Solution to Project Euler problem 34

db4
Aaron Schaefer 2008-01-28 03:37:14 -05:00
parent 840c401cb5
commit 38bc7d7f75
3 changed files with 52 additions and 4 deletions

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! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math.ranges project-euler.common sequences ;
IN: project-euler.034
! http://projecteuler.net/index.php?section=problems&id=34
! DESCRIPTION
! -----------
! 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
! Find the sum of all numbers which are equal to the sum of the factorial of
! their digits.
! Note: as 1! = 1 and 2! = 2 are not sums they are not included.
! SOLUTION
! --------
! We can reduce the upper bound a little by calculating 7 * 9! = 2540160, and
! then reducing one of the 9! to 2! (since the 7th digit cannot exceed 2), so we
! get 2! + 6 * 9! = 2177282 as an upper bound.
! We can then take that one more step, and notice that the largest factorial
! sum a 7 digit number starting with 21 or 20 is 2! + 1! + 5 * 9! or 1814403.
! So there can't be any 7 digit solutions starting with 21 or 20, and therefore
! our numbers must be less that 2000000.
<PRIVATE
: digit-factorial ( n -- n! )
{ 1 1 2 6 24 120 720 5040 40320 362880 } nth ;
: factorion? ( n -- ? )
dup number>digits [ digit-factorial ] sigma = ;
PRIVATE>
: euler034 ( -- answer )
3 2000000 [a,b] [ factorion? ] subset sum ;
! [ euler034 ] 10 ave-time
! 15089 ms run / 725 ms GC ave time - 10 trials
MAIN: euler034

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! Problems using each public word
! -------------------------------
! cartesian-product - #4, #27
! cartesian-product - #4, #27, #29, #32, #33
! collect-consecutive - #8, #11
! log10 - #25, #134
! max-path - #18, #67
! number>digits - #16, #20, #30
! number>digits - #16, #20, #30, #34
! propagate-all - #18, #67
! sum-proper-divisors - #21
! tau* - #12

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! Copyright (c) 2007 Aaron Schaefer.
! Copyright (c) 2007, 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: definitions io io.files kernel math.parser sequences vocabs
vocabs.loader project-euler.ave-time project-euler.common math
@ -9,7 +9,8 @@ USING: definitions io io.files kernel math.parser sequences vocabs
project-euler.017 project-euler.018 project-euler.019 project-euler.020
project-euler.021 project-euler.022 project-euler.023 project-euler.024
project-euler.025 project-euler.026 project-euler.027 project-euler.028
project-euler.029 project-euler.030 project-euler.067 project-euler.134
project-euler.029 project-euler.030 project-euler.031 project-euler.032
project-euler.033 project-euler.034 project-euler.067 project-euler.134
project-euler.169 project-euler.173 project-euler.175 ;
IN: project-euler