Project Euler - problem 57

extra/project-euler/057/057.factor

@@ -0,0 +1,43 @@
+! Copyright (c) 2008 Samuel Tardieu
+! See http://factorcode.org/license.txt for BSD license.
+USING: kernel math math.functions math.parser sequences ;
+IN: project-euler.057
+
+! http://projecteuler.net/index.php?section=problems&id=57
+
+! DESCRIPTION
+! -----------
+
+! It is possible to show that the square root of two can be expressed
+! as an infinite continued fraction.
+
+! √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213...
+
+! By expanding this for the first four iterations, we get:
+
+! 1 + 1/2 = 3/2 = 1.5
+! 1 + 1/(2 + 1/2) = 7/5 = 1.4
+! 1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666...
+! 1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379...
+
+! The next three expansions are 99/70, 239/169, and 577/408, but the
+! eighth expansion, 1393/985, is the first example where the number of
+! digits in the numerator exceeds the number of digits in the
+! denominator.
+
+! In the first one-thousand expansions, how many fractions contain a
+! numerator with more digits than denominator?
+
+! SOLUTION
+! --------
+
+: longer-numerator? ( seq -- ? )
+    >fraction [ number>string length ] bi@ > ; inline
+
+: euler057 ( -- answer )
+    0 1000 [ drop 2 + recip dup 1+ longer-numerator? ] count nip ;
+
+! [ euler057 ] time
+! 3.375118 seconds
+
+MAIN: euler057

extra/project-euler/project-euler.factor

@@ -15,13 +15,13 @@ USING: definitions io io.files io.pathnames kernel math math.parser
     project-euler.041 project-euler.042 project-euler.043 project-euler.044
     project-euler.045 project-euler.046 project-euler.047 project-euler.048
     project-euler.052 project-euler.053 project-euler.055 project-euler.056
-    project-euler.059 project-euler.067 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.057 project-euler.059 project-euler.067 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 ;
 IN: project-euler
 
 <PRIVATE