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- Committer: Aaron Bentley
- Date: 2005-09-10 23:15:33 UTC
- mto: (1185.3.4)
- mto: This revision was merged to the branch mainline in revision 1390.
- Revision ID: aaron.bentley@utoronto.ca-20050910231533-e3860a46890c2c71
Cleanup and test-fixing
added
removed
bzrlib/graph.py
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# Dijkstra's algorithm for shortest paths
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# David Eppstein, UC Irvine, 4 April 2002
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# http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/117228
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from priodict import priorityDictionary
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def dijkstra(G,start,end=None):
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"""
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Find shortest paths from the start vertex to all
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vertices nearer than or equal to the end.
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The input graph G is assumed to have the following
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representation: A vertex can be any object that can
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be used as an index into a dictionary. G is a
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dictionary, indexed by vertices. For any vertex v,
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G[v] is itself a dictionary, indexed by the neighbors
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of v. For any edge v->w, G[v][w] is the length of
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the edge. This is related to the representation in
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<http://www.python.org/doc/essays/graphs.html>
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where Guido van Rossum suggests representing graphs
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as dictionaries mapping vertices to lists of neighbors,
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however dictionaries of edges have many advantages
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over lists: they can store extra information (here,
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the lengths), they support fast existence tests,
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and they allow easy modification of the graph by edge
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insertion and removal. Such modifications are not
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needed here but are important in other graph algorithms.
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Since dictionaries obey iterator protocol, a graph
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represented as described here could be handed without
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modification to an algorithm using Guido's representation.
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Of course, G and G[v] need not be Python dict objects;
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they can be any other object that obeys dict protocol,
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for instance a wrapper in which vertices are URLs
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and a call to G[v] loads the web page and finds its links.
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The output is a pair (D,P) where D[v] is the distance
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from start to v and P[v] is the predecessor of v along
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the shortest path from s to v.
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Dijkstra's algorithm is only guaranteed to work correctly
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when all edge lengths are positive. This code does not
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verify this property for all edges (only the edges seen
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before the end vertex is reached), but will correctly
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compute shortest paths even for some graphs with negative
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edges, and will raise an exception if it discovers that
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a negative edge has caused it to make a mistake.
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"""
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D = {} # dictionary of final distances
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P = {} # dictionary of predecessors
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Q = priorityDictionary() # est.dist. of non-final vert.
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Q[start] = 0
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for v in Q:
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D[v] = Q[v]
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if v == end: break
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for w in G[v]:
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vwLength = D[v] + G[v][w]
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if w in D:
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if vwLength < D[w]:
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raise ValueError, \
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"Dijkstra: found better path to already-final vertex"
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elif w not in Q or vwLength < Q[w]:
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Q[w] = vwLength
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P[w] = v
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return (D,P)
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def shortest_path(G,start, end):
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"""
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Find a single shortest path from the given start vertex
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to the given end vertex.
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The input has the same conventions as Dijkstra().
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The output is a list of the vertices in order along
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the shortest path.
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"""
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D,P = dijkstra(G,start,end)
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print D,P
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Path = []
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while 1:
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Path.append(end)
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if end == start: break
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end = P[end]
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Path.reverse()
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return Path
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def closest(distances, pending):
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closest = None
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for node in pending:
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distance = distances[node]
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if distance is None:
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continue
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if closest is None or distance < closest[1]:
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closest = (node, distance)
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return closest[0]
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def relax(node, distances, graph):
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for child in graph[node]:
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new_distance = distances[node] + graph[node][child]
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if distances[child] is None or distances[child] < new_distance:
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print "setting %s to %d, from %s(%d)" % (child, new_distance, node,
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distances[node])
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distances[child] = new_distance
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def farthest_node(graph, start):
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done = set()
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distances = {}
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pending = set(graph.keys())
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for node in graph:
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distances[node] = None
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distances[start] = 0
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while len(done) < len(distances):
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node = closest(distances, pending)
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done.add(node)
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pending.remove(node)
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relax(node, distances, graph)
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print distances
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distfirst = [(d, n) for n, d in distances.iteritems()]
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return distfirst[-1][1]
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def farthest_nodes_ab(graph, start):
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lines = [start]
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predecessors = {}
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endpoints = {}
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while len(lines) > 0:
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new_lines = set()
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for line in lines:
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for child in graph[line]:
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if child not in predecessors:
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new_lines.add(child)
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predecessors[child] = line
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else:
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endpoints[line] = None
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lines = new_lines
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distances = []
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for endpoint in endpoints:
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path = []
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node = endpoint
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while node != start:
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path.append(node)
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node = predecessors[node]
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distances.append((len(path), endpoint))
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distances.sort(reverse=True)
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return [d[1] for d in distances]
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def max_distance(node, ancestors, distances):
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"""Calculate the max distance to an ancestor. Return None if"""
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best = None
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best = distances[node]
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for ancestor in ancestors[node]:
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if ancestor not in ancestors:
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print ancestor
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continue
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if ancestor not in distances:
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return None
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def farthest_node(graph, ancestors, start):
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assert 'A' in graph
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distances = {start: 0}
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lines = set([start])
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while len(lines) > 0:
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