mirror of
https://github.com/correl/euler.git
synced 2024-11-30 11:09:52 +00:00
131 lines
4.3 KiB
Python
131 lines
4.3 KiB
Python
"""Find the maximum sum travelling from the top of the triangle to the base.
|
|
|
|
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)
|
|
"""
|
|
|
|
from e012 import triangle
|
|
|
|
class Vertex:
|
|
"""Holds information on each vertex in the triangle
|
|
|
|
The weight represents the weight of any edge between an adjacent vertex and
|
|
this one
|
|
"""
|
|
def __init__(self, value):
|
|
self.value = value
|
|
self.weight = 100 - self.value
|
|
self.min_distance = float('+inf')
|
|
self.previous_vertex = None
|
|
self.adjacent = []
|
|
def add_adjacent(self, vertex):
|
|
self.adjacent.append(vertex)
|
|
def __cmp__(self, other):
|
|
return cmp(self.min_distance, other.min_distance)
|
|
def __repr__(self):
|
|
return '{0} ({1})'.format(self.value, [a.value for a in self.adjacent])
|
|
|
|
class Triangle:
|
|
def __init__(self, vertex_data):
|
|
self.vertices = []
|
|
i = 0
|
|
row = 1
|
|
for v in vertex_data:
|
|
if (i >= triangle(row)):
|
|
row = row + 1
|
|
vertex = Vertex(v)
|
|
if row > 1:
|
|
# Find upwards adjacent vertices
|
|
above_row = self.vertices[triangle(row - 2):triangle(row - 1)]
|
|
total_this_row = triangle(row) - triangle(row - 1)
|
|
pos = i - triangle(row - 1) + 1
|
|
start = int((pos / float(total_this_row)) * len(above_row)) - 1
|
|
end = int(((pos + 1) / float(total_this_row)) * len(above_row))
|
|
adjacent = above_row[start if start >= 0 else 0:end]
|
|
for a in adjacent:
|
|
vertex.add_adjacent(a)
|
|
self.vertices.append(vertex)
|
|
i = i + 1
|
|
self.rows = row
|
|
if len(self.vertices) != triangle(self.rows):
|
|
raise Exception('Invalid vertex set')
|
|
def find_path(self):
|
|
"""Implementation of Dijkstra's algorithm"""
|
|
|
|
# Reset vertice info
|
|
for v in self.vertices:
|
|
v.min_distance = float('+inf')
|
|
v.previous_vertex = None
|
|
orig = Vertex(100)
|
|
orig.min_distance = 0
|
|
adjacent = self.vertices[triangle(self.rows - 1):]
|
|
for a in adjacent:
|
|
orig.add_adjacent(a)
|
|
Q = [orig] + [v for v in self.vertices]
|
|
while len(Q) > 0:
|
|
u = min(Q)
|
|
if u.min_distance == float('+inf'):
|
|
return False
|
|
Q.remove(u)
|
|
for v in u.adjacent:
|
|
distance = u.min_distance + v.weight
|
|
if distance < v.min_distance:
|
|
v.min_distance = distance
|
|
v.previous_vertex = u
|
|
return True
|
|
def get_path(self):
|
|
"""Returns the found path as a list of vertices, from the top of the
|
|
triangle to the bottom
|
|
"""
|
|
|
|
v = self.vertices[0]
|
|
path = [v]
|
|
for i in range(self.rows - 1):
|
|
v = v.previous_vertex
|
|
if not v:
|
|
raise Exception('Missing or incomplete path!')
|
|
path.append(v)
|
|
return path
|
|
|
|
def main():
|
|
vertex_data = []
|
|
with open('p018/triangle.txt', 'r') as f:
|
|
while True:
|
|
line = f.readline()
|
|
if not line:
|
|
break
|
|
vertex_data = vertex_data + [int(v) for v in line.split(' ')]
|
|
t = Triangle(vertex_data)
|
|
t.find_path()
|
|
path = t.get_path()
|
|
print 'Path', [v.value for v in path]
|
|
print 'Sum', sum([v.value for v in path])
|
|
|
|
if __name__ == '__main__':
|
|
main()
|