PHP - how to calculate the best possible grid layout for reservations and timeslots [closed]

We have a reservation grid for materials. For example when you have 4 "vechtsloep"

How can we calculate the best possible fit of the colored timeslots (those are reserved) and calculate the empty timeslots (gray slots and if the slot fits).

You can also order 1, 2, 3 or 4 boats, so the timeslots can be of height 1 till 4. This make the ideal fit of reservations more difficult.

I also tried the CSS grid-auto-flow dense, however the slots have labels and with the dense property it can be set everywhere.

Is there a formula to calculate the best fitting layout ?

Here is a second example (bit more complicated)

We have here 9 E-vecht sloep, but the grid is way out next to Luxe e-sloep. Also sometimes (this can happen) a 2 row reserved slot and 2 single reserved slots are more optimal placed then 2x 2 row reserved slots

source https://stackoverflow.com/questions/76297005/php-how-to-calculate-the-best-possible-grid-layout-for-reservations-and-timesl