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I've got a route that contains objects. Each one has value 0 or 1. I need unique route ID which will identify any objects order. Currently I'm doing it using binary number that is converted to decimal (see picture).

Objects

The problem is, that amount of objects in route is up to 15. So, decimal number will be very big (up to 32767) with many values, that will never be used.
How to convert that number, to another unique value, but much smaller (<255)? I need to do that, only by using simple arithmetical operators (+,-,*,div).

Djent
  • 101

3 Answers3

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You have the equivalent of 15 bits of information that you must save. The largest binary number represented by 15 bits is 32767, and it is by no means no coincidence that this is also the maximum number of possible combinations (-1).

You cannot reduce this number without first providing some sort of simplification rule (i.e. the number must be an odd number, the number must be a palindrome, etc.). Otherwise any combination of the 15 bits is allowed.

While you may perform mathematical operations to simplify this number just the same, you'd be losing information in the process, and hence it would be one-directional (you could not figure out the original number by reversing the mathematical operation(s)).

Neil
  • 22,848
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Assumed, you will travel only a certain subset of all possible routes ever.

In that case, you could use a mapping between the routebits and a incremented numerical id. You will have to store that mapping somewhere, but this way every path used gets an unique id assigned, which can be used to refer to it later.

I'm not so sure if this is an efficient way to do it, but you didn't ask for that aspect.

JensG
  • 2,473
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It's impossible because each route may be reached (or not?). You have as many routes as 2^15

Maybe You have to consider fact that some of them will never appears (is it true?). So You can number only this of them which can be reached. This will decrease Your number of ways.

To decrease number of routes to be from 0 to 255 You have to eliminate about 2^7 routes. This may mean that seven objects will have always the same value (0 or 1).

For example

  • ffff1101fff10111
  • ffff0101fff00101
  • ffff0111fff10100

etc...

Andrzej Reduta
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