title: optimized grid for rectangular items
body: <p>I have N rectangular items with an aspect ratio Aitem (X:Y).<br>
  I have a rectangular display area with an aspect ratio Aview</p>
  
  <p>The items should be arranged in a table-like layout (i.e. r rows, c columns).</p>
  
  <p>what is the ideal grid rows x columns, so that individual items are largest?
  (rows * colums >= N, of course - i.e. there may be "unused" grid places).</p>
  
  <p>A simple algorithm could iterate over rows = 1..N, calculate the required number of columns, and keep the row/column pair with the largest items. </p>
  
  <p>I wonder if there's a non-iterative algorithm, though (e.g. for Aitem = Aview = 1, rows / cols can be approximated by sqrt(N)).</p>