I'm wondering if there is an "optimal" solution for this problem:
I have a n x m (pixel) sized space with p preexisting rectangled - objects in various sizes on it. Now I want to place q (same sized) new objects in this space without any overlapping.
The algorithm I came up with:
- Create array A[][] with the size
[(n)/(size_of_object_from_q)]x[(n)/(size_of_object_from_q)] Iterate all Elements from p and for each:
mark all fields in A[][] as occupied, where the element "lies"Place all elements from q in the according places where the fields in A[][] are not marked
(Boy, I hope I could make that understandable...)
Is there any better way to do this? Any help would really be appreciated!
From a brief search in the internet, it seems that optimal rectangle packing is an NP-hard problem. I would guess that smart people in the academia found some approximation algorithms for that, so it is an option for googling.
But I would try to make the simple method work first:
- Divide your objects into sizes according to their width
- Try placing them line-by-line from the largest to the smallest.
My guess is that in many cases this naive solution will work.
If I understand the question, it sounds like you are looking for an "optimal" bin packing algorithm (aka the Knapsack Problem). That's an NP-Complete problem, although your description sounds like you can probably brute-force your way to an optimal solution.
I know this isn't a specific answer to your question, but it may be useful to research and/or dig into the graphviz source code. graphviz offers a number of layout models, including neato, which attempts to minimize a global energy function.
Wikipedia has some pseudo-code for force-base algorithms.
来源：https://stackoverflow.com/questions/1799662/object-positioning-algorithm