38 lines
1016 B
Factor
38 lines
1016 B
Factor
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! Copyright (c) 2009 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.functions math.ranges project-euler.common sequences ;
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IN: project-euler.063
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! http://projecteuler.net/index.php?section=problems&id=63
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! DESCRIPTION
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! -----------
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! The 5-digit number, 16807 = 7^5, is also a fifth power. Similarly, the
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! 9-digit number, 134217728 = 8^9, is a ninth power.
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! How many n-digit positive integers exist which are also an nth power?
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! SOLUTION
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! --------
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! Only have to check from 1 to 9 because 10^n already has too many digits.
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! In general, x^n has n digits when:
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! 10^(n-1) <= x^n < 10^n
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! ...take the left side of that equation, solve for n to see where they meet:
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! n = log(10) / [ log(10) - log(x) ]
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! Round down since we already know that particular value of n is no good.
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: euler063 ( -- answer )
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9 [1,b] [ log [ 10 log dup ] dip - /i ] sigma ;
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! [ euler063 ] 100 ave-time
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! 0 ms ave run time - 0.0 SD (100 trials)
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SOLUTION: euler063
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