Slow solution to Project Euler problem 92

db4
Aaron Schaefer 2008-02-09 22:13:01 -05:00
parent 96853249a4
commit a34c5aabed
3 changed files with 59 additions and 4 deletions

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@ -0,0 +1,55 @@
! Copyright (c) 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: combinators.lib kernel math math.ranges namespaces project-euler.common
sequences ;
IN: project-euler.092
! http://projecteuler.net/index.php?section=problems&id=92
! DESCRIPTION
! -----------
! A number chain is created by continuously adding the square of the digits in
! a number to form a new number until it has been seen before.
! For example,
! 44 -> 32 -> 13 -> 10 -> 1 -> 1
! 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89
! Therefore any chain that arrives at 1 or 89 will become stuck in an endless
! loop. What is most amazing is that EVERY starting number will eventually
! arrive at 1 or 89.
! How many starting numbers below ten million will arrive at 89?
! SOLUTION
! --------
<PRIVATE
: next-link ( n -- m )
number>digits [ sq ] sigma ;
: chain-ending ( n -- m )
dup 1 = over 89 = or [ next-link chain-ending ] unless ;
: lower-endings ( -- seq )
567 [1,b] [ chain-ending ] map ;
: fast-chain-ending ( seq n -- m )
dup 567 > [ next-link ] when 1- swap nth ;
PRIVATE>
: euler092 ( -- answer )
lower-endings 9999999 [1,b] [ fast-chain-ending 89 = ] with count ;
! [ euler092 ] time
! 68766 ms run / 372 ms GC time
! TODO: solution is still too slow, maybe try using a 10000000-byte array that
! keeps track of each number in the chain and their endings
MAIN: euler092

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@ -14,7 +14,7 @@ IN: project-euler.common
! log10 - #25, #134
! max-path - #18, #67
! nth-triangle - #12, #42
! number>digits - #16, #20, #30, #34
! number>digits - #16, #20, #30, #34, #35, #38, #43, #52, #55, #56, #92
! palindrome? - #4, #36, #55
! pandigital? - #32, #38
! pentagonal? - #44, #45
@ -78,7 +78,7 @@ PRIVATE>
] if ;
: number>digits ( n -- seq )
number>string string>digits ;
[ dup zero? not ] [ 10 /mod ] [ ] unfold reverse nip ;
: nth-triangle ( n -- n )
dup 1+ * 2 / ;

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@ -15,8 +15,8 @@ USING: definitions io io.files kernel math math.parser project-euler.ave-time
project-euler.041 project-euler.042 project-euler.043 project-euler.044
project-euler.045 project-euler.048 project-euler.052 project-euler.053
project-euler.056 project-euler.067 project-euler.075 project-euler.079
project-euler.097 project-euler.134 project-euler.169 project-euler.173
project-euler.175 ;
project-euler.092 project-euler.097 project-euler.134 project-euler.169
project-euler.173 project-euler.175 ;
IN: project-euler
<PRIVATE