--- /dev/null
+! Copyright (c) 2009 Guillaume Nargeot.
+! See http://factorcode.org/license.txt for BSD license.
+USING: arrays kernel math math.ranges project-euler.common sequences ;
+IN: project-euler.085
+
+! http://projecteuler.net/index.php?section=problems&id=85
+
+! DESCRIPTION
+! -----------
+
+! By counting carefully it can be seen that a rectangular grid measuring
+! 3 by 2 contains eighteen rectangles.
+
+! Although there exists no rectangular grid that contains exactly two million
+! rectangles, find the area of the grid with the nearest solution.
+
+
+! SOLUTION
+! --------
+
+! A grid measuring x by y contains x * (x + 1) * y * (x + 1) rectangles.
+
+<PRIVATE
+
+: distance ( m -- n )
+ 2000000 - abs ;
+
+: rectangles-count ( a b -- n )
+ 2dup [ 1 + ] bi@ * * * 4 / ;
+
+: unique-products ( a b -- seq )
+ tuck [a,b] [
+ over dupd [a,b] [ 2array ] with map
+ ] map concat nip ;
+
+: max-by-last ( seq seq -- seq )
+ [ [ last ] bi@ < ] most ;
+
+: array2 ( seq -- a b )
+ [ first ] [ last ] bi ;
+
+: convert ( seq -- seq )
+ array2 [ * ] [ rectangles-count distance ] 2bi 2array ;
+
+: area-of-nearest ( -- n )
+ 1 2000 unique-products
+ [ convert ] [ max-by-last ] map-reduce first ;
+
+PRIVATE>
+
+: euler085 ( -- answer )
+ area-of-nearest ;
+
+! [ euler085 ] 100 ave-time
+! 2285 ms ave run time - 4.8 SD (100 trials)
+
+SOLUTION: euler085
project-euler.055 project-euler.056 project-euler.057 project-euler.058
project-euler.059 project-euler.063 project-euler.067 project-euler.069
project-euler.071 project-euler.073 project-euler.075 project-euler.076
- project-euler.079 project-euler.092 project-euler.097 project-euler.099
- project-euler.100 project-euler.116 project-euler.117 project-euler.134
- project-euler.148 project-euler.150 project-euler.151 project-euler.164
- project-euler.169 project-euler.173 project-euler.175 project-euler.186
- project-euler.190 project-euler.203 project-euler.215 ;
+ project-euler.079 project-euler.085 project-euler.092 project-euler.097
+ project-euler.099 project-euler.100 project-euler.116 project-euler.117
+ project-euler.134 project-euler.148 project-euler.150 project-euler.151
+ project-euler.164 project-euler.169 project-euler.173 project-euler.175
+ project-euler.186 project-euler.190 project-euler.203 project-euler.215 ;
IN: project-euler
<PRIVATE