018.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

#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:

#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

DATA = '''
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
'''
DATA = list(map(int, DATA.split()))

start = 1
size = 2
pool = DATA[:]
while start < len(DATA):
    for i in range(start+1, start+size-1):
        pool[i] += max(pool[i-size], pool[i-size+1])
    pool[start] += pool[start-size+1]
    pool[start+size-1] += pool[start-1]
    start += size
    size += 1
print(max(pool[len(pool)-size+1:]))