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answers:

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My question is in my title. I am trying to develop a logic so that I can scale fixed aspect ratio windows to cover most of the screen without overlapping eachother. There could be two three or four windows. There could be an alignment parameter also.

A: 

You my friend will want to start reading this

http://stackoverflow.com/questions/729640/optimal-layout-algorithm

this is a common problem in 2d game development ... think about the problem of how to pack sprites onto a sprite sheet. IE it well understood in 2d especvially seeing a you are dealing with rectangles. I am assuming that they are fixed aspect ratio and different sizes or else its simple maths. If i am wrong just shout and i will give you an algorithm.

There is another question on here about the

I don't want to go on and on because that link will lead you to where you want to be ...

this shuold be interesting http://primes.utm.edu/glossary/xpage/SieveOfEratosthenes.html

there was a good question bout the sieve ... well worth a read also http://stackoverflow.com/questions/1287607/help-speed-up-this-algorithm-sieve-of-eratosthenes

John Nicholas