/********************************************************* http://projecteuler.net/problem=18 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) This Picat model is based on the one created by Hakan Kjellerstrand, hakank@gmail.com See also my Picat page: http://www.hakank.org/picat/ *********************************************************/ main => go. go => euler18. euler18 => p18(Tri), pp(1,1,Sum,Tri), writeln(max_val=Sum), nl. table (+,+,max,nt) % nt means that argument is not tabled pp(Row,_Column,Sum,Tri),Row>Tri.length => Sum=0. pp(Row,Column,Sum,Tri) ?=> pp(Row+1,Column,Sum1,Tri), Sum = Sum1+Tri[Row,Column]. pp(Row,Column,Sum,Tri) => pp(Row+1,Column+1,Sum1,Tri), Sum = Sum1+Tri[Row,Column]. 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}}.