Total circles area: Difference between revisions

Approximate area: 21.56503660593628004</pre>

Runtime is about 7.6 seconds. DMD 2.061, -O -release -inline -noboundscheck.

=={{header|Haskell}}==

{{trans|Python}}

<lang haskell>data Circle = Circle { cx :: Double, cy :: Double, cr :: Double }

<pre>Approximated area: 21.564955642878786</pre>

 

Breaking down circles to non-intersecting arcs and assemble zero winding paths, then calculate their areas. Pro: precision doesn't depend on a step size, so no need to wait longer for a more precise result; Con: probably not numerically stable in marginal situations, which can be catastrophic.

<lang haskell>{-# LANGUAGE GeneralizedNewtypeDeriving #-}

div: 16384 unk: 75301 est: 21.565017 wet: 21.560920 dry: 21.569115 diff: 0.008195 error: -7.683898e-011</pre>

Here the "diff" is calculated by subtracting the known wet and dry areas from the total area, and the "error" is the difference between that and the sum of the areas of the unknown blocks, to give a rough idea of how much floating point roundoff error we've accumulated.

=={{header|Python}}==

This implements a regular grid sampling. For this problems this is more efficient than a Montecarlo sampling.

<lang python>from collections import namedtuple

<pre>Approximated area: 21.561559772</pre>

 

<lang python>from math import floor, ceil, sqrt

 

* And the square of the radius computed outside the main loops.

 

from math import sqrt

from itertools import count

except:

pass

 

# Remove duplicates and sort, largest first.

if __name__ == '__main__':

main(circles)</lang>

{{out}}

<pre>python3 total_circle_area.py