Question

I am given a list of months (TOTAL_NUM_MONTHS) and from this list I need to select only 12 months proportionally. I have following algorithm up to now:

IF TOTAL_NUM_MONTHS<12 THEN
   STEP = 1
ELSE IF (TOTAL_NUM_MONTHS % 12 == 0) THEN
   STEP = TOTAL_NUM_MONTHS / 12
ELSE
   STEP = ???

So, if total number of months is less then 12 I will select all of them, and if it is divisible to 12 then I will select them with a step equal to TOTAL_NUM_MONTHS/12.

Question: What to do if the total number of months is not divisible to 12 ? How to calculate the step in order to select 12 months from the given list of months proportionally ?

Answer 1

Maybe you should take a step of variable length for each iteration, something like:

step(i) = step(i-1) + NUM_MONTHS/12.0, step(0) = 0.0 [note: step(i) is a floating point number and not an integer]

And use floor(step(i)) to chose element. [assuming here NUM_MONTHS > 12]

i is the step’s number. You chose a[i] = floor(step(i)) as your i’th element for each 0 <= i < 12

The idea is to create a monotonically increasing function that distributes uniformly. It doesn’t get more uniform then NUM_MONTHS/12 size, with floating points. So, you calculate it with floating points – and then use floor(step(i)) to get the integer out of it.

This method ensures 2 things:

1. No element is chosen twice [because NUM_MONTHS/12 > 1]
2. The maximum difference between every two steps is 1.

Also note that if NUM_STEPS % 12 == 0 this method decays to your else if and behave the same.