Euler program (python) problem 18

Maximum Path Sum Iproblem 18

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top t O 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 is only 16384 routes, it's possible to solve this problem by trying every route. However, problem, is the same challenge with a triangle containing one-hundred rows; It cannot is solved by brute force, and requires a clever method! ; o)

Python Code:

import Math
SQRT=MATH.SQRT


a=[ 75,95,64,17,47,82,18,35,87,10,20,4,82,47,65,19,1,23,75,3,34,88,2,77,73,7,63,67,99,65,4,28,6,16,70,92,41,41,26,56,83,40,80 , 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 , 14,91,43,58,50,27,29,48,63,66,4,68,89,53,67,30,73,16,69,87,40,31,4,62,98,27,23,9,70,98,73,93,38,53,60,4,23]
K=len (a)
def func (x):
    Sun=getsun (x)
    If sun[1]<k:
        Return A[x]+max (func (Sun[0]), func (Sun[1]))
    Else:
        return a[x]
dict={ };
def getsun (x):
    redult=[];
    K=int ((sqrt (1+8*x) 1)/2) +1
    return [x+k,x+k+1]


Print (func (0))

Time:<1s

Euler program (python) problem 18