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PO
 

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  1. PO
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    <p>I've managed to come up with a 'relatively' optimal solution. Partially based on Zac's pseudocode answer.</p> <pre><code> //total number of tiles var tile_count : Number = numberOfSlides; //height of rectangle var b : Number = unscaledHeight; //width of rectanlge var a : Number = unscaledWidth; //divide the area but the number of tiles to get the max area a tile could cover //this optimal size for a tile will more often than not make the tiles overlap, but //a tile can never be bigger than this size var maxSize : Number = Math.sqrt((b * a) / tile_count); //find the number of whole tiles that can fit into the height var numberOfPossibleWholeTilesH : Number = Math.floor(b / maxSize); //find the number of whole tiles that can fit into the width var numberOfPossibleWholeTilesW : Number = Math.floor(a / maxSize); //works out how many whole tiles this configuration can hold var total : Number = numberOfPossibleWholeTilesH * numberOfPossibleWholeTilesW; //if the number of number of whole tiles that the max size tile ends up with is less than the require number of //tiles, make the maxSize smaller and recaluate while(total &lt; tile_count){ maxSize--; numberOfPossibleWholeTilesH = Math.floor(b / maxSize); numberOfPossibleWholeTilesW = Math.floor(a / maxSize); total = numberOfPossibleWholeTilesH * numberOfPossibleWholeTilesW; } return maxSize; </code></pre> <p>What this does is to work out the total area of the rectanlge, then divide it by the required number of tiles. As each tile is a square I can SQRT this so that I get the max size of the optimal tile.</p> <p>With this optimal size I then check to see how many WHOLE tiles I can fit into the width &amp; height. Multiply these together and if it is less than the required number of tiles then I reduce the optimal size and perform the checking again until all of the tiles fit the rectanlge.</p> <p>I could optimise this further by doing something like reduce the optimal size by -2 insted of -1 each time and then if all the tiles fit increase by 1 just to make sure that I've not missed a valid size. or I could jump back more than -2, say -10 then if they all tiles fit increase by 5, then if the don't fit reduce by -2 etc until I get an optimal fit.</p> <p>Check out <a href="http://kennethsutherland.com/flex/stackover/SlideSorterOK.html" rel="nofollow noreferrer">http://kennethsutherland.com/flex/stackover/SlideSorterOK.html</a> for my example. Thanks for all the various info.</p>
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    1. COI have posted a solution that doesn't use any loops. I realize this question was asked a long time ago, but it was a fun problem to solve :) http://stackoverflow.com/questions/868997/max-square-size-for-unknown-number-inside-rectangle/1656634#1656634
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