I'm ashamed that I knew so little about...

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This post will not be related to programming. I want to write about something that I've read about recently. I think that it's extremely interesting. Besides it is important for me. I'm talking about Lvov school of mathematics, a group of brilliant Polish mathematicians who worked in Lvov before World War II and had a great impact on contemporary mathematic. You may be surprised that even famous people like John von Neumann visited Lvov in order to talk with them.

Have you heard about them? If you come from Poland there is a chance that you heard although it is not very well know topic. And it is a pity because Polish people should be proud because of their achievements. If you are not from Poland there is a bigger chance that you heard about people like Stefan Banach, Stanisław Ulam or Hugo Steinhaus. Just to mention 3 mathematicians who were a part of Lvov school of mathematics.

These were very special people. Stefan Banach established very important part of mathematic known as functional analysis, was the author of many theorems (e.g. Banach space), has his own planetoid 16856. He had written his PhD thesis within 6 months and after that he needed only 7 years to become a professor. I'm pretty sure that every mathematician knows his name.

Stanisław Ulam had took part in Project Manhattan and then worked on the hydrogen bomb. In the 40s wrote one of the first (if not the first) program playing chess. He also proposed Monte Carlo method. When Kennedy became a president in 1960 Ulam as an advisor was asked which important project should be started. He suggested an expedition to the moon what Kennedy approved!

Hugo Steinhaus did so many things that I don't know what to choose. He "discovered" Stefan Banach so without him Lvov school of mathematics could have never been created. He invented introwizor, ancestor of modern computed tomography, which was patented in many countries in Europe and in USA. One of his books Mathematical Snapshots, that was originally published in 1938, is still available on Amazon! He also worked on game theory. You can say that many people did it. However, Steinhaus had done so 20 years before someone used this term.

I'll stop now because I could write and write about them. Instead I'll cite 2 short anecdotes that show that these were really extraordinary people (based on Genialni. Lwowska szkoła matematyczna by Mariusz Urbanek, unfortunately available only in Polish).

Stefan Banach has never finished his studies, he didn't like bureaucracy, formalisms and official titles. Because of that he had a problem with his PhD. It wasn't important for him. He wanted to focus on mathematics. His friends decided to cheat him a little bit and one day they told him that some important people frrm the capital have a few questions and only he can help. He didn't have any problems to answer all these questions, but he didn't know that it was his examination for the degree of doctor ;) Thanks to this small fraud he received PhD title.

In Lvov there was a restaurant "Szkocka" ("Scotch") and mathematicians like to spend there a lot of time of course at talking about mathematics. Noise and bustle didn't bother them. They also had a habit to write down proofs and theorems on the table with a pencil. The problem was that on the next day tables were cleaned and all the work was lost. To solve a problem the owner of the restaurant was asked to set this table aside and not to clean it until everything will be transferred to paper. This was a task of students.

I hope that I convinced you that you should at least know what is Lvov school of mathematics (especially if you come from Poland or if you are mathematician). Personally, I'm ashamed that I knew so little about it before.

Ray Tracing a Black Hole in C#

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A friend of mine Mikołaj Barwicki has published very interesting article about visualisation of black holes on codeproject. So far he received a grade 5 from 43 readers. It is a great result! If you interested in ray tracing, black holes, numerical analysis or parallel computing it is an article for you.

What every blogger should do if using someone else's code #2

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This time I'd like to write about WPFLocalizationExtension library which makes localization of WPF applications easy. I've been using it for 4 years in my projects and it simply works. To be honest I've just realized that the version I'm using is considerably outdated. However, for all this time I haven't encountered problems that would make me to download a newer version of WPFLocalizationExtension.

I think that it is a quite good recommendation. So, if you work with WPF and you need to localize your application I encourage to give a chance to WPFLocalizationExtension.

How to solve Transportation problem in Excel?

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I think that most of you have heard about Transportation problem. We have N factories and M mines/producers. Each factory needs and each mine can provide particular amount of resources. We have to transport these resources from mines to factories. What is obvious it costs money and this cost depends on the distance between factories and mines. We have to find such an allocation that will minimize this cost.

In order to solve this problem we can use linear programming and one of the most popular algorithms are simplex or stepping stone algorithm. However, today I will not write directly about them but I will show how to solve this problem in Excel. Yes, I'm talking about good old Excel. Surprised?

Excel has an Add-in called Solver which will do a job for us. I'll explain how to do it using a simple example with 3 factories and 3 mines. Here is a table that shows costs of transport between mines and factories. For example, if we want to move 10 units from Mine 1 to Factory 1 then a cost will be 10 *c11.

Transportation Cost	Factory 1	Factory 2	Factory 3
Mine 1	c11	c12	c13
Mine 2	c21	c22	c23
Mine 3	c31	c32	c33

We also need another table with supplies and demands. Below is an example. The numbers is the first column shows how many resources each mine can provide and the numbers in the the first row shows how many resources are needed by each factory.

The last row and the last column show sums of allocated resources in each row and in each column. These columns are needed to easily configure Solver. In this example some resources have been already allocated and we need to optimally allocate remaining ones i.e. x12, x13....

Supply\Demand	150	50	50	Allocation sums for mines
40	10	x12	x13	10
110	x21	x22	x23	0
100	x31	x32	20	20
Allocation sums for factories	10	0	20

We also we have to define limitations and a cost function. The first limitation is that found allocations should be non negative i.e.

x12, x13 ... >= 0

Besides we want to allocate all resources available in mines and each factory should receive required amount of resources i.e.

40 = 10 + x12 + x13
110 = x21 + x22 + x23
100 = x31 + x32 + 20
150 = 10 + x21 + x31
50 = x12 + x22 + x32
50 = x31 + x32 + 20

Because we have a column and a row with allocation sums it will be very easy to enter these allocations into Solver. It is also worth saying that in general these limitations can be different, for example we can have more resources than needed. Of course, in this case formulas above would be also different.

A cost function is also easy. We want to minimise the following sum which is equal to total cost of moving resources from mines to factories:

c11 * 10 + c12 * x12 + c13 * x13 + ....

Now we have everything to solve a problem in Excel. Firstly we have to enable Solver. To do so open Excel options, select Add-ins. Then find Solver on the list and confirm with OK (this procedure can vary in different versions of Excel).

I've already prepared a spreadsheet with all required equations and data for you. You can download it here (you have to download this file locally and do not use online Excel application). To run Solver go to Data tab and select Solver in Analysis category. Then select Solve button and all missing allocations will be populated. Easy, isn't it? Now, a few words about using Solver.

Here is a screenshot with Solver Parameters. A cell in a red circle contains a cost formula. This formula will be minimized (see a green rectangle). Yellow rectangle contains cells that will be modified by an algorithm and finally blue rectangle contains six formulas explained in the previous post.

The next screenshot shows additional options of Solver. You can display this window by pressing Options button in Solver Parameters window. I want to point 2 selected options. Assume Linear Model tells Solver that it deals with linear programming problem and Assume Non-Negative tells Solver that we are interested only in non-negative results.

As you can see much more options are available. I encourage you to experiment with them and also with different costs, limitations, number of mines/factories and problems.

Interview Questions for Programmers by MK #2

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I prepared this question a long time ago in order to check knowledge of basic good practices.

Question #2
You have the following method which is responsible for updating a client in a database:

public void UpdateClient(
   int id,
   string name,
   string secondname,
   string surname,
   string salutation,
   int age,
   string sex,
   string country,
   string city,
   string province,
   string address,
   string postalCode,
   string phoneNumber,
   string faxNumber,
   string country2,
   string city2,
   string province2,
   string address2,
   string postalCode2,
   string phoneNumber2,
   string faxNumber2,
   ...)
{
   //...
}

Do you think that this code requires any refactoring? If yes, give your proposition. A database access technology doesn't matter in this question.

Answer #2
The basic problem with this method is that it has so many parameters. It is an error prone, difficult to maintain and use approach. I suggest to change the signature of this method in the following way:

public void UpdateClient(Client client)
{
   //...
}

Where Client is a class that models clients. It can look in the following way:

public class Client
{
   public int Id { get; set; }
   public string Name { get; set; }
   public string Secondname { get; set; }
   public string Surname { get; set; }
   public string Salutation { get; set; }
   public int Age { get; set; }
   public string Sex { get; set; }
   public Address MainAddress{ get; set; }
   public Address AdditionalAdddress { get; set; }
   /* More properties */
}

Address class contains details (country, city..) of addresses.

Comments #2
You may also write much more e.g.:

• It may be good to introduce enums for properties like 'Sex' which can take values only from the strictly limited range.
• UpdateClient method should inform a caller about the result of an update operation e.g. by returning a code.

However, the most important thing is to say that UpdateClient method shouldn't have so many parameters. Personally, if I see a code as above I immediately want to reduce the number of parameters. This question seemed and still seems to be very easy, however not all candidates were able to answer it. Maybe it should be more accurate. For example, I should have stressed that a candidate should focus ONLY on available code. What do you think?