54 lines
1.4 KiB
Factor
54 lines
1.4 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer, Slava Pestov.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.ranges project-euler.common sequences ;
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IN: project-euler.092
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! http://projecteuler.net/index.php?section=problems&id=92
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! DESCRIPTION
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! -----------
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! A number chain is created by continuously adding the square of the digits in
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! a number to form a new number until it has been seen before.
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! For example,
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! 44 -> 32 -> 13 -> 10 -> 1 -> 1
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! 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89
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! Therefore any chain that arrives at 1 or 89 will become stuck in an endless
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! loop. What is most amazing is that EVERY starting number will eventually
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! arrive at 1 or 89.
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! How many starting numbers below ten million will arrive at 89?
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! SOLUTION
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! --------
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<PRIVATE
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: next-link ( n -- m )
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number>digits [ sq ] map-sum ;
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: chain-ending ( n -- m )
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dup [ 1 = ] [ 89 = ] bi or [ next-link chain-ending ] unless ;
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: lower-endings ( -- seq )
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567 [1,b] [ chain-ending ] map ;
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: fast-chain-ending ( seq n -- m )
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dup 567 > [ next-link ] when 1 - swap nth ;
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PRIVATE>
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: euler092 ( -- answer )
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lower-endings 9999999 [1,b] [ fast-chain-ending 89 = ] with count ;
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! [ euler092 ] 10 ave-time
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! 33257 ms ave run time - 624.27 SD (10 trials)
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! TODO: this solution is not very efficient, much better optimizations exist
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SOLUTION: euler092
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