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
Run this solution at repl.io
here.
#----INPUT DATA INTO A bottom left diagonal matrix----
with open("data.txt") as txtfile:
data = txtfile.read()
temp = [line.split(" ") for line in data.splitlines()]
mat = [[int(i) for i in line] for line in temp]
#create a 15 x 15 matrix with zeros for empty elements
for line in mat:
length = len(line)
line.extend((15-length)*[0])
"""Concept: look at the 2nd last row, and sum together the
largest element either directly below or below and 1 to the right.
By following the path upwards we can guarantee a maximum path sum with minimal steps.
"""
#the depth of the triangle
tridepth = 15
#repeat process 13 times
for x in range(0,tridepth-1):
i = 0 #re-initialise row index
j = 0 #re-initialise column index
#for each number in the current 2nd last row
for elem in mat[-2]:
if elem != 0:
#check each element below and to the direct
#right of elem in the 2nd last row
m = max(mat[-1][j],mat[-1][j+1])
#store the sum in the matrix
mat[-2][i] = elem + m
i += 1
j += 1
#remove (slice) the final row from the current matrix
mat = mat[:-1]
answer = mat[0][0]
print(answer)