47 lines
1021 B
Factor
47 lines
1021 B
Factor
! Copyright (c) 2008 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.ranges ;
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IN: project-euler.028
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! http://projecteuler.net/index.php?section=problems&id=28
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! DESCRIPTION
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! -----------
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! Starting with the number 1 and moving to the right in a clockwise direction a
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! 5 by 5 spiral is formed as follows:
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! 21 22 23 24 25
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! 20 7 8 9 10
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! 19 6 1 2 11
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! 18 5 4 3 12
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! 17 16 15 14 13
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! It can be verified that the sum of both diagonals is 101.
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! What is the sum of both diagonals in a 1001 by 1001 spiral formed in the same way?
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! SOLUTION
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! --------
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! For a square sized n by n, the sum of corners is 4n² - 6n + 6
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<PRIVATE
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: sum-corners ( n -- sum )
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dup 1 = [ [ sq 4 * ] keep 6 * - 6 + ] unless ;
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: sum-diags ( n -- sum )
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1 swap 2 <range> [ sum-corners ] sigma ;
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PRIVATE>
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: euler028 ( -- answer )
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1001 sum-diags ;
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! [ euler028 ] 100 ave-time
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! 0 ms run / 0 ms GC ave time - 100 trials
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MAIN: euler028
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