## Question

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)

parse :: String -> [[Integer]]
parse = map (map read . words) . lines

best :: [Integer] -> [Integer]
best row = map maximum choices where
choices = zipWith (\a b -> a : [b]) row (tail row)

maxStep :: [Integer] -> [Integer] -> [Integer]
maxStep current next = zipWith (+) next (best current)

maxPath :: [[Integer]] -> Integer
maxPath [[x]] = x
maxPath (current:next:rest) = maxPath $(maxStep current next) : rest main :: IO () main = do str <- readFile "/home/zach/code/euler/018/triangle.txt" print$ maxPath $reverse$ parse str
$ghc -O2 -o max-route max-route.hs$ time ./max-route
real   0m0.002s
user   0m0.000s
sys    0m0.000s

## Python

#!/usr/bin/env python
def find_sum(triangle):
def get_options(row, index):
return triangle[row+1][index], triangle[row+1][index+1]
row = len(triangle) - 2
while True:
try:
for index, node in enumerate(triangle[row]):
best = max([node + option for option in get_options(row, index)])
triangle[row][index] = best
row -= 1
except:
return triangle[0][0]

def main():
triangle_str = '''\
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'''

triangle = [[int(digit) for digit in line.strip().split()] for line in triangle_str.splitlines()]
print(find_sum(triangle))

if __name__ == "__main__":
main()
$time python3 triangle-max.py real 0m0.020s user 0m0.012s sys 0m0.004s ## Ruby #!/usr/bin/env ruby triangle_str = <<EOS 75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 EOS triangle = triangle_str.each_line.map { |line| line.split.map(&:to_i) } (triangle.length - 2).downto(0) do |y| triangle[y].length.times do |x| triangle[y][x] += [triangle[y+1][x], triangle[y+1][x+1]].max end end puts triangle[0][0]$ time ruby max-route.rb
real   0m0.027s
user   0m0.024s
sys    0m0.000s

Questions? Comments? Send me an email: z@chdenton.com