47 lines
1.2 KiB
Factor
47 lines
1.2 KiB
Factor
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! Copyright (c) 2007 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: combinators.lib kernel math math.functions math.ranges namespaces
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project-euler.common sequences ;
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IN: project-euler.021
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! http://projecteuler.net/index.php?section=problems&id=21
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! DESCRIPTION
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! -----------
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! Let d(n) be defined as the sum of proper divisors of n (numbers less than n
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! which divide evenly into n).
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! If d(a) = b and d(b) = a, where a != b, then a and b are an amicable pair and
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! each of a and b are called amicable numbers.
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! For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44,
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! 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4,
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! 71 and 142; so d(284) = 220.
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! Evaluate the sum of all the amicable numbers under 10000.
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! SOLUTION
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! --------
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<PRIVATE
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: d ( n -- sum )
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dup sqrt >fixnum 2 swap [a,b] [
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[ 2dup divisor? [ 2dup / + , ] [ drop ] if ] each drop
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] { } make sum 1+ ;
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: amicable-pair? ( n m -- ? )
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{ [ 2dup = not ] [ 2dup d = ] } && 2nip ;
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PRIVATE>
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: euler021 ( -- answer )
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10000 [1,b] [ dup dup d amicable-pair? [ drop 0 ] unless ] sigma ;
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! [ euler021 ] 100 ave-time
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! 328 ms run / 10 ms GC ave time - 100 trials
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MAIN: euler021
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