# -*- coding: utf-8 -*-
# Copyright (C) 2004-2019 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
#
# Authors: Salim Fadhley <salimfadhley@gmail.com>
# Matteo Dell'Amico <matteodellamico@gmail.com>
"""Shortest paths and path lengths using the A* ("A star") algorithm.
"""
from heapq import heappush, heappop
from itertools import count
import networkx as nx
from networkx.utils import not_implemented_for
__all__ = ['astar_path', 'astar_path_length']
[docs]@not_implemented_for('multigraph')
def astar_path(G, source, target, heuristic=None, weight='weight'):
"""Returns a list of nodes in a shortest path between source and target
using the A* ("A-star") algorithm.
There may be more than one shortest path. This returns only one.
Parameters
----------
G : NetworkX graph
source : node
Starting node for path
target : node
Ending node for path
heuristic : function
A function to evaluate the estimate of the distance
from the a node to the target. The function takes
two nodes arguments and must return a number.
weight: string, optional (default='weight')
Edge data key corresponding to the edge weight.
Raises
------
NetworkXNoPath
If no path exists between source and target.
Examples
--------
>>> G = nx.path_graph(5)
>>> print(nx.astar_path(G, 0, 4))
[0, 1, 2, 3, 4]
>>> G = nx.grid_graph(dim=[3, 3]) # nodes are two-tuples (x,y)
>>> nx.set_edge_attributes(G, {e: e[1][0]*2 for e in G.edges()}, 'cost')
>>> def dist(a, b):
... (x1, y1) = a
... (x2, y2) = b
... return ((x1 - x2) ** 2 + (y1 - y2) ** 2) ** 0.5
>>> print(nx.astar_path(G, (0, 0), (2, 2), heuristic=dist, weight='cost'))
[(0, 0), (0, 1), (0, 2), (1, 2), (2, 2)]
See Also
--------
shortest_path, dijkstra_path
"""
if source not in G or target not in G:
msg = 'Either source {} or target {} is not in G'
raise nx.NodeNotFound(msg.format(source, target))
if heuristic is None:
# The default heuristic is h=0 - same as Dijkstra's algorithm
def heuristic(u, v):
return 0
push = heappush
pop = heappop
# The queue stores priority, node, cost to reach, and parent.
# Uses Python heapq to keep in priority order.
# Add a counter to the queue to prevent the underlying heap from
# attempting to compare the nodes themselves. The hash breaks ties in the
# priority and is guaranteed unique for all nodes in the graph.
c = count()
queue = [(0, next(c), source, 0, None)]
# Maps enqueued nodes to distance of discovered paths and the
# computed heuristics to target. We avoid computing the heuristics
# more than once and inserting the node into the queue too many times.
enqueued = {}
# Maps explored nodes to parent closest to the source.
explored = {}
while queue:
# Pop the smallest item from queue.
_, __, curnode, dist, parent = pop(queue)
if curnode == target:
path = [curnode]
node = parent
while node is not None:
path.append(node)
node = explored[node]
path.reverse()
return path
if curnode in explored:
continue
explored[curnode] = parent
for neighbor, w in G[curnode].items():
if neighbor in explored:
continue
ncost = dist + w.get(weight, 1)
if neighbor in enqueued:
qcost, h = enqueued[neighbor]
# if qcost <= ncost, a less costly path from the
# neighbor to the source was already determined.
# Therefore, we won't attempt to push this neighbor
# to the queue
if qcost <= ncost:
continue
else:
h = heuristic(neighbor, target)
enqueued[neighbor] = ncost, h
push(queue, (ncost + h, next(c), neighbor, ncost, curnode))
raise nx.NetworkXNoPath("Node %s not reachable from %s" % (source, target))
[docs]def astar_path_length(G, source, target, heuristic=None, weight='weight'):
"""Returns the length of the shortest path between source and target using
the A* ("A-star") algorithm.
Parameters
----------
G : NetworkX graph
source : node
Starting node for path
target : node
Ending node for path
heuristic : function
A function to evaluate the estimate of the distance
from the a node to the target. The function takes
two nodes arguments and must return a number.
Raises
------
NetworkXNoPath
If no path exists between source and target.
See Also
--------
astar_path
"""
if source not in G or target not in G:
msg = 'Either source {} or target {} is not in G'
raise nx.NodeNotFound(msg.format(source, target))
path = astar_path(G, source, target, heuristic, weight)
return sum(G[u][v].get(weight, 1) for u, v in zip(path[:-1], path[1:]))