Not to complicate the issue but is this tiles with grout tolerance allowance between the tiles?
If I were thinking of how I would do it then I'd place the tiles as solids in a given grid arrangement overlapping the room boundary, get the total volume of this grid arrangement = Vol1
Cut the room shape out of this tile arrangement to get the volume again = Vol2
You can then get the volume inside the room by deducting Vol2 from Vol1.
Separate out the disjoined solids in Vol2 (I believe there is a function for that).
Then you can also identify the cut tiles around the perimeter of the room in Vol2 because each of those have a volume less than a tile. This is the inverse volume so you deduct each of these from the tile size to give you each partial tile size and it's location. I speak in terms of volumes because volume are easy to determine from solids and then you can divide by tile thickness.
Also I'm using the inverse because I know the boundary of the room to use for deducting from the overall set. I could do it the other way around (deduct the excess from around the room) but I would have to allow a border around the room to ensure all the excess tiles are deducted and this seems slightly more complicated in determining that border width (probably a tile size plus an allowance).
I think where you start the tiling becomes arbitrary in a sense because rarely in reality are tiles set out on site to such precision. I imagine you usually start from the centre and work your way out to the edges so it gives the impression of symmetry. I'm wondering how many variations you'd get by changing the tile offset i.e. if all the tiles are the same size do you cover the variations by offsetting through the tile unit dimensions? Do you then discount arrangements that lead to impractical tile sizes?
In the end what area of tiles do you need to fill a room of 10m2? Workmanship will play a large part in how many tiles you need so costs are usually not that specific. It'll likely be 10m2 worth of tiles + tolerance because I can't sell you half tiles (you cut them). Also I'll sell you boxes of 20 tiles not individual ones. Then there is colour variations in tiles perhaps you have a pettern and you want to know how many of each colour?