48 lines
1.3 KiB
Factor
48 lines
1.3 KiB
Factor
! 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.ranges project-euler.common sequences ;
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IN: project-euler.034
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! http://projecteuler.net/index.php?section=problems&id=34
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! DESCRIPTION
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! -----------
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! 145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
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! Find the sum of all numbers which are equal to the sum of the factorial of
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! their digits.
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! Note: as 1! = 1 and 2! = 2 are not sums they are not included.
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! SOLUTION
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! --------
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! We can reduce the upper bound a little by calculating 7 * 9! = 2540160, and
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! then reducing one of the 9! to 2! (since the 7th digit cannot exceed 2), so we
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! get 2! + 6 * 9! = 2177282 as an upper bound.
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! We can then take that one more step, and notice that the largest factorial
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! sum a 7 digit number starting with 21 or 20 is 2! + 1! + 5 * 9! or 1814403.
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! So there can't be any 7 digit solutions starting with 21 or 20, and therefore
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! our numbers must be less that 2000000.
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<PRIVATE
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: digit-factorial ( n -- n! )
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{ 1 1 2 6 24 120 720 5040 40320 362880 } nth ;
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: factorion? ( n -- ? )
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dup number>digits [ digit-factorial ] map-sum = ;
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PRIVATE>
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: euler034 ( -- answer )
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3 2000000 [a,b] [ factorion? ] filter sum ;
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! [ euler034 ] 10 ave-time
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! 5506 ms ave run time - 144.0 SD (10 trials)
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SOLUTION: euler034
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