#Maximum path sum II
#Problem 67
#
#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 in triangle.txt (right click and 
#'Save Link/Target As...'), a 15K text file containing a triangle with
#one-hundred rows.
#
#NOTE: This is a much more difficult version of Problem 18. It is not possible
#to try every route to solve this problem, as there are 299 altogether! If you
#could check one trillion (1012) routes every second it would take over twenty
#billion years to check them all. There is an efficient algorithm to solve it. ;o)

f = open( "p067_triangle.txt", "r" )
a = [[ int(n) for n in line.split(' ') ] for line in f]

for i in reversed(range(0,len(a)-1)):
    for j in range(0,len(a[i])):
        a[i][j] += max(a[i+1][j],a[i+1][j+1])


print(a[0][0])



