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
 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Alfred 3.4.1 - Quick launcher for apps a...
Alfred is an award-winning productivity application for OS X. Alfred saves you time when you search for files online or on your Mac. Be more productive with hotkeys, keywords, and file actions at... Read more
Maintenance 2.2.7 - System maintenance u...
Maintenance is a system maintenance and cleaning utility. It allows you to run miscellaneous tasks of system maintenance: Check the status of the hard disk Repair permissions Run periodic scripts... Read more
NeoOffice 2017 - Mac-tailored, OpenOffic...
NeoOffice is a complete office suite for OS X. With NeoOffice, users can view, edit, and save OpenOffice documents, PDF files, and most Microsoft Word, Excel, and PowerPoint documents. NeoOffice 3.x... Read more
SyncTwoFolders 2.2.4 - Syncs two user-sp...
SyncTwoFolders simply synchronizes two folders. It supports synchronization across mounted network drives and it is a possibility to run a simulation showing in a log what will be done. Please visit... Read more
Hopper Disassembler 4.2.13- - Binary dis...
Hopper Disassembler is a binary disassembler, decompiler, and debugger for 32- and 64-bit executables. It will let you disassemble any binary you want, and provide you all the information about its... Read more
iFFmpeg 6.4.3 - Convert multimedia files...
iFFmpeg is a comprehensive media tool to convert movie, audio and media files between formats. The FFmpeg command line instructions can be very hard to master/understand, so iFFmpeg does all the hard... Read more
Firefox 55.0.2 - Fast, safe Web browser.
Firefox offers a fast, safe Web browsing experience. Browse quickly, securely, and effortlessly. With its industry-leading features, Firefox is the choice of Web development professionals and casual... Read more
FileZilla 3.27.1 - Fast and reliable FTP...
FileZilla (ported from Windows) is a fast and reliable FTP client and server with lots of useful features and an intuitive interface. Version 3.27.1: Fixed Vulnerabilities: Change client... Read more
Merlin Project 4.2.7 - $289.00
Merlin Project is the leading professional project management software for OS X. If you plan complex projects on your Mac, you won’t get far with a simple list of tasks. Good planning raises... Read more
Dashlane 4.8.4 - Password manager and se...
Dashlane is an award-winning service that revolutionizes the online experience by replacing the drudgery of everyday transactional processes with convenient, automated simplicity - in other words,... Read more

Roll to Win with Game of Dice’s new upda...
Joycity’s hit Game of Dice gets a big new update this week, introducing new maps, mechanics, and even costumes. The update sets players loose on an exciting new map, The Cursed Tower, that allows folks to use special Runes mid-match. If you feel... | Read more »
Bottom of the 9th (Games)
Bottom of the 9th 1.0.1 Device: iOS iPhone Category: Games Price: $4.99, Version: 1.0.1 (iTunes) Description: Play the most exciting moment of baseball in this fast-paced dice and card game! | Read more »
The best apps for viewing the solar ecli...
If you somehow missed the news, many parts of the United States will be witness to a total solar eclipse on August 21 for the first time in over 90 years. It'll be possible to see the eclipse in at least some capacity throughout the continental U... | Read more »
The 5 best mobile survival games
Games like ARK: Survival Evolved and Conan Exiles have taken the world of gaming by storm. The market is now flooded with hardcore survival games that send players off into the game's world with nothing but maybe the clothes on their back. Never... | Read more »
Portal Walk (Games)
Portal Walk 1.0 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0 (iTunes) Description: Portal Walk is adventure and relaxing platform game about Eugene. Eugene stuck between worlds and trying to find way back home.... | Read more »
Technobabylon (Games)
Technobabylon 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: City of Newton, 2087. Genetic engineering is the norm, the addictive Trance has replaced almost any need for human interaction,... | Read more »
5 reasons why 2v2 is the best mode in Cl...
Supercell has been teasing fans with 2v2 windows that allow players to team up for limited periods of time. The Summer of 2v2 was just this past July, but players are already clamoring for more of that sweet, sweet team-based action. The fans have... | Read more »
The best deals on the App Store this wee...
It seems like the week's only just started, and yet here we are with a huge pile of discounted games to sort through. There are some real doozies on sale this week. We're talking some truly stellar titles. Let's take a look at four of the best... | Read more »
Cat Quest Guide - How to become a purrfe...
Cat Quest is an absolutely charming open-world RPG that's taken the gaming world quite by storm. This game about a world populated by furry kitty warriors is actually a full-length RPG with sturdy mechanics and a lovely little story. It's certainly... | Read more »
Silly Walks Guide - How to strut your st...
Silly Walks is an all new adventure game that lives up to its name. It sees you playing as a variety of snack foods as you teeter-totter your way to rescue your friends from the evil blender and his villainous minions. It's all very . . . well... | Read more »

Price Scanner via MacPrices.net

13-inch 2.3GHz MacBook Pros on sale for $100...
Amazon has the new 2017 13″ 2.3GHz MacBook Pros on sale today for $100 off MSRP, each including free shipping: – 13″ 2.3GHz/128GB Space Gray MacBook Pro (MPXQ2LL/A): $1199.99 $100 off MSRP – 13″ 2.... Read more
New iOS 11 Productivity Features Welcome But...
The iOS community is in late summer holding mode awaiting the September arrival of the iPhone 8 and iOS 11. iOS 11 public betas have been available for months — number six was released this week —... Read more
Samsung Electronics Launches New Portable SSD...
Samsung Electronics America, Inc. has announced the launch of Samsung Portable SSD T5 – its newest portable solid state drive (PSSD) that raises the bar for the performance of external memory... Read more
TrendForce Reports YoY Gain of 3.6% for 2Q17...
Market research firm TrendForce reports that the global notebook shipments for this second quarter registered a sequential quarterly increase of 5.7% and a year-on-year increase of 3.6%, totaling 39.... Read more
Sale! 10-inch iPad Pros for $50 off MSRP, no...
B&H Photo has 10.5″ iPad Pros in stock today and on sale for $50 off MSRP. Each iPad includes free shipping, and B&H charges sales tax in NY & NJ only: – 10.5″ 64GB iPad Pro: $599, save $... Read more
Sale! 2017 13-inch Silver 2.3GHz MacBook Pro...
Amazon has new 2017 13″ 2.3GHz/128GB Silver MacBook Pro on sale today for $100 off MSRP including free shipping. Their price is the lowest available for this model from any reseller: – 13″ 2.3GHz/... Read more
WaterField Unveils Collaboratively-Designed,...
In collaboration with customers and seasoned travelers, San Francisco maker WaterField Designs set out to create the preeminent carry-on system to improve the experience of frequent fliers. The... Read more
Miya Notes Mac-Client for Google Keep (Launch...
MacPlus Software has announced te launch of Miya Notes for Google Keep 1.0, a powerful Mac-client for Google Keep. Millions of people use Google Keep on their phones and online, but a convenient Mac... Read more
Apple refurbished iMacs available starting at...
Apple has previous-generation Certified Refurbished 2015 21″ & 27″ iMacs available starting at $849. Apple’s one-year warranty is standard, and shipping is free. The following models are... Read more
2017 13-inch MacBook Airs on sale for $100 of...
B&H Photo new 2017 13″ MacBook Airs on sale today for $100 off MSRP, starting at $899: – 13″ 1.8GHz/128GB MacBook Air (MQD32LL/A): $899, $100 off MSRP – 13″ 1.8GHz/256GB MacBook Air (MQD42LL/A... Read more

Jobs Board

Development Operations and Site Reliability E...
Development Operations and Site Reliability Engineer, Apple Payment Gateway Job Number: 57572631 Santa Clara Valley, California, United States Posted: Jul. 27, 2017 Read more
Frameworks Engineering Manager, *Apple* Wat...
Frameworks Engineering Manager, Apple Watch Job Number: 41632321 Santa Clara Valley, California, United States Posted: Jun. 15, 2017 Weekly Hours: 40.00 Job Summary Read more
*Apple* Customer Experience (ACE) Leader - A...
…management to deliver on business objectivesTraining partner store staff on Apple products, services, and merchandising guidelinesCoaching partner store staff on Read more
*Apple* Solutions Consultant (ASC) - Poole -...
Job Summary The people here at Apple don't just create products - they create the kind of wonder that's revolutionised entire industries. It's the diversity of those Read more
Business Development Manager, *Apple* iClou...
Job Summary Apple is seeking an entrepreneurial person to help grow the Apple iCloud business, a service that is integral to the Apple customer experience. Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.