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weighted normalized distribution (math challenge)

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Hey smart people,


Im not sure if the topic title describes my problem very well but,...


I have a math problem that's been holding me up.

Maybe someone out there can help.


Say I have a bunch of points with normalized values

sorted by highest to lowest like...


@ptnum      @value

0                 .9

1                 .4

2                 .3

3                 .01



How do I now remap "value" for each point so that the total adds up to one?

BUT this new distributed remapped value is weighted by the original value.



The obvious thing to do would be: (@value/sum of @value) but the result is:



@ptnum      @value             @simple normalized

0                  .9                      .55

1                  .4                      .24

2                  .3                      .186

3                  .01                    .00621



This kind of remapping is not ideal because  point 0 is has a very high value which gets lost.

In the case above I could keep point 0 at .9 the distribute the remaining .1 across the rest of the points.

Which I know how to do but what happens when you have a case like:



@ptnum      @value           

0                  .6                      

1                  .58                    

2                  .52                   

3                  .1    

4                  .1             



In this case I would need to average the first three points then distribute the remainder across the rest of the points.

Is there a really smart solution out there that doesnt involve setting up test conditions then adapting the code?


I've attached a hip file that demonstrated the problem..






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