-
Notifications
You must be signed in to change notification settings - Fork 0
/
Problem018.py
executable file
·85 lines (75 loc) · 2.6 KB
/
Problem018.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
#!/usr/bin/python3
#coding:utf8
# http://projecteuler.net/problem=18
#
# PROBLEM CONTENT:
# 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
#
# 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)
# EXPLANATION:
# Work from the bottom up, converting each node in the maximum 'score' one
# could get if decided to pick that node.
# From a row of N elements, generate a row of N-1 elements by choosing the
# greatest of two adjacent numbers. The nth entry of this new row is the value
# of the highest scoring node the nth node from the row on top could pick. We
# can then sum the new row to the one of top and iteratively repeat the process
# until we get to the top.
import time
def initialise():
with open('Problem018.data') as triangleFile:
lines = triangleFile.readlines()
triangle = []
for line in lines:
tmpList = line.split()
# Parse str to int
triangle.append(list(map(int, tmpList)))
return triangle
def main():
triangle = initialise()
for index, row in reversed(list(enumerate(triangle))):
# From row of N elements generate a row of N-1 elements by choosing the
# greatest of two adjacent numbers.
newRow = []
if len(row) == 1:
newRow.append(row[0])
else:
for i in range(0, len(row)-1):
newRow.append(max(row[i], row[i+1]))
# Sum it to the previous row and repeat the process
if (index != 0):
for i in range(0, len(newRow)):
triangle[index-1][i] += newRow[i]
print(triangle[0])
if __name__ == '__main__':
start = time.time()
main()
elapsed = time.time() - start
print('Solved in %.2f seconds' % elapsed)