Lotto Algorithms - Permutations, Combinations - Xtreme Visual Basic Talk

2. Comparison of the 2 Algorithms

The odometer landing is both concise and efficient, so it wins the "style" award, and it as well can hold VAST games (cognate a million balls from a billion!).

On the other hand, for analytical purposes, there is a fatal flaw - you can't impart "distance" on this odometer - you chalk up no notion where in the file you are from the in fashion settings.

So the odometer can't call upon you the reinstate to questions alike this:

To reply these requires the index mapping functions. The front send is approximately 11 million, as it turns absent:

And the moment query, the midpoint site?

The mapping functions avow us to incision the unabridged virtual fix into a ok typical grid, and shorten it accordingly. Generating sequential string members is slightly less efficient than the Odometer, on the contrary even a brief fraction of the worth of either printing or otherwise displaying or (worse) storing them all.

Since the Odometer wealth doesn't hope for any measurement of the magnitude of the complete feasible combination fix, it can attempt with games of comic magnitude.

Momentarily you can't discharge that with index mapping functions through you simply can't much store the numbers required (in the dispute of a 10-from-50000 entertainment the figure of combinations needs a million or so digits to symbolize!).

Nevertheless that's exclusive an artificial restriction, as the principles news types in VB allow us collection of scope to imitation all contemporary games of control, plus extension to expand seamlessly to preferable games approximating "40 from 100", in reality any amusement for which the complete place dimensions (figure of imaginable combinations) is less than 75 x 10 ^ 27.

This is in fact admirable - you can choose any K (digit of balls to pick) for all values of N up to 99. At N = 100 you can alone animation to K = 46 (just shy of the finishing borderline at K=50) . On the other hand you'd usually custom smaller K besides, so that lets you accretion N all the more besides - e.g. you can base 10-from-1000

You'll message that 75 x 10^27 is rather larger than the maximum DISTANT price in VB. The index mapping functions practice Variant (Decimal) variables where required, which gives us access to what are effectively triple-length Longs' (96-bit integers).

We used this approach to extend the scale of the modern supply that we posted to calculate the amount of Combinations(N, K) http://www.xtremevbtalk.com/showthread.php?t=129902

And that's while you'll scrutinize some Variant variables in the Index Mapping functions below, nevertheless not the Odometer ones.