Solution to Project Euler problem 38

db4
Aaron Schaefer 2008-02-01 14:45:29 -05:00
parent 6394eb70bf
commit e37f2101c6
4 changed files with 63 additions and 7 deletions

View File

@ -1,7 +1,7 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib hashtables kernel math math.combinatorics math.parser
math.ranges project-euler.common sequences sorting ;
math.ranges project-euler.common sequences ;
IN: project-euler.032
! http://projecteuler.net/index.php?section=problems&id=32
@ -63,9 +63,6 @@ PRIVATE>
: source-032a ( -- seq )
50 [1,b] 2000 [1,b] cartesian-product ;
: pandigital? ( n -- ? )
number>string natural-sort "123456789" = ;
! multiplicand/multiplier/product
: mmp ( pair -- n )
first2 2dup * [ number>string ] 3apply 3append 10 string>integer ;

View File

@ -0,0 +1,55 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.parser math.ranges project-euler.common sequences ;
IN: project-euler.038
! http://projecteuler.net/index.php?section=problems&id=38
! DESCRIPTION
! -----------
! Take the number 192 and multiply it by each of 1, 2, and 3:
! 192 × 1 = 192
! 192 × 2 = 384
! 192 × 3 = 576
! By concatenating each product we get the 1 to 9 pandigital, 192384576. We
! will call 192384576 the concatenated product of 192 and (1,2,3)
! The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4,
! and 5, giving the pandigital, 918273645, which is the concatenated product of
! 9 and (1,2,3,4,5).
! What is the largest 1 to 9 pandigital 9-digit number that can be formed as
! the concatenated product of an integer with (1,2, ... , n) where n > 1?
! SOLUTION
! --------
! Only need to search 4-digit numbers starting with 9 since a 2-digit number
! starting with 9 would produce 8 or 11 digits, and a 3-digit number starting
! with 9 would produce 7 or 11 digits.
<PRIVATE
: (concat-product) ( accum n multiplier -- m )
pick length 8 > [
2drop 10 swap digits>integer
] [
[ * number>digits over push-all ] 2keep 1+ (concat-product)
] if ;
: concat-product ( n -- m )
V{ } clone swap 1 (concat-product) ;
PRIVATE>
: euler038 ( -- answer )
9123 9876 [a,b] [ concat-product ] map [ pandigital? ] subset supremum ;
! [ euler038 ] 100 ave-time
! 37 ms run / 1 ms GC ave time - 100 trials
MAIN: euler038

View File

@ -1,5 +1,5 @@
USING: arrays combinators.lib kernel math math.functions math.miller-rabin
math.parser math.primes.factors math.ranges namespaces sequences ;
math.parser math.primes.factors math.ranges namespaces sequences sorting ;
IN: project-euler.common
! A collection of words used by more than one Project Euler solution
@ -12,6 +12,7 @@ IN: project-euler.common
! log10 - #25, #134
! max-path - #18, #67
! number>digits - #16, #20, #30, #34
! pandigital? - #32, #38
! propagate-all - #18, #67
! sum-proper-divisors - #21
! tau* - #12
@ -67,6 +68,9 @@ PRIVATE>
: number>digits ( n -- seq )
number>string string>digits ;
: pandigital? ( n -- ? )
number>string natural-sort "123456789" = ;
! Not strictly needed, but it is nice to be able to dump the triangle after the
! propagation
: propagate-all ( triangle -- newtriangle )

View File

@ -11,8 +11,8 @@ USING: definitions io io.files kernel math.parser sequences vocabs
project-euler.025 project-euler.026 project-euler.027 project-euler.028
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.067 project-euler.134 project-euler.169
project-euler.173 project-euler.175 ;
project-euler.037 project-euler.038 project-euler.067 project-euler.134
project-euler.169 project-euler.173 project-euler.175 ;
IN: project-euler
<PRIVATE