Solution to Project Euler problem 102

diff --git a/extra/project-euler/102/102-tests.factor b/extra/project-euler/102/102-tests.factor
new file mode 100644 (file)
index 0000000..897f21a
--- /dev/null
+++ b/extra/project-euler/102/102-tests.factor
@@ -0,0 +1,4 @@
+USING: project-euler.102 tools.test ;
+IN: project-euler.102.tests
+
+[ 228 ] [ euler102 ] unit-test

diff --git a/extra/project-euler/102/102.factor b/extra/project-euler/102/102.factor
new file mode 100644 (file)
index 0000000..2ad1437
--- /dev/null
+++ b/extra/project-euler/102/102.factor
@@ -0,0 +1,64 @@
+! Copyright (c) 2009 Guillaume Nargeot.
+! See http://factorcode.org/license.txt for BSD license.
+USING: arrays grouping io.encodings.ascii io.files kernel math 
+math.parser sequences splitting project-euler.common ;
+IN: project-euler.102
+
+! http://projecteuler.net/index.php?section=problems&id=102
+
+! DESCRIPTION
+! -----------
+
+! Three distinct points are plotted at random on a Cartesian plane, for which
+! -1000 ≤ x, y ≤ 1000, such that a triangle is formed.
+
+! Consider the following two triangles:
+
+! A(-340,495), B(-153,-910), C(835,-947)
+! X(-175,41), Y(-421,-714), Z(574,-645)
+
+! It can be verified that triangle ABC contains the origin, whereas triangle
+! XYZ does not.
+
+! Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text
+! file containing the co-ordinates of one thousand "random" triangles, find the
+! number of triangles for which the interior contains the origin.
+
+! NOTE: The first two examples in the file represent the triangles in the
+! example given above.
+
+
+! SOLUTION
+! --------
+
+! A triangle of coordinates (x1, y1) (x2, y2) (x3, y3) contains
+! the origin when (ab * bc > 0) and (bc * ca > 0) where:
+! ab = x1 * (y2 - y1) - y1 * (x2 - x1)
+! bc = x2 * (y3 - y2) - y2 * (x3 - x2)
+! ca = x3 * (y1 - y3) - y3 * (x1 - x3)
+
+<PRIVATE
+
+: source-102 ( -- seq )
+    "resource:extra/project-euler/102/triangles.txt"
+    ascii file-lines [
+        "," split [ string>number ] map 2 group
+    ] map ;
+
+: det ( coord coord -- n )
+    dupd [ [ last ] bi@ - ] [ [ first ] bi@ - ] 2bi 2array
+    [ [ first ] bi@ * ] [ [ last ] bi@ * ] 2bi - ;
+
+: include-origin? ( coord-seq -- ? )
+    dup first suffix 2 clump [ [ first ] [ last ] bi det ] map
+    2 clump [ product 0 > ] all? ;
+
+PRIVATE>
+
+: euler102 ( -- answer )
+    source-102 [ include-origin? ] count ;
+
+! [ euler102 ] 100 ave-time
+! 12 ms ave run time - 0.92 SD (100 trials)
+
+SOLUTION: euler102

diff --git a/extra/project-euler/102/triangles.txt b/extra/project-euler/102/triangles.txt
new file mode 100644 (file)
index 0000000..d43312a
--- /dev/null
+++ b/extra/project-euler/102/triangles.txt
@@ -0,0 +1,1000 @@
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diff --git a/extra/project-euler/project-euler.factor b/extra/project-euler/project-euler.factor
index 5a0155738ac2b0e7234f74a7e51c29ee2ff81247..f0e40674da0f7b887bcb2676aa01f502066dd9e4 100644 (file)
--- a/extra/project-euler/project-euler.factor
+++ b/extra/project-euler/project-euler.factor
@@ -19,11 +19,11 @@ USING: definitions io io.files io.pathnames kernel math math.parser
     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.085 project-euler.092 project-euler.097
-    project-euler.099 project-euler.100 project-euler.112 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.099 project-euler.100 project-euler.102 project-euler.112
+    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