diff --git a/extra/project-euler/044/044.factor b/extra/project-euler/044/044.factor new file mode 100644 index 0000000000..6369cb5372 --- /dev/null +++ b/extra/project-euler/044/044.factor @@ -0,0 +1,50 @@ +! Copyright (c) 2008 Aaron Schaefer. +! See http://factorcode.org/license.txt for BSD license. +USING: kernel math math.functions math.ranges project-euler.common sequences ; +IN: project-euler.044 + +! http://projecteuler.net/index.php?section=problems&id=44 + +! DESCRIPTION +! ----------- + +! Pentagonal numbers are generated by the formula, Pn=n(3nāˆ’1)/2. The first ten +! pentagonal numbers are: + +! 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ... + +! It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, +! 70 āˆ’ 22 = 48, is not pentagonal. + +! Find the pair of pentagonal numbers, Pj and Pk, for which their sum and +! difference is pentagonal and D = |Pk āˆ’ Pj| is minimised; what is the value of D? + + +! SOLUTION +! -------- + +! Brute force using a cartesian product and an arbitrarily chosen limit. + + [ 24 * 1+ sqrt 1+ 6 / 1 mod zero? ] [ drop f ] if ; + +: sum-and-diff? ( m n -- ? ) + 2dup + -rot - [ pentagonal? ] 2apply and ; + +PRIVATE> + +: euler044 ( -- answer ) + 2500 [1,b] [ nth-pentagonal ] map dup cartesian-product + [ first2 sum-and-diff? ] subset [ first2 - abs ] map infimum ; + +! [ euler044 ] 10 ave-time +! 8924 ms run / 2872 ms GC ave time - 10 trials + +! TODO: this solution is ugly and not very efficient...find a better algorithm + +MAIN: euler044 diff --git a/extra/project-euler/project-euler.factor b/extra/project-euler/project-euler.factor index ef28cf8778..36a9069d77 100644 --- a/extra/project-euler/project-euler.factor +++ b/extra/project-euler/project-euler.factor @@ -12,9 +12,10 @@ USING: definitions io io.files kernel math math.parser project-euler.ave-time project-euler.029 project-euler.030 project-euler.031 project-euler.032 project-euler.033 project-euler.034 project-euler.035 project-euler.036 project-euler.037 project-euler.038 project-euler.039 project-euler.040 - project-euler.041 project-euler.042 project-euler.043 project-euler.048 - project-euler.052 project-euler.067 project-euler.075 project-euler.097 - project-euler.134 project-euler.169 project-euler.173 project-euler.175 ; + project-euler.041 project-euler.042 project-euler.043 project-euler.044 + project-euler.048 project-euler.052 project-euler.067 project-euler.075 + project-euler.097 project-euler.134 project-euler.169 project-euler.173 + project-euler.175 ; IN: project-euler