ProjectEuler/P018.py at master · mcleu/ProjectEuler · GitHub

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# -*- 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:
#
# 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)
#==============================================================================

import numpy as np

TrigRaw = '''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'''

#TrigRaw = '''3
#7 4
#2 4 6
#8 5 9 3'''

Trig = TrigRaw.split('\n')
length = len(Trig)
TrigA = np.zeros([length,length])

ii, jj = 0, 0
for Vector in Trig:
    jj = 00
    Line = Vector.split(' ')
    for Element in Line:
        TrigA[ii,jj] = int(Element)
        jj += 1
    ii += 1

TrigS = np.zeros(np.shape(TrigA))


ii, jj = 0, 0
for Vector in TrigA:
    jj = 00
    for Element in Vector:
#        print Element, ii, jj
        if ii==0:
            TrigS[ii,jj] = TrigA[ii,jj]
        elif jj==0:
            TrigS[ii,jj] = TrigA[ii,jj] + TrigS[ii-1,jj]
        else:
            TrigS[ii,jj] = TrigA[ii,jj] + max([TrigS[ii-1,jj-1], TrigS[ii-1,jj]])
        jj += 1
    ii += 1

#print TrigS[-1]
print max(TrigS[-1])
#1074