2

The question is really simple, i have an array of random sized squares (width, height) and a fixed width surface. What's the best efficient algorithm to arrange squares on this surface? There must be no useless gap between squares. Is it possible at all? Without using AI or heavy processing?

Something similar to this picture, but assume that my surface is not bounded at bottom, its a fixed-width and unbounded height surface.

  • It might not always be possible to arrange the squares without a gap. –  Jul 27 '12 at 08:00
  • A related problem that might help you are boxing algorithms, check [this post](http://stackoverflow.com/questions/140406/how-can-i-programmatically-determine-how-to-fit-smaller-boxes-into-a-larger-pack) out – Miquel Jul 27 '12 at 08:03

3 Answers3

6

This problem is called 2d bin packing. Here's a way to tackle it:

http://codeincomplete.com/posts/2011/5/7/bin_packing/

Ben Ruijl
  • 4,973
  • 3
  • 31
  • 44
0

For such thing you could either use a variation of the Bin Packing Problem, where you try to pack as many squares as possible in your sheet or else use the (what probably seems more appropriate) Cutting Stock Algorithm.

Note however, that in both cases, it is highly unlikely that you will have no gaps between your squares.

npinti
  • 51,780
  • 5
  • 72
  • 96
0

This type of optimization problems are known as Linear programming (linear optimization). The bad news is it's complex.

Take a look at Simplex algorithm algebraic method, there are more general numeric methods, search for interior point methods.

There are free libraries like: LP_SOLVE

Branimir
  • 4,327
  • 1
  • 21
  • 33