/*
  Euler Problem 18 in B-Prolog

  """
  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 4
  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)
  """

  Answer: max_val=1074
  
  This is a backport of my Picat model http://hakank.org/picat/euler18.pi


  
  Model created by Hakan Kjellerstrand, hakank@gmail.com
  See also my B-Prolog page: http://www.hakank.org/bprolog/

*/

go :-
        time(euler18).

%%
%% 0.0s
%%
euler18 :-
        p18(Tri),
        pp(1,1,Tri,Sum),
        writeln(max_val=Sum).

p18(Triangle) :- 
        Triangle  = [[75],
                     [95,64],
                     [17,47,82],
                     [18,35,87,10],
                     [20, 4,82,47,65],
                     [19, 1,23,75, 3,34],
                     [88, 2,77,73, 7,63,67],
                     [99,65, 4,28, 6,16,70,92],
                     [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, 4,68,89,53,67,30,73,16,69,87,40,31],
                     [ 4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23]].

%%
%% From Neng-Fa Zhou.
%%
:- table pp(+,+,+,max).
pp(Row,_Column,Tri,Sum) :-
        length(Tri,Len),
        Row > Len,
        Sum is 0.
pp(Row,Column,Tri,Sum) :-
        length(Tri,Len),
        Row =< Len,
        Row1 is Row+1,
        pp(Row1,Column,Tri,Sum1),
        matrix_element(Tri,Row,Column,TriRC),
        Sum is Sum1 + TriRC.

pp(Row,Column,Tri,Sum) :-
        length(Tri,Len),
        Row =< Len,
        Row1 is Row + 1, 
        Column1 is Column + 1,
        pp(Row1,Column1,Tri,Sum1),
        matrix_element(Tri,Row,Column,TriRC),        
        Sum is Sum1 + TriRC.    

matrix_element(X, I, J, Val) :-
        nth1(I, X, Row),
        nth1(J, Row, Val).