Square arrays from non-square numbers

//  PROBLEM
//  so I've run into this at least twice now, where I want to loop through a single 
//  "0 to whatever" range of numbers, but within that loop use the current iteration to 
//  address a 2D array.
//
//  this is in Processing, so the actual use case is creating a 2D grid of coordinates
//  from that single range of numbers. Usually I do it with two loops, ie. loop
//  through i and then loop through j within that loop. But I'm finding cases where
//  I want to loop through just i, and derive separate X and Y coordinates from the 
//  current value of i. Easy to do if i is a square, but what if it's irregular?
//
//  I'm not sure if I'm explaining it very well, but here's what I came up with. I thought
//  it was a neat bit of math. Code in Processing / Java.


int count = 1337;

for (int i = 0; i < count; i++) {

  float sqc = sqrt(count);

  X = (sqc - ((count - (i + 1)) % sqc));
  Y = ceil(sqc - (sqc - (i + 1) / sqc));

}

Processing's quick enough on the sqrt, hasn't been a problem. And yeah, I can't use two loops, which is why I did it this way in the first place.

Seems like this method works though, and keeps the math a bit lighter:

int s = ceil(sqrt(count)); 
for(int i = 0; i < count; i++) {
  X = i % s;
  Y = i / s;
}

(via http://twitter.com/jasonstitt/status/13468280866 )

What would be a use case for this?

Right, that's much better. But I'm really curious how you are using this loop! When count = 17, it produces this:

00 01 02 03 04
05 06 07 08 09
10 11 12 13 14
15 16

Here is an alternative that starts at the origin and expands outwards in a triangle:

x = y = 0;

for (int i = 0; i < count; ++i)
{
    ... do something with x and y ...
    if (x == 0) {
        x = y + 1;
        y = 0;
    } else {
        --x;
        ++y;
    }
}

For count = 17 it does this:

00 01 03 06 10 15
02 04 07 11 16
05 08 12
09 13
14

So yeah, what is this for? Does it produce pretty pictures? Is it a secret? :)

It's for aligning coordinates in a grid. Say I want to set up a variable number of squares without having to worry about them matching up perfectly. Done.