When moving from the apex of the following triangle to the bottom, the maximum sum of the numbers is 23.
3 7 4 2 4 6 8 5 9 3 In this example 3 + 7 + 4 + 9 = 23.
When moving the following triangle from the apex to the bottom, find the maximum sum. (Omitted) Note: There are at most 16384 routes here, so you can try all the patterns. Problem 67 is the same problem, but with 100 lines, it can't be brute-forced. We need a smarter way. http://odz.sakura.ne.jp/projecteuler/index.php?cmd=read&page=Problem%2018
It's annoying, so I ended it with recursion.
def get_next_max(i,j,L1,L2):
if L2[i][j] == 0:
if i == len(L1)-1:
L2[i][j] = L1[i][j]
else:
L2[i][j] = L1[i][j] + max(get_next_max(i+1,j,L1,L2),get_next_max(i+1,j+1,L1,L2))
return L2[i][j]
def main():
L1 = [
[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, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23]
]
L2 = [[0 for j in range(len(L1[i]))] for i in range(len(L1))]
ans = get_next_max(0,0,L1,L2)
#print ans
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