! Copyright (c) 2007 Samuel Tardieu, Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math math.ranges project-euler.common sequences ;
IN: project-euler.018

! http://projecteuler.net/index.php?section=problems&id=18

! DESCRIPTION
! -----------

! By starting at the top of the triangle below and moving to adjacent numbers
! on the row below, the maximum total from top to bottom is 23.

!        3
!       7 5
!      2 4 6
!     8 5 9 3

! That is, 3 + 7 + 4 + 9 = 23.

! Find the maximum total from top to bottom of the triangle below:

!                                 75
!                               95  64
!                             17  47  82
!                           18  35  87  10
!                         20  04  82  47  65
!                       19  01  23  75  03  34
!                     88  02  77  73  07  63  67
!                   99  65  04  28  06  16  70  92
!                 41  41  26  56  83  40  80  70  33
!               41  48  72  33  47  32  37  16  94  29
!             53  71  44  65  25  43  91  52  97  51  14
!           70  11  33  28  77  73  17  78  39  68  17  57
!         91  71  52  38  17  14  91  43  58  50  27  29  48
!       63  66  04  68  89  53  67  30  73  16  69  87  40  31
!     04  62  98  27  23  09  70  98  73  93  38  53  60  04  23

! NOTE: As there are only 16384 routes, it is possible to solve this problem by
! trying every route. However, Problem 67, is the same challenge with a
! triangle containing one-hundred rows; it cannot be solved by brute force, and
! requires a clever method! ;o)


! SOLUTION
! --------

! Propagate from bottom to top the longest cumulative path. This is very
! efficient and will be reused in problem 67.

<PRIVATE

: source-018 ( -- triangle )
    {                              75
                                 95  64
                               17  47  82
                             18  35  87  10
                           20  04  82  47  65
                         19  01  23  75  03  34
                       88  02  77  73  07  63  67
                     99  65  04  28  06  16  70  92
                   41  41  26  56  83  40  80  70  33
                 41  48  72  33  47  32  37  16  94  29
               53  71  44  65  25  43  91  52  97  51  14
             70  11  33  28  77  73  17  78  39  68  17  57
           91  71  52  38  17  14  91  43  58  50  27  29  48
         63  66  04  68  89  53  67  30  73  16  69  87  40  31
       04  62  98  27  23  09  70  98  73  93  38  53  60  04  23
     } 15 [1,b] [ cut swap ] map nip ;

PRIVATE>

: euler018 ( -- answer )
    source-018 propagate-all first first ;

! [ euler018 ] 100 ave-time
! 0 ms ave run time - 0.29 SD (100 trials)


! ALTERNATE SOLUTIONS
! -------------------

: euler018a ( -- answer )
    source-018 max-path ;

! [ euler018a ] 100 ave-time
! 0 ms ave run time - 0.39 SD (100 trials)

SOLUTION: euler018a