2008-02-08 19:28:30 -05:00
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! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math project-euler.common ;
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IN: project-euler.045
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! http://projecteuler.net/index.php?section=problems&id=45
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! DESCRIPTION
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! -----------
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! Triangle, pentagonal, and hexagonal numbers are generated by the following
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! formulae:
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! Triangle Tn = n(n + 1) / 2 1, 3, 6, 10, 15, ...
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! Pentagonal Pn = n(3n − 1) / 2 1, 5, 12, 22, 35, ...
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! Hexagonal Hn = n(2n − 1) 1, 6, 15, 28, 45, ...
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! It can be verified that T285 = P165 = H143 = 40755.
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! Find the next triangle number that is also pentagonal and hexagonal.
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! SOLUTION
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! --------
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! All hexagonal numbers are also triangle numbers, so iterate through hexagonal
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! numbers until you find one that is pentagonal as well.
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<PRIVATE
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: nth-hexagonal ( n -- m )
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dup 2 * 1- * ;
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DEFER: next-solution
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2008-02-08 20:43:44 -05:00
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: (next-solution) ( n hexagonal -- hexagonal )
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2008-02-08 19:28:30 -05:00
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dup pentagonal? [ nip ] [ drop next-solution ] if ;
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: next-solution ( n -- m )
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1+ dup nth-hexagonal (next-solution) ;
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PRIVATE>
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: euler045 ( -- answer )
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143 next-solution ;
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! [ euler045 ] 100 ave-time
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2008-11-05 01:11:15 -05:00
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! 12 ms ave run time - 1.71 SD (100 trials)
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2008-02-08 19:28:30 -05:00
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2009-03-19 00:05:32 -04:00
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SOLUTION: euler045
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