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Solution to Project Euler problem 188

db4
Guillaume Nargeot 2009-10-12 21:38:34 +09:00
parent f97ede3d91
commit 5548324303
3 changed files with 48 additions and 1 deletions

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extra/project-euler/188/188-tests.factor Executable file
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USING: project-euler.188 tools.test ;
IN: project-euler.188.tests
[ 95962097 ] [ euler188 ] unit-test

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extra/project-euler/188/188.factor Executable file
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! Copyright (c) 2009 Guillaume Nargeot.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.functions project-euler.common ;
IN: project-euler.188
! http://projecteuler.net/index.php?section=problems&id=188
! DESCRIPTION
! -----------
! The hyperexponentiation or tetration of a number a by a positive integer b,
! denoted by a↑↑b or ^(b)a, is recursively defined by:
! a↑↑1 = a,
! a↑↑(k+1) = a^(a↑↑k).
! Thus we have e.g. 3↑↑2 = 3^3 = 27, hence
! 3↑↑3 = 3^27 = 7625597484987 and
! 3↑↑4 is roughly 10^(3.6383346400240996*10^12).
! Find the last 8 digits of 1777↑↑1855.
! SOLUTION
! --------
! Using modular exponentiation.
! http://en.wikipedia.org/wiki/Modular_exponentiation
<PRIVATE
: hyper-exp-mod ( a b m -- e )
1 rot [ [ 2dup ] dip swap ^mod ] times 2nip ;
PRIVATE>
: euler188 ( -- answer )
1777 1855 10 8 ^ hyper-exp-mod ;
! [ euler188 ] 100 ave-time
! 4 ms ave run time - 0.05 SD (100 trials)
SOLUTION: euler188

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extra/project-euler/project-euler.factor
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@ -24,7 +24,7 @@ USING: definitions io io.files io.pathnames kernel math math.parser
project-euler.116 project-euler.117 project-euler.124 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.188 project-euler.190 project-euler.203 project-euler.215 ;
IN: project-euler
<PRIVATE