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Optimize solution to Project Euler problem 28

db4
Aaron Schaefer 2008-01-18 00:43:15 -05:00
parent 4cba26462d
commit ccb8ad98ec
1 changed files with 6 additions and 21 deletions
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27
extra/project-euler/028/028.factor
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@ -25,35 +25,20 @@ IN: project-euler.028
! SOLUTION
! --------
! Noticed patterns in the diagnoal numbers starting from the origin going to
! the corners and used these instead of generating the entire spiral:
! ne -> (2n + 1)² from 0 .. n
! se -> (4 * n²) - (10 * n) + 7 from 1 .. n
! sw -> (4 * n²) + 1 from 0 .. n
! nw -> (4 * n²) - (6 * n) + 3 from 1 .. n
! For a square sized n by n, the sum of corners is 4n² - 6n + 6
<PRIVATE
: ne ( m -- n )
2 * 1+ sq ;
: sum-corners ( n -- sum )
dup 1 = [ [ sq 4 * ] keep 6 * - 6 + ] unless ;
: se ( m -- n )
[ sq 4 * ] keep 10 * - 7 + ;
: sw ( m -- n )
sq 4 * 1+ ;
: nw ( m -- n )
[ sq 4 * ] keep 6 * - 3 + ;
: spiral-diags ( n -- sum )
1+ 2 / [ [ ne ] sigma ] keep [ [ sw ] sigma ] keep
[1,b] [ [ se ] sigma ] keep [ nw ] sigma 3 - [ + ] 3apply ;
: sum-diags ( n -- sum )
1 swap 2 <range> [ sum-corners ] sigma ;
PRIVATE>
: euler028 ( -- answer )
1001 spiral-diags ;
1001 sum-diags ;
! [ euler027 ] 100 ave-time
! 0 ms run / 0 ms GC ave time - 100 trials