64 lines
1.6 KiB
Factor
64 lines
1.6 KiB
Factor
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! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays kernel math.primes.factors
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math.ranges project-euler.common sequences sorting ;
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IN: project-euler.124
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! http://projecteuler.net/index.php?section=problems&id=124
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! DESCRIPTION
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! -----------
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! The radical of n, rad(n), is the product of distinct prime factors of n.
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! For example, 504 = 2^3 × 3^2 × 7, so rad(504) = 2 × 3 × 7 = 42.
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! If we calculate rad(n) for 1 ≤ n ≤ 10, then sort them on rad(n),
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! and sorting on n if the radical values are equal, we get:
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! Unsorted Sorted
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! n rad(n) n rad(n) k
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! 1 1 1 1 1
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! 2 2 2 2 2
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! 3 3 4 2 3
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! 4 2 8 2 4
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! 5 5 3 3 5
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! 6 6 9 3 6
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! 7 7 5 5 7
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! 8 2 6 6 8
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! 9 3 7 7 9
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! 10 10 10 10 10
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! Let E(k) be the kth element in the sorted n column; for example,
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! E(4) = 8 and E(6) = 9.
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! If rad(n) is sorted for 1 ≤ n ≤ 100000, find E(10000).
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! SOLUTION
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! --------
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<PRIVATE
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: rad ( n -- n )
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unique-factors product ; inline
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: rads-upto ( n -- seq )
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[0,b] [ dup rad 2array ] map ;
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: (euler124) ( -- seq )
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100000 rads-upto sort-values ;
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PRIVATE>
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: euler124 ( -- answer )
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10000 (euler124) nth first ;
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! [ euler124 ] 100 ave-time
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! 373 ms ave run time - 17.61 SD (100 trials)
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! TODO: instead of the brute-force method, making the rad
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! array in the way of the sieve of eratosthene would scale
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! better on bigger values.
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SOLUTION: euler124
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