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For 2023 (and 2024 ...) - we are now fully retired from IT training.
We have made many, many friends over 25 years of teaching about Python, Tcl, Perl, PHP, Lua, Java, C and C++ - and MySQL, Linux and Solaris/SunOS too. Our training notes are now very much out of date, but due to upward compatability most of our examples remain operational and even relevant ad you are welcome to make us if them "as seen" and at your own risk.

Lisa and I (Graham) now live in what was our training centre in Melksham - happy to meet with former delegates here - but do check ahead before coming round. We are far from inactive - rather, enjoying the times that we are retired but still healthy enough in mind and body to be active!

I am also active in many other area and still look after a lot of web sites - you can find an index ((here))
How many times ... has this loco headed west through Tenby? - Python exceptions

If you have a stock of 117 locomotives on your railway, and each is on the front of a train through Tenby as it heads for Pembroke just 12 times a year (it's a Summer Saturday Special working!), will - in the course of their 30 year life - every locomotive have worked that train? Will the reason that no-one has a photo of a certain loco there be because no-one's ever taken the photo (or you haven't found it), or because the loco has never been there?

A very similar question / mathermatics applies to other events which apply randomly to and one of a limited number of members of a resource group. It almost (but not quite) applies to lottery draws - in fact it does apply to the FIRST number drawn each time and the frequency of that, but subsequent draws are skewed as the later balls are drawn from the diministed pool.

The answer - with my numbers - is that there's only about a 1 in 200 (0.5%) chance that every locomotive has headed a train west through Tenby ... it's just the lack of photographic or other evidence to show it that is worrying our enquirer. A more typical set of results:
  [5, 13, 28, 32, 16, 12, 8, 2, 0, 1]
• 5 locomotives haven't been
• 13 have been just once
• 28 twice
• 32 thrice
• and so on ...
• and one has made it no less than 9 times!

I've run a simulation (rather than a theoretic analysis) - in Python, program's [here], running it 32 times to show the spread of the results. It's rather similar to the approach that's known as the "Monte Carlo method", where a series of simulations are run, based on different random sequences, and the results are then collated and the commonality is used to indicate what will probably happen in real life, with the spread showing what alternatives are likely. It's a very interesting approach in weather forecasting, where the randomness is noise and fluctuation on measurements, and the method can show not only the spread of possibilty to the forecasters, but it will also show those days where there's some sort of pivotal split in the weather, and tiny inaccuracies in readings can lead the weather to head off in totally different directions.

As I wrote my example, I had no idea what the maximum number of times a locomotive headed the train would be. I COULD have started off with a counter array filled with zeros. However, that would have needed to be 117 elements long and (statistically) would "never" have been used. OK for my 117 samples, but what if I had a million? So I used a different approach.

Statring off with a list of zero length, I "assumed" that I could just add one to the counter I wanted. Now that will throw an IndexError if the counter element doesn't yet exist, and if that happens I keep adding a zero onto the end of my list until I have enough elements there to handle the so-far most-used unit of my 117. Here's the code:

  counter = []
    for eventcount in units:
      while True:
        try:
         counter[eventcount] += 1
         break
        except:
         counter += [0]


and - run multiple times - some of the results:
  [6, 17, 22, 30, 18, 13, 6, 4, 1]
  [7, 14, 27, 27, 20, 9, 6, 6, 1]
  [6, 19, 26, 20, 17, 20, 5, 3, 0, 0, 1]
  [5, 18, 23, 30, 20, 7, 10, 3, 0, 0, 1]
  [5, 17, 29, 21, 18, 18, 4, 4, 1]
  [5, 16, 24, 34, 18, 7, 8, 2, 2, 1]

(written 2012-11-05, updated 2012-11-10)

 
Associated topics are indexed as below, or enter http://melksh.am/nnnn for individual articles
Y109 - Python - Exceptions
  [381] Exceptions in Python - (2005-07-17)
  [1042] Nested exceptions in Python - (2007-01-18)
  [1236] Trying things in Python - (2007-06-18)
  [2018] UnboundLocalError - Python Message - (2009-01-31)
  [2281] Python - using exceptions to set a fallback - (2009-07-12)
  [2368] Python - fresh examples of all the fundamentals - (2009-08-20)
  [2408] Robust user input (exception handling) example in Python - (2009-09-17)
  [2622] Handling unusual and error conditions - exceptions - (2010-02-03)
  [2994] Python - some common questions answered in code examples - (2010-10-10)
  [2998] Using an exception to initialise a static variable in a Python function / method - (2010-10-13)
  [3177] Insurance against any errors - Volcanoes and Python - (2011-02-19)
  [3433] Exceptions - a fail-safe way of trapping things that may go wrong - (2011-09-11)
  [3441] Pressing ^C in a Python program. Also Progress Bar. - (2011-09-15)
  [3664] Error checking in a Python program - making your program robust via exceptions - (2012-03-22)
  [3930] Reporting the full stack trace when you catch a Python exception - (2012-11-22)
  [4029] Exception, Lambda, Generator, Slice, Dict - examples in one Python program - (2013-03-04)
  [4161] Python varables - checking existance, and call by name or by value? - (2013-08-27)
  [4444] Elements of an exception in Python - try, except, else, finally - (2015-02-28)


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