, because our little newspaper has only a small accounting staff with no time to reconcile Payments.

The problem is with a couple of the newspaper's larger customers. These customers don't always pay promptly, and some of them don't reference the invoice when they pay. To make things worse, they sometimes pay part of an invoice, or pay multiple invoices with a simple payment.

Your job is to help sort this all out. The prototype for the code you should write is:

#include "OSUtils.h"

typedef struct Invoice {
   DateTimeRec   invoiceDate;      /* date on which customer was invoiced */
   long       invoiceAmount;      /* amount customer was invoiced */
   long      invoiceNumber;         /* reference invoice number */
} Invoice;

typedef struct Payment {
   DateTimeRec   paymentDate;      /* date payment was submitted */
   long       paymentAmount;      /* amount of payment */
   long      paymentNumber;         /* reference payment number */
} Payment;

typedef struct Reconciliation {
   long      paymentNumber;   
      /* reference number of payment being applied */
   long      invoiceNumber;   
      /* reference number of invoice to which payment is applied, zero if duplicate */
   long      appliedAmount;
      /* amount of referenced payment being applied to this invoice */
} Reconciliation;

long /* number of reconciliation records returned */ ReconcilePayments (
   const Invoice theInvoices[],
      /* invoices to reconcile, sorted by increasing date */
   const Payment thePayments[],
      /* payments to reconcile, sorted by increasing date */
   Reconciliation theReconciliation[],
      /* return reconciliation here */
   long numberOfReconciliationRecords,
      /* number of theReconciliation records preallocated */
   long *lateDollarDays         /* see problem description */
);

The objective of this Challenge is to determine which of the Invoices sent to a problematic customer have been settled by a sequence of Payments. Your ReconcilePayments routine needs to examine theInvoices and thePayments input arrays and produce an array of Reconciliation records. Each Reconciliation record must contain the paymentNumber of the Payment being matched, the invoiceNumber of the Invoice being matched, and the amount of the Payment being applied to the Invoice. A given paymentNumber may appear in multiple Reconciliation records, if the Payment reimbursed more than one Invoice. A given invoiceNumber may also appear in multiple Reconciliation records, if partial payment was provided by more than one Payment record.

There are a few things that you can rely on during your reconciliation. Customers never pay in advance - the payment date is never earlier than the date(s) of the Invoice(s) being paid. Customers might make a partial payment, but when they do so they never combine the partial payment with payment for any other Invoice.

Payments might be matched to Invoices in a number of ways, so more than one solution might exist. We have some constraints, however, that reduce the amount of ambiguity. Since we are going to use your results to charge interest to our problem customer, and we want to be as fair as possible, you must apply Payments to the earliest applicable Invoice. If the Payment matches a single Invoice exactly, or matches the sum of a number of Invoices exactly, you must apply the Payment to that (those) Invoice(s). If a Payment exactly matches the balance of an Invoice that has been partially paid by a previous Payment, you must apply the Payment to the balance of that Invoice, unless some other rule applies (e.g., an earlier Invoice that is exactly paid by this Payment).

To support assessing an interest charge for our problematic customers, you need to help the accounting department by calculating how much this customer is in arrears. Specifically, you need to calculate the number of dollar-days the customer is overdue. This is the sum, for each unpaid or partially unpaid Invoice, of the unpaid balance of the Invoice times the number of days the Payment is late. The unpaid amount is simply the amount remaining after your Reconciliation calculations, and the number of days late is the difference between the date of the most recent Payment and the date of the relevant Invoice. The sum of the dollar-days these Payments are late must be returned in the lateDollarDays parameter of the ReconcilePayments call.

Remember that you cannot apply a Payment to more than one Invoice unless the Payment exactly totals the original amount of those Invoices - you cannot simply apply partial Payments to the oldest Invoices to minimize the lateDollarDays value.

The winner will be the solution that correctly calculates the lowest lateDollarDays result. Among tie values, the entry with the lowest execution time will be the winner.

This will be a native PowerPC Challenge, using the CodeWarrior Pro 5 environment. Solutions may be coded in C, C++, or Pascal.

This Challenge was suggested by Ernst Munter, who adds two Challenge points to his lead for the suggestion. Thanks, Ernst!

One final point. I've received some letters from people who would like to participate in the Challenge, but who find the problems too difficult (despite my best efforts to simplify them), or who find our veteran contestants to be too dominating. I'd really like to find a way that new contestants could feel comfortable playing, so I'm considering ways to revise the prize structure or the points system to make that possible, while still being fair to our regular contestants. If you have any thoughts along this line, please drop me a suggestion at progchallenge@mactech.com.

Three Months Ago Winner

Congratulations to ... - oops, there is no one whom we can congratulate for winning the July RAID 5+ Challenge. The problem, you might recall, was to design a disk input-output system that would survive the loss of two disks in the array. A number of folks wrote to say that the problem was impossible, which must come as a surprise to the vendors who marketed solutions to this problem. In any case, this is one of those rare months when no one submitted a solution.

Is the problem impossible? Imagine a sequence of disks A, B, C, D, and E. Further, imagine that those disks are striped as follows:

         A0   B0   C0   D0   E0
         A1   B1   C1   D1   E1
         A2   B2   C2   D2   E2
         A3   B3   C3   D3   E3
         A4   B4   C4   D4   E4

Now, according to the problem statement, the actual data capacity of our array only requires N-2 of the available N disks. So, to implement protection against the loss of one disk, we can imagine calculating parity for block (stripe) n across disks A, B, C, D, and E. Call those parity blocks P1, P2, ..., Then imagine calculating another parity block, one for each disk. Call those parity blocks PA, PB, ... PE. Then lay those parity blocks out something like this:

         PB   B0   C0   D0   P0
         A1   B1   C1   P1   PA
         A2   B2   P2   PE   E2
         A3   P3   PD   D3   E3
         P4   PC   C4   D4   E4

Notice that the parity blocks are rotated across the available disks, but that the parity requires the capacity of only two disks. Note also that there is the equivalent of 3 disks of information distributed across the 5 physical disks. So what happens when two disks fail? How do we recover a block? Let's say that disks A and B fail, and that we want to recover block A1. (Failing these two disks actually represents a worst case, since the parity block PB for the failed disk B is on the other failed disk.) We have ten missing blocks of information (6 data blocks and 4 parity blocks), and we have the following parity equations, with the known elements bolded:

          1:   B0 + C0 + D0   + P0 = 0
          2: A1 + B1 + C1      + P1 = 0
          3: A2 + B2      + E2 + P2 = 0
          4: A3      + D3 + E3 + P3 = 0
          5:      C4 + D4 + E4 + P4 = 0
          6:   A1 + A2 + A3   + PA = 0
          7: B0 + B1 + B2      + PB = 0
          8: C0 + C1      + C4 + PC = 0
          9: D0      + D3 + D4 + PD = 0
         10:      E2 + E3 + E4 + PE = 0

The first equation allows one to determine B0, the second A1+B1, the third A2+B2, the fourth A3+P3, the fifth P4, and the eighth PC. The final two equations are all known quantities and do not help. This leaves us with the following:

          1:   B0 + C0 + D0   + P0 = 0
          2: A1 + B1 + C1      + P1 = 0 (A1 + B1 known)
          3: A2 + B2      + E2 + P2 = 0 (A2 + B2 known)
          4: A3      + D3 + E3 + P3 = 0 (A3 + P3 known)
          5:      C4 + D4 + E4 + P4 = 0
          6:   A1 + A2 + A3   + PA = 0 (A1 + A2 + A3 known)
          7: B0 + B1 + B2      + PB = 0 (B1 + B2 + PB known)
          8: C0 + C1      + C4 + PC = 0
          9: D0      + D3 + D4 + PD = 0
         10:      E2 + E3 + E4 + PE = 0

This gives us 5 remaining equations and 7 unknowns (A1, A2, A3, B1, B3, P3, and PB). So, it looks like we are short a couple of equations to arrive at a unique solution. But we've ignored an additional constraint imposed by parity, that x+x=0. By enumerating all possible values of these seven remaining unknowns, and determining which constraints are satisfied by each combination, it turns out that only one combination of values satisfies all constraints. So it seems to me that a solution ought to be possible. If you think I've missed something, please let me know and I'll continue the discussion!

There is also a fair amount of literature on RAID schemes beyond RAID 5. If you're interested, you might start out at <http://www.pdl.cs.cmu.edu/RAID/RAID.html> and take it from there.

Top Contestants

Listed here are the Top Contestants for the Programmer's Challenge, including everyone who has accumulated 10 or more points during the past two years. The numbers below include points awarded over the 24 most recent contests, including points earned by this month's entrants.

Rank Name Points
1. Munter, Ernst 243
2. Saxton, Tom 106
3. Maurer, Sebastian 78
4. Rieken, Willeke 65
5. Boring, Randy 50
6. Shearer, Rob 47
7. Taylor, Jonathan 26
8. Brown, Pat 20
9. Downs, Andrew 12
10. Jones, Dennis 12
11. Day, Mark 10
12. Duga, Brady 10
13. Fazekas, Miklos 10
14. Murphy, ACC 10
15. Selengut, Jared 10
16. Strout, Joe 10

There are three ways to earn points: (1) scoring in the top 5 of any Challenge, (2) being the first person to find a bug in a published winning solution or, (3) being the first person to suggest a Challenge that I use. The points you can win are:

1st place 20 points
2nd place 10 points
3rd place 7 points
4th place 4 points
5th place 2 points
finding bug 2 points
suggesting Challenge 2 points
 
AAPL
$107.80
Apple Inc.
+0.82
MSFT
$46.82
Microsoft Corpora
+0.77
GOOG
$558.34
Google Inc.
+8.03

MacTech Search:
Community Search:

Software Updates via MacUpdate

Vitamin-R 2.20b1 - Personal productivity...
Vitamin-R creates the optimal conditions for your brain to work at its best by structuring your work into short bursts of distraction-free, highly focused activity alternating with opportunities for... Read more
Dropbox 2.10.44 - Cloud synchronization...
Dropbox is an application that creates a special Finder folder that automatically syncs online and between your computers. It allows you to both backup files and keep them up-to-date between systems... Read more
Sandvox 2.9.2 - Easily build eye-catchin...
Sandvox is for Mac users who want to create a professional looking website quickly and easily. With Sandvox, you don't need to be a Web genius to build a stylish, feature-rich, standards-compliant... Read more
Cocktail 8.0.1 - General maintenance and...
Cocktail is a general purpose utility for OS X that lets you clean, repair and optimize your Mac. It is a powerful digital toolset that helps hundreds of thousands of Mac users around the world get... Read more
LibreOffice 4.3.3.2 - Free Open Source o...
LibreOffice is an office suite (word processor, spreadsheet, presentations, drawing tool) compatible with other major office suites. The Document Foundation is coordinating development and... Read more
VMware Fusion 7.0.1 - Run Windows apps a...
VMware Fusion allows you to create a Virtual Machine on your Mac and run Windows (including Windows 8.1) and Windows software on your Mac. Run your favorite Windows applications alongside Mac... Read more
OneNote 15.3.2 - Free digital notebook f...
OneNote is your very own digital notebook. With OneNote, you can capture that flash of genius, that moment of inspiration, or that list of errands that's too important to forget. Whether you're at... Read more
Audio Hijack Pro 2.11.4 - Record and enh...
Audio Hijack Pro drastically changes the way you use audio on your computer, giving you the freedom to listen to audio when you want and how you want. Record and enhance any audio with Audio Hijack... Read more
Iridient Developer 3.0.0 beta 3 - Powerf...
Iridient Developer (was RAW Developer) is a powerful image conversion application designed specifically for OS X. Iridient Developer gives advanced photographers total control over every aspect of... Read more
TextWrangler 4.5.11 - Free general purpo...
TextWrangler is the powerful general purpose text editor, and Unix and server administrator's tool. Oh, and also, like the best things in life, it's free. TextWrangler is the "little brother" to... Read more

Latest Forum Discussions

See All

Monster Flash Review
Monster Flash Review By Jordan Minor on October 31st, 2014 Our Rating: :: ALONE IN THE DARKUniversal App - Designed for iPhone and iPad Solid shooting and a surprising amount of spooky tension make Monster Flash a great portable... | Read more »
Retry Review
Retry Review By Rob Thomas on October 31st, 2014 Our Rating: :: SOARING HIGHUniversal App - Designed for iPhone and iPad Flappy who? Let Retry wash all those bad bird-related memories away on a cool retro-flavored flight… right... | Read more »
Dementia: Book of the Dead Review
Dementia: Book of the Dead Review By Lee Hamlet on October 31st, 2014 Our Rating: :: A TOUGH READUniversal App - Designed for iPhone and iPad A witch hunter is sent after a demonic book in the spooky but short-lived Dementia: Book... | Read more »
Card Dungeon, the Semi-Board Game Roguel...
Card Dungeon, the Semi-Board Game Roguelike, Has Been Renovated Posted by Jessica Fisher on October 31st, 2014 [ permalink ] | Read more »
Logitech Protection + Power iPhone5/5S C...
Made by: Logitech Price: $99.99 Hardware/iOS Integration Rating: 3 out of 5 stars Usability Rating: 0.5 out of 5 stars Reuse Value Rating: 0.75 out of 5 stars Build Quality Rating: 0.75 out of 5 stars Overall Rating: 1.25 out of 5 stars | Read more »
This Is Not a Test Goes Free, Permanentl...
This Is Not a Test Goes Free, Permanently Posted by Jessica Fisher on October 31st, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »
Swap Heroes Review
Swap Heroes Review By Campbell Bird on October 31st, 2014 Our Rating: :: STRATEGIC SWAPPINGUniversal App - Designed for iPhone and iPad Rotate a cast of heroes to fend of waves of monsters in this difficult, puzzle rpg.   | Read more »
Night Sky Pro™ (Reference)
Night Sky Pro™ 3.0.1 Device: iOS Universal Category: Reference Price: $2.99, Version: 3.0.1 (iTunes) Description: Night Sky Pro™Wonder No More™ Night Sky Pro™ is the ultimate stargazing experience. From the creators of the original... | Read more »
Audio Defence : Zombie Arena (Games)
Audio Defence : Zombie Arena 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: A zombie shooter audio game. Made from gut-wrenching 3D binaural sound, for a new kind of weird immersion. You... | Read more »
RPG Asdivine Hearts (Games)
RPG Asdivine Hearts 1.1.0 Device: iOS Universal Category: Games Price: $3.99, Version: 1.1.0 (iTunes) Description: SPECIAL PRICE50% OFF (USD 7.99 -> USD 3.99)!!! Travel alongside four companions and a cat in the adventure of a... | Read more »

Price Scanner via MacPrices.net

Apple now offering refurbished 2014 13-inch R...
The Apple Store is now offering Apple Certified Refurbished 2014 13″ Retina MacBook Pros for up to $270 off the cost of new models. An Apple one-year warranty is included with each model, and... Read more
Apple Regains Momentum As Windows Stutters An...
The latest smartphone sales data from Kantar Worldpanel ComTech, for the three months to March 2014, shows Apple performing strongly in the first quarter of the year, with sales bouncing back in... Read more
Worldwide Smartphone Shipments Increase 25.2%...
New smartphone releases and an increased emphasis on emerging markets drove global smartphone shipments above 300 million units for the second consecutive quarter, according to preliminary data from... Read more
Apple now offering refurbished 2014 15-inch M...
The Apple Store is now offering Apple Certified Refurbished 2014 15″ Retina MacBook Pros for up to $400 off the cost of new models. An Apple one-year warranty is included with each model, and... Read more
Apple drops prices on refurbished 2013 Retina...
The Apple Store has dropped prices on 2013 Apple Certified Refurbished 13″ and 15″ Retina MacBook Pros, with Retina models now available starting at $999. Apple’s one-year warranty is standard, and... Read more
New 2.8GHz Mac mini on sale for $949, save $5...
Abt Electronics has the new 2.8GHz Mac mini in stock and on sale for $949.05 including free shipping. Their price is $50 off MSRP, and it’s the lowest price available for this model from any reseller... Read more
Sale! 3.7GHz Quad Core Mac Pro available for...
 B&H Photo has the 3.7GHz Quad Core Mac Pro on sale for $2649 including free shipping plus NY sales tax only. Their price is $350 off MSRP, and it’s the lowest price for this model from any... Read more
Mujjo Steps Up The Game With Refined Touchscr...
Netherlands based Mujjo have just launched their Refined Touchscreen Gloves, stepping up their game. The gloves feature a updated elegant design that takes these knitted gloves to the next level. A... Read more
Sale! Preorder the new 27-inch 5K iMac for $2...
 Abt Electronics has the new 27″ 3.5GHz 5K iMac on sale and available for preorder for $2374.05 including free shipping. Their price is $125 off MSRP, and it’s the lowest price available for this... Read more
Simplex Solutions Inc. Brings Secure Web Surf...
New York based Simplex Solutions Inc. has announced the release and immediate availability of Private Browser 1.0, its revolutionary new secure web browser developed for iPhone, iPad and iPod touch... Read more

Jobs Board

Position Opening at *Apple* - Apple (United...
**Job Summary** Every day, business customers come to the Apple Store to discover what powerful, easy-to-use Apple products can do for them. As a Business Leader, Read more
Sr. Manager, *Apple* Deployment Programs fo...
**Job Summary** Apple is seeking candidates for a new position on the Education Content and Technology team. iPad and Mac is in the hands of millions of teachers and Read more
*Apple* Solutions Consultant (ASC) - Apple I...
…important role that the ASC serves is that of providing an excellent Apple Customer Experience. Responsibilities include: * Promoting Apple products and solutions Read more
*Apple* Solutions Consultant (ASC) - Apple I...
…important role that the ASC serves is that of providing an excellent Apple Customer Experience. Responsibilities include: * Promoting Apple products and solutions Read more
*Apple* Solutions Consultant (ASC) - Apple I...
…important role that the ASC serves is that of providing an excellent Apple Customer Experience. Responsibilities include: * Promoting Apple products and solutions Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.