This problem seemed like something which should be solvable with but a few lines of code.
Unfortunately, once I actually started to write the thing, I've realized it's not as simple as it sounds.
What I need is a set of X random numbers, each of which is between A and B and they all add up to X. The exact variables for the problem I'm facing seem to be even simpler: I need 5 numbers, between -1 and 1 (note: these are rational (floating point) numbers), which add up to 1.
My initial "few lines of code, should be easy" approach was to randomize 4 numbers between -1 and 1 (which is simple enough), and then make the last one
1-(sum of previous numbers). This quickly proved wrong, as the last number could just as well be larger than 1 or smaller than -1.
What would be the best way to approach this problem?
PS. Just for reference: I'm using C#, but I don't think it matters. I'm actually having trouble creating a good enough solution for the problem in my head.
I also wanted to provide my current solution to the problem, but do remember that it's quite imperfect and it was created as a quick fix to the initial problem!
- Generate 4 random numbers between -1 and 1
- Create a "final" number
- If the final number is >1 or <-1, then:
- Get the "amount" over 1 / under -1 and make the last number a 1 / -1
- Find another number which can accept this amount and still inside the brackets
- If no number can take the amount (it's too large / too small) then divide the amount in half and try again for each half
- Randomize the order of the generated numbers and return them
This works in the sense that this algorithm generates 5 numbers which are between -1 and 1 and their sum is 1. However the downside is that quite often one of the generated numbers is a 1 (or -1), which doesn't feel very random.