47 lines
1.2 KiB
Factor
47 lines
1.2 KiB
Factor
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! Copyright (c) 2010 Aaron Schaefer. All rights reserved.
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! The contents of this file are licensed under the Simplified BSD License
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! A copy of the license is available at http://factorcode.org/license.txt
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USING: grouping kernel math math.ranges project-euler.common sequences ;
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IN: project-euler.206
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! http://projecteuler.net/index.php?section=problems&id=206
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! DESCRIPTION
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! -----------
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! Find the unique positive integer whose square has the form
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! 1_2_3_4_5_6_7_8_9_0, where each “_” is a single digit.
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! SOLUTION
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! --------
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! Through mathematical analysis, we know that the number must end in 00, and
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! the only way to get the last digits to be 900, is for our answer to end in
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! 30 or 70.
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<PRIVATE
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! 1020304050607080900 sqrt, rounded up to the nearest 30 ending
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CONSTANT: lo 1010101030
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! 1929394959697989900 sqrt, rounded down to the nearest 70 ending
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CONSTANT: hi 1389026570
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: form-fitting? ( n -- ? )
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number>digits 2 group [ first ] map
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{ 1 2 3 4 5 6 7 8 9 0 } = ;
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: candidates ( -- seq )
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lo lo 40 + [ hi 100 <range> ] bi@ append ;
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PRIVATE>
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: euler206 ( -- answer )
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candidates [ sq form-fitting? ] find-last nip ;
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! [ euler206 ] 100 ave-time
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! 321 ms ave run time - 8.33 SD (100 trials)
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SOLUTION: euler206
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