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I have a collection of different sized squares and rectangles that I want to fit together using PHP into one large square/rectangle. The squares are usually images that I want to make into a montage - but sometimes they are simply math objects.

Are there any PHP algorithms for this and what is this type of thing called?

Update: After more searching I think what I want is called the bin packing problem. However, I would also like to add a certain amount of randomization for certain types of packing problems (like images) to allow human interest.

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  • Are these objects fixed in size... i.e. You want to find the range of images that will fit into a defined "box". Or are you wanting to scale these images (retaining aspect) into a pre-defined box? Commented Jul 13, 2011 at 16:06
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    I think this question is very close to what I need: stackoverflow.com/questions/4904049/php-array-performance Commented Jul 13, 2011 at 16:25
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    There are algorithms, and there are implementations of these algorithms for specific languages, like PHP. I suggest making this question language-agnostic because it's QI (quite interesting). Commented Jul 13, 2011 at 20:25
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    There's always math.stackexchange.com to get some mathemagicians into it. Apparently they have ben talking about this for a while as well: math.stackexchange.com search for the bin packing problem Commented Jul 15, 2011 at 10:45
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    Look to the garment industry where fitting oddly sized pattern pieces optimally on yardage of cloth is a priority, plus the lumber industry who fit cuts into logs. Commented Jul 16, 2011 at 2:45

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2D Bin packing is NP-hard problem. There are however approximation algorithms.

Look at this code (and explanation). It contains multiple algorithms and there is a GUI:

Solving the 2D Packing Problem

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Sorry for the -1 but the linked site requires you register and login to view it, which isnt normally a problem but they require address.. company, company size.. ect. Shouldnt have to provide that for an answer.
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I have a wrote a 1d bin-packing algorithm in php. You want to look for best-fit, first-fit, and so on. But it's not for a 2d problem, maybe you want to look for the knapsack-problem?

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I found a PHP-version of the knapsack-problem, but I'm not sure how it relates to a 2D area to fill yet.
@Xeon: At least you have an algorithm with 2 variables, weight and cost. Maybe you can modify it? Another app is drools-planer.
The problem is that formula uses only one constraint and one priority. So it's just a glorified 1D algorithm. I need something that handles 2 constraints (with an optional priority).
@Xeon: I see, did you tried a Floyd-Warshall algorithm or Edmond's maximum matching algorithm?
@Xeon: Maybe a spatial-index or a quadtree? A si reduces the 2d complexity to a 1d complexity.
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I think you can use Semulated Annealing algorithm. I have used it to fill rectangular newspaper pages by rectangular advertisements. As you said you can start it by randomized solution and then you can slowly reach to a good solution. See here http://codetuner.blogspot.com/2010/03/simulated-annealing-approach-to.html. I have used it to solve pagination problem. I think you can use it for you r requirement too.

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