Euler18.py

# -*- coding: utf-8 -*-
"""
Maximum path sum I
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)

Answer: 1074
Ricky Kwok, rickyk9487@gmail.com, 2014-10-24
"""

def get_max_path(tri_array, depth):
    """ Returns the maximum path for each node by computing the maximum
        path of each of the two children starting from bottom up. """
    max_path = [0] * len(tri_array)
    max_path[depth * (depth-1) / 2: depth * (depth+1) / 2] = tri_array[depth * (depth-1) / 2: depth * (depth + 1) / 2]
    for r in range(depth - 1, 0, -1):
        for c in range(r):
            # Iterates from the bottom-most row, left to rigth
            max_child = max(max_path[r * (r + 1) / 2 + c], max_path[r * (r + 1) / 2 + c + 1])
            max_path[r * (r - 1) / 2 + c] = tri_array[r * (r - 1) / 2 + c] + max_child
    return max(max_path)

def triangle_to_array(triangle):
    """ Converts the string provided into an array of ints."""
    nodes = list(triangle.split("\n"))
    depth, row, tri_array  = 15, 0, []
    for node in nodes:
        integer, col  = node.split(" "), 0
        row += 1
        for elt in integer:
            elt = int(elt)
            tri_array.append(elt)
            col += 1
    return get_max_path(tri_array, depth)

def main():
    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"""
    print triangle_to_array(triangle)
    
if __name__ == "__main__":
    main()