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Project Euler Problem 18

on project euler, erlang, python

Maximum path sum I.

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

Link to original description
Source code examples on Github

Erlang version

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#!/usr/bin/env escript
%% -*- erlang -*-
%%! -smp enable -sname p18
% vim:syn=erlang

-mode(compile).

main(_) ->
    io:format("Answer: ~p ~n", [test18()]).

test18() ->
    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]    
    ],
    lists:max(lists:flatten(test18i(Triangle, 1, 75))).

v(M,L) -> lists:nth(M, L).

test18i([_|[]], _, A) -> A;
test18i(_, 0, A)      -> A;
test18i([_|T], M, A)  -> [test18i(T, M, v(M, v(1,T))+A)] ++ [test18i(T, M+1, v(M+1, v(1,T))+A)].

Python version

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#!/usr/bin/python

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, ),
)

def path(triangle, num):
    s = triangle[0][0]
    col = 0
    for row in xrange(1, len(triangle)):
        if num % 2: col = col + 1
        num = num / 2
        s = s + triangle[row][col]
    return s

print max(path(triangle, n) for n in xrange(0, 16384))