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A* routing for a connection graph of Yorckstraße
"""An implementation of the A* searching algorithm.
dyoo@hkn.eecs.berkeley.edu
I got so disgusted at my previous attempt at A*, so here I go again.
Hopefully this version will be easier on the eyes.
A* is a search algorithm that's similar to Dijkstra's algorithm: given
a graph, a start node, and a goal, A* will search for the shortest
path toward the goal.
To help it get there faster, we can provide a heuristic that evaluates
how far we are from that goal. With a good heuristic, finding an
optimal solution takes MUCH less time.
The main function that one would use is aStar(). Take a look at
_testAStar() to see how it's used.
This code is under MIT license.
The MIT License
Copyright (c) 2008 Danny Yoo
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
from priorityqueue import PriorityQueue
def aStar(start, goal, neighbor_func, distance_func, heuristic_func):
"""Returns a sequence of nodes that optmizes for the least cost
from the start node to the goal.
Let's describe the data that we pass to this function:
start: the start of the search.
goal: the goal of the search.
neighbor_func: a function that, given a state, returns a list of
neighboring states.
distance_func: a function that takes two nodes, and returns
the distance between them.
heuristic_func: a function that takes two nodes, and returns
the heuristic distance between them.
Each state mush be hashable --- each state must support the
hash() function.
"""
pqueue = PriorityQueue()
g_costs = {start : 1}
parents = {start : start}
pqueue.push(heuristic_func(start, goal), start)
while not pqueue.isEmpty():
next_cost, next_node = pqueue.pop()
g_costs[next_node] = g_costs[parents[next_node]] \
+ distance_func(next_node, parents[next_node])
if next_node == goal: break
children = neighbor_func(next_node)
for child in children:
updateChild(goal, distance_func, heuristic_func,
child, next_node, parents, g_costs, pqueue)
return getPathToGoal(start, goal, parents)
def updateChild(goal, distance_func, heuristic_func,
child, next_node, parents, g_costs, pqueue):
"""Appropriately update the parents, g_costs, and pqueue structures.
This is a helper function, since aStar() was getting a bit bulky."""
if g_costs.has_key(child): return
f = g_costs[next_node] + distance_func(next_node, child) \
+ heuristic_func(child, goal)
if pqueue.push(f, child):
parents[child] = next_node
def getPathToGoal(start, goal, parents):
"""Given the hash of parental links, follow back and return the
chain of ancestors."""
try:
results = []
while goal != start:
results.append(goal)
goal = parents[goal]
results.append(start)
results.reverse()
return results
except KeyError: return []
def _testGetPathToGoal():
parents = { 1 : 2,
2 : 3,
3 : 4,
4 : 5 }
goal = 1
print getPathToGoal(goal, parents)
######################################################################
### The rest of this is implementation scaffolding and test stuff.
### Take a look at it to see how to use this implementation.
######################################################################
class _DistanceDictWrapper:
"""_DistanceDictWrapper is a class wrapper over a dictionary of
(node1,node2) to distances. It's set up to make a dictionary look
like a callable function. Futhermore, it assumes that distance is
transitive, so that finding __call__(node1, node2) is the same as
__call__(node2, node1)."""
def __init__(self, dict):
self.dict = dict
def __call__(self, m, n):
"""Return the distance between m and n.
Since distance is symmetric, we'll try from m->n, or n->m"""
if m == n: return 0
if self.dict.has_key((m, n)):
return self.dict[(m, n)]
if self.dict.has_key((n, m)):
return self.dict[(n, m)]
return None
class _Neighbor:
"""A quicky class that lets us get the neighbors of a graph,
given a distance function, and a list of all nodes."""
def __init__(self, nodes, dist_func):
self.nodes = nodes
self.dist_func = dist_func
def __call__(self, node):
"""Return the neighbors of a node."""
results = []
for n in self.nodes:
## if n == node: continue # superfluous, since zero
## # is a false value
if self.dist_func(n, node): results.append(n)
return results
def _testAStar():
"""Given the graph:
3 1
/-----b----\
a |1 d
\-----c----/
1 2
I do a few tests to make sure that A* looks like it works ok.
Note: as of now, I don't have a heuristic function set up ---
basically, I'm testing to make sure that it works as Dijkstra's
algorithm. If you want to see the heuristic stuff in action, see
eight_puzzle.py.
"""
# There might be better suited A* algorithms (and representations for this)
# http://scriptogr.am/jdp/post/pathfinding-with-python-graphs-and-a-star
# http://brandon.sternefamily.net/files/astar.txt
# https://hkn.eecs.berkeley.edu/~dyoo/python/astar/a_star_search_2.py
# https://gist.github.com/1687840#file_astar.py
# http://stackoverflow.com/questions/4159331/python-speed-up-an-a-star-pathfinding-algorithm
# Or we could use the GPS coordinates as grid coordinates
# http://stackoverflow.com/questions/4159331/python-speed-up-an-a-star-pathfinding-algorithm
# https://github.com/elemel/python-astar/blob/master/src/astar_demo.py
# https://www.google.com/fusiontables/embedviz?viz=MAP&q=select+col7+from+1yHx-9xRpcVU5B4oboTfiSSR4y8so6cV1zAALoU0&h=false&lat=52.49216510989638&lng=13.370220703651414&z=17&t=1&l=col7&y=2&tmplt=3
dist_func = _DistanceDictWrapper({('GG', 'S1NordS') : 100, ('S1NordS', 'S1NordN') : 0,
('S1NordS', 'U7S') : 20, ('S1NordN', 'U7N') : 20,
('S1NordN', 'S1NordS'): 20, ('U7N', 'U7N2'): 40,
('U7S', 'S25') : 50, ('U7N2', 'S25'): 20,
('U7N2', 'S25'): 20
})
nodes = ['GG', 'S1NordS', 'S1NordN', 'U7N', 'U7S', 'U7N2', 'S25']
neighbor_func = _Neighbor(nodes, dist_func)
null_heuristic = lambda x, y: 0
print "neighbors of S1NordS", neighbor_func('S1NordS')
print "path from GG to U7S"
print aStar('GG', 'U7S', neighbor_func, dist_func, null_heuristic)
print "path from GG to S25"
print aStar('GG', 'S25', neighbor_func, dist_func, null_heuristic)
if __name__ == '__main__':
_testAStar()
neighbors of S1NordS ['GG', 'S1NordN', 'U7S']
path from GG to U7S
['GG', 'S1NordS', 'U7S']
path from GG to S25
['GG', 'S1NordS', 'U7S', 'S25']
[Finished in 0.1s]
GG = Großgörchenstraße
S1NordS = S1 North Exit South of the road
S1NordN = S1 North Exit North of the road
U7S = U7 entrance South of the road
etc.
"""priorityqueue.py --- a simple priority queue.
dyoo@hkn.eecs.berkeley.edu
A simple implementation of a priority queue. It's not pretty, nor is
it that efficient. Still, it's usable, and I know that I can improve
it by using an array heap later."""
class PriorityQueue:
def __init__(self):
self.values = []
def __len__(self):
"""Return the number of elements in the queue."""
return len(self.values)
def push(self, priority, value):
"""Add an element to the queue.
Only add if the value doesn't already exist in the queue, or
if the priority is smaller than the one existing in the queue.
If addition is successful, then return 1. Else, return 0."""
search_result = self._find(value)
if search_result and search_result[0] <= priority:
return 0
elif search_result:
del self.values[self.values.index(search_result)]
self.values.append((priority, value))
self.values.sort(_psort)
return 1
def pop(self):
"""Return the element with the smallest priority."""
assert not self.isEmpty()
priority, value = self.values[0]
del self.values[0]
return (priority, value)
def isEmpty(self):
"""return 1 if the queue is empty, 0 otherwise."""
return len(self.values) == 0
def _find(self, value):
"""Helper function to see if a value already exists in the queue."""
for (p, v) in self.values:
if value == v: return (p, v)
return None
def _psort(x, y):
return cmp(x[0], y[0])
def _test():
"""We expect to see:
(1, 'd')
(5, 'a')
(12, 'b')
(14, 'c')
"""
x = PriorityQueue()
data = [(10, 'a'), (12, 'b'), (14, 'c'), (5, 'a'), (1, 'd')]
for p, v in data:
x.push(p, v)
while not x.isEmpty():
print x.pop()
if __name__ == '__main__': _test()
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