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Calculating the Coverage of Combs by your Lotto Number Set
 LottoPoster Forums : LOTTO PROBABILITY, COVERAGE AND PROGRAMMING : Calculating the Coverage of Combs by your Lotto Number Set
Message Icon Topic: Coverage Calculation Speed in VBA, VB, C# and C++ Post Reply Post New Topic
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Colin F
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Quote Colin F Replybullet Topic: Coverage Calculation Speed in VBA, VB, C# and C++
    Posted: May 03 2009 at 10:02pm
The objective is to achieve a sub 1 sec time in a visual environment to calculate the coverage of say 44 45 46 47 48 49 by testing all the 13,983,816 possiblities and establishing a count of match Threes in a Pool 49, Pick 6 Lotto game. The combinations would then be flagged as covered in an array or whatever so it would be bypasses for the next combination to calculate. The algorithm you use should give an accurate count whatever the combination entered ie 260624 for the first block. 
 
If iteration is not used then there must be a way of keeping track of what is covered for further block processing and counting the Coverage. The iteration algorithm I used to obtain these Coverage Calculation times is basically the same in all the four languages allowing for syntax differences and was supplied by Michael Harrington mentored by John Rawson in a thread I started called Coverage Calculation in VBA, VB, C# and C++ and can be viewed here. The initial times shown in the thread were based on older slower code than what I was currently using to attract more attention which it did; I had got it down to 70 sec in VBA and 7 sec in VB 2008 on a 1.8 GHz computer. Michael's times were impressively better at 6.5 sec and 0.44 sec respectively. 
 
From the code supplied at the message board you may want to add a couple of improvements for the first two loops, as I do, to opt out when it is greater than the max integer in the block. Obviously, this will not have any effect on our test block of 44 45 46 47 48 49.
 
I should mention that Michael's code simply counts the extent to which a subset Three in the Play Set is in the 13,983,816 possibilities. When you are generating sets and in my case making sure a Three is not repeated the code is not as simple nor as fast. 
 
Michael came up with a faster algorithm better than the 0.44 sec by breaking the 49c6 into 4 groups: -
  •  4c1 x 6c6   =          1    
  • 43c1 x 6c5   =        258
  • 43c2 x 6c4   =     13,545
  • 43c3 x 6c4   =    246,820
  •        Total      260,624

This is OK for calculating 1 block - the problem still remains to keep track of what is covered for calculation on multiple blocks as the flow through the lexicographic order has been lost - so, it is still a work in progress. Maybe combinadics can be used?

 The times below are adequate for my use using the iteration method.
 
What is your real processor speed? I downloaded this free program CPUSpeedPro and had to adjust my speed from what I thought was 2.4 GHz as shown by XP to 1.8 GHz as tested. You can access tested speeds of current and old CPU's from around the world.
 
Coverage Calculation Times Compared for Different Languages

                          1.8 GHz             Est 3 GHz (x.6)

VBA                       6.52 sec               3.91 sec
(Access or Excel)

VB 2008                   0.44 sec               0.26 sec

 
C#                        0.64 sec               0.38 sec
 
C++                       4.00 sec               2.40 sec
without Boolean Vector  < 0.5 sec               < .5 sec
 
Why does C++ give such a relatively high time? If I remove the 13983816 Vector Boolean which is taking up a lot of contiguous memory it gives the fastest time. But how then does one keep track of what is covered? If you would like to give a time for the code in C++ go ahead - just let us know how fast your processor is and how large the RAM and how you are going to keep track of what is covered.
 
C# is managed memory and does not have to be contiguous for its arrays .
 
VB rules! You can get a free copy of Visual Basic Express here:
http://www.microsoft.com/Express/VB/ 
 
I use Visual Studio Standard which includes VB, C# and C++ with intellisense in the IDE. Study what you need and what you get before forking out for the considerably more expensive Professional edition.
 
nb If by the time you read this the thread at the newsgroup has gone stale you are welcome to make comments here. If you have not registered you can still comment in this forum as a guest.
 
Colin Fairbrother
 
ps
On May 17th Michael Harrington published what is pretty well the final
version of the Coverage Calculation code after some mentoring by John
Rawson. The objective of an under 1 second calculation time was
achieved for not only 1 line but also 163.

Here are the times for the various languages as tested for a 1.8 GHz
processor (except C++ where a calculation is made from John Rawson's
accepted time of 0.2 sec on a 3 GHz processor and the assumption is
made that  the code for this task is pretty similar) : -

                                     1,8 GHz         3.0 GHz
                                     Processor     Processor

VBA                               3.00 sec       1.65 sec
(Access or Excel)

C#                                  0.45 sec       0.25 sec

VB 2008                          0.42 sec       0.25 sec

C++                                0.36 sec       0.20 sec

Congratulations to Michael Harrington. I for one will find some of the
tricks and techniques used to be useful in speeding up some internal
programs I use.

Colin Fairbrother
www.lottotowin.com

 
Lotto Draws have no relationship to one another; the integers serve just as identifiers. Any prediction calculation on one history of draws for a same type game is just as irrelevant as another.
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thornc
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Quote thornc Replybullet Posted: August 11 2010 at 6:07pm
Here's an interesting article related to this -> http://www.codeproject.com/KB/recipes/combinations_cpp_2.aspx.

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