90 lines
2.9 KiB
Factor
90 lines
2.9 KiB
Factor
! Copyright (c) 2007 Samuel Tardieu, Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math project-euler.common sequences ;
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IN: project-euler.018
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! http://projecteuler.net/index.php?section=problems&id=18
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! DESCRIPTION
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! -----------
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! By starting at the top of the triangle below and moving to adjacent numbers
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! on the row below, the maximum total from top to bottom is 23.
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! 3
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! 7 5
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! 2 4 6
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! 8 5 9 3
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! That is, 3 + 7 + 4 + 9 = 23.
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! Find the maximum total from top to bottom of the triangle below:
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! 75
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! 95 64
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! 17 47 82
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! 18 35 87 10
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! 20 04 82 47 65
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! 19 01 23 75 03 34
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! 88 02 77 73 07 63 67
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! 99 65 04 28 06 16 70 92
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! 41 41 26 56 83 40 80 70 33
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! 41 48 72 33 47 32 37 16 94 29
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! 53 71 44 65 25 43 91 52 97 51 14
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! 70 11 33 28 77 73 17 78 39 68 17 57
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! 91 71 52 38 17 14 91 43 58 50 27 29 48
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! 63 66 04 68 89 53 67 30 73 16 69 87 40 31
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! 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
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! NOTE: As there are only 16384 routes, it is possible to solve this problem by
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! trying every route. However, Problem 67, is the same challenge with a
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! triangle containing one-hundred rows; it cannot be solved by brute force, and
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! requires a clever method! ;o)
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! SOLUTION
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! --------
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! Propagate from bottom to top the longest cumulative path. This is very
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! efficient and will be reused in problem 67.
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<PRIVATE
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: source-018 ( -- triangle )
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{ 75
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95 64
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17 47 82
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18 35 87 10
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20 04 82 47 65
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19 01 23 75 03 34
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88 02 77 73 07 63 67
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99 65 04 28 06 16 70 92
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41 41 26 56 83 40 80 70 33
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41 48 72 33 47 32 37 16 94 29
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53 71 44 65 25 43 91 52 97 51 14
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70 11 33 28 77 73 17 78 39 68 17 57
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91 71 52 38 17 14 91 43 58 50 27 29 48
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63 66 04 68 89 53 67 30 73 16 69 87 40 31
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04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
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} 15 [ 1+ cut swap ] map nip ;
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PRIVATE>
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: euler018 ( -- answer )
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source-018 propagate-all first first ;
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! [ euler018 ] 100 ave-time
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! 0 ms run / 0 ms GC ave time - 100 trials
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! ALTERNATE SOLUTIONS
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! -------------------
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: euler018a ( -- answer )
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source-018 max-path ;
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! [ euler018a ] 100 ave-time
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! 0 ms run / 0 ms GC ave time - 100 trials
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MAIN: euler018a
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