Harmonize spelling

[factor.git] / extra / project-euler / 151 / 151.factor

diff --git a/extra/project-euler/151/151.factor b/extra/project-euler/151/151.factor
index b2bbbcc0da15f9cf9c8a8422d1e66392f38ca197..45777ae56aba66981401d0657a19f67953f320d6 100644 (file)
--- a/extra/project-euler/151/151.factor
+++ b/extra/project-euler/151/151.factor
@@ -1,18 +1,49 @@
-! Copyright (c) 2008 Eric Mertens
+! Copyright (c) 2008 Eric Mertens.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: sequences combinators kernel sequences.lib math math.order
-assocs namespaces ;
+USING: assocs combinators kernel math math.order namespaces sequences project-euler.common ;
 IN: project-euler.151
 
+! http://projecteuler.net/index.php?section=problems&id=151
+
+! DESCRIPTION
+! -----------
+
+! A printing shop runs 16 batches (jobs) every week and each batch requires a
+! sheet of special color-proofing paper of size A5.
+
+! Every Monday morning, the foreman opens a new envelope, containing a large
+! sheet of the special paper with size A1.
+
+! He proceeds to cut it in half, thus getting two sheets of size A2. Then he
+! cuts one of them in half to get two sheets of size A3 and so on until he
+! obtains the A5-size sheet needed for the first batch of the week.
+
+! All the unused sheets are placed back in the envelope.
+
+! At the beginning of each subsequent batch, he takes from the envelope one
+! sheet of paper at random. If it is of size A5, he uses it. If it is larger,
+! he repeats the 'cut-in-half' procedure until he has what he needs and any
+! remaining sheets are always placed back in the envelope.
+
+! Excluding the first and last batch of the week, find the expected number of
+! times (during each week) that the foreman finds a single sheet of paper in
+! the envelope.
+
+! Give your answer rounded to six decimal places using the format x.xxxxxx .
+
+
+! SOLUTION
+! --------
+
 SYMBOL: table
 
 : (pick-sheet) ( seq i -- newseq )
     [
-        <=> sgn
+        <=>
         {
-            { -1 [ ] }
-            {  0 [ 1- ] }
-            {  1 [ 1+ ] }
+            { +lt+ [ ] }
+            { +eq+ [ 1 - ] }
+            { +gt+ [ 1 + ] }
         } case
     ] curry map-index ;
 
@@ -28,14 +59,19 @@ DEFER: (euler151)
 : (euler151) ( x -- y )
     table get [ {
         { { 0 0 0 1 } [ 0 ] }
-        { { 0 0 1 0 } [ { 0 0 0 1 } (euler151) 1+ ] }
-        { { 0 1 0 0 } [ { 0 0 1 1 } (euler151) 1+ ] }
-        { { 1 0 0 0 } [ { 0 1 1 1 } (euler151) 1+ ] }
-        [ [ dup length [ pick-sheet ] with map sum ] [ sum ] bi / ]
+        { { 0 0 1 0 } [ { 0 0 0 1 } (euler151) 1 + ] }
+        { { 0 1 0 0 } [ { 0 0 1 1 } (euler151) 1 + ] }
+        { { 1 0 0 0 } [ { 0 1 1 1 } (euler151) 1 + ] }
+        [ [ dup length <iota> [ pick-sheet ] with map-sum ] [ sum ] bi / ]
      } case ] cache ;
 
-: euler151 ( -- n )
+: euler151 ( -- answer )
     [
         H{ } clone table set
         { 1 1 1 1 } (euler151)
     ] with-scope ;
+
+! [ euler151 ] 100 ave-time
+! ? ms run time - 100 trials
+
+SOLUTION: euler151