Number distribution

Question

Problem: We have x checkboxes and we want to check y of them evenly.

Example 1: select 50 checkboxes of 100 total.

[-]
[x]
[-]
[x]
...

Example 2: select 33 checkboxes of 100 total.

[-]
[-]
[x]
[-]
[-]
[x]
...

Example 3: select 66 checkboxes of 100 total:

[-]
[x]
[x]
[-]
[x]
[x]
...

But we're having trouble to come up with a formula to check them in code, especially once you go 11/111 or something similar. Anyone has an idea?

Answer 1

Let's first assume y is divisible by x. Then we denote p = y/x and the solution is simple. Go through the list, every p elements, mark 1 of them.

Now, let's say r = y%x is non zero. Still p = y/x where / is integer devision. So, you need to:

• In the first p-r elements, mark 1 elements
• In the last r elements, mark 2 elements

Note: This depends on how you define evenly distributed. You might want to spread the r sections withx+1 elements in between p-r sections with x elements, which indeed is again the same problem and could be solved recursively.

Alright so it wasn't actually correct. I think this would do though:

Regardless of divisibility:

• if y > 2*x, then mark 1 element every p = y/x elements, x times.
• if y < 2*x, then mark all, and do the previous step unmarking y-x out of y checkboxes (so like in the previous case, but x is replaced by y-x)

Note: This depends on how you define evenly distributed. You might want to change between p and p+1 elements for example to distribute them better.