Question

I’m trying to divide an integer N <= 12, which is a number of work days, to 12 months, so that if I divide 12 months into
periods of 1, 2, 3, 4 or 6 months, the number of days in these periods should be as equal as possible.

For example:

If N = 6, the array should look like this :

1 0 1 0 1 0 1 0 1 0 1 0 or 0 1 0 1 0 1 0 1 0 1 0

N = 4

1 0 0 1 0 0 1 0 0 1 0 0

N = 3

1 0 0 1 0 0 1 0 0 0 0 0

N = 2

1 0 0 0 0 0 1 0 0 0 0 0

edit:

what I mean by “as equal as possible” is that when I divide this array into periods, the number of work days in these periods shouldn’t differ by more than 1.

Answer 1

EDIT — Improved for the general case, assumed you were only asking for 1,2,3,4,6 as in question!

What you want is to modulate N by a given period. (My terminology is likely entirely wrong 😀 Should probably go read up on my high school physics again!)

Have some Ruby..

def spread_it(n)
  d = 12.0 / n
  (0..11).map do |index|
    (12.0 - (index % d) > 11.0) ? '1' : '0'
  end
end

(1..12).each do |n|
  puts "N=#{n} - #{spread_it n}"
end

Output is:

N=1 - ["1", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0"]
N=2 - ["1", "0", "0", "0", "0", "0", "1", "0", "0", "0", "0", "0"]
N=3 - ["1", "0", "0", "0", "1", "0", "0", "0", "1", "0", "0", "0"]
N=4 - ["1", "0", "0", "1", "0", "0", "1", "0", "0", "1", "0", "0"]
N=5 - ["1", "0", "0", "1", "0", "1", "0", "0", "1", "0", "1", "0"]
N=6 - ["1", "0", "1", "0", "1", "0", "1", "0", "1", "0", "1", "0"]
N=7 - ["1", "0", "1", "0", "1", "0", "1", "1", "0", "1", "0", "1"]
N=8 - ["1", "0", "1", "1", "0", "1", "1", "0", "1", "1", "0", "1"]
N=9 - ["1", "0", "1", "1", "1", "0", "1", "1", "1", "0", "1", "1"]
N=10 - ["1", "0", "1", "1", "1", "1", "1", "0", "1", "1", "1", "1"]
N=11 - ["1", "0", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1"]
N=12 - ["1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1", "1"]

Better now? 🙂