\c@sdZddlZdjddgZdddd d gZd Zdddd Zdddd Z ddZ ddZ dS(s Compute the shortest paths and path lengths between nodes in the graph. These algorithms work with undirected and directed graphs. For directed graphs the paths can be computed in the reverse order by first flipping the edge orientation using R=G.reverse(copy=False). iNs s%Aric Hagberg s+Sérgio Nery Simões t shortest_pathtall_shortest_pathstshortest_path_lengthtaverage_shortest_path_lengththas_pathcCs5ytj|||}Wntjk r0tSXtS(sReturn True if G has a path from source to target, False otherwise. Parameters ---------- G : NetworkX graph source : node Starting node for path target : node Ending node for path (tnxRtNetworkXNoPathtFalsetTrue(tGtsourcettargettsp((sb/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/generic.pyRs cCs|dkr`|dkrN|dkr6tj|}q]tj|d|}qtjdn|dkr|dkrtj||}qtj||d|}n<|dkrtj|||}ntj||||}|S(sCompute shortest paths in the graph. Parameters ---------- G : NetworkX graph source : node, optional Starting node for path. If not specified compute shortest paths for all connected node pairs. target : node, optional Ending node for path. If not specified compute shortest paths for every node reachable from the source. weight : None or string, optional (default = None) If None, every edge has weight/distance/cost 1. If a string, use this edge attribute as the edge weight. Any edge attribute not present defaults to 1. Returns ------- path: list or dictionary If the source and target are both specified return a single list of nodes in a shortest path. If only the source is specified return a dictionary keyed by targets with a list of nodes in a shortest path. If neither the source or target is specified return a dictionary of dictionaries with path[source][target]=[list of nodes in path]. Examples -------- >>> G=nx.path_graph(5) >>> print(nx.shortest_path(G,source=0,target=4)) [0, 1, 2, 3, 4] >>> p=nx.shortest_path(G,source=0) # target not specified >>> p[4] [0, 1, 2, 3, 4] >>> p=nx.shortest_path(G) # source,target not specified >>> p[0][4] [0, 1, 2, 3, 4] Notes ----- There may be more than one shortest path between a source and target. This returns only one of them. For digraphs this returns a shortest directed path. To find paths in the reverse direction first use G.reverse(copy=False) to flip the edge orientation. See Also -------- all_pairs_shortest_path() all_pairs_dijkstra_path() single_source_shortest_path() single_source_dijkstra_path() tweights%Target given but no source specified.N( tNoneRtall_pairs_shortest_pathtall_pairs_dijkstra_patht NetworkXErrortsingle_source_shortest_pathtsingle_source_dijkstra_pathtbidirectional_shortest_patht dijkstra_path(R R R R tpaths((sb/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/generic.pyR+s;       cCs|dkr`|dkrN|dkr6tj|}q]tj|d|}qtjdn|dkr|dkrtj||}qtj||d|}nL|dkrtj|||}t|d}ntj ||||}|S(sCompute shortest path lengths in the graph. This function can compute the single source shortest path lengths by specifying only the source or all pairs shortest path lengths by specifying neither the source or target. Parameters ---------- G : NetworkX graph source : node, optional Starting node for path. If not specified compute shortest path lengths for all connected node pairs. target : node, optional Ending node for path. If not specified compute shortest path lengths for every node reachable from the source. weight : None or string, optional (default = None) If None, every edge has weight/distance/cost 1. If a string, use this edge attribute as the edge weight. Any edge attribute not present defaults to 1. Returns ------- length : number, or container of numbers If the source and target are both specified return a single number for the shortest path. If only the source is specified return a dictionary keyed by targets with a the shortest path as keys. If neither the source or target is specified return a dictionary of dictionaries with length[source][target]=value. Raises ------ NetworkXNoPath If no path exists between source and target. Examples -------- >>> G=nx.path_graph(5) >>> print(nx.shortest_path_length(G,source=0,target=4)) 4 >>> p=nx.shortest_path_length(G,source=0) # target not specified >>> p[4] 4 >>> p=nx.shortest_path_length(G) # source,target not specified >>> p[0][4] 4 Notes ----- For digraphs this returns the shortest directed path. To find path lengths in the reverse direction use G.reverse(copy=False) first to flip the edge orientation. See Also -------- all_pairs_shortest_path_length() all_pairs_dijkstra_path_length() single_source_shortest_path_length() single_source_dijkstra_path_length() R s%Target given but no source specified.iN( RRtall_pairs_shortest_path_lengthtall_pairs_dijkstra_path_lengthRt"single_source_shortest_path_lengtht"single_source_dijkstra_path_lengthRtlentdijkstra_path_length(R R R R Rtp((sb/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/generic.pyRsC      cCs|jr0tj|sQtjdqQn!tj|sQtjdnd}|dkrxx|D].}tj||}|t|j7}qjWn?x<|D]4}tj ||d|}|t|j7}qWt |}|||dS(sReturn the average shortest path length. The average shortest path length is .. math:: a =\sum_{s,t \in V} \frac{d(s, t)}{n(n-1)} where `V` is the set of nodes in `G`, `d(s, t)` is the shortest path from `s` to `t`, and `n` is the number of nodes in `G`. Parameters ---------- G : NetworkX graph weight : None or string, optional (default = None) If None, every edge has weight/distance/cost 1. If a string, use this edge attribute as the edge weight. Any edge attribute not present defaults to 1. Raises ------ NetworkXError: if the graph is not connected. Examples -------- >>> G=nx.path_graph(5) >>> print(nx.average_shortest_path_length(G)) 2.0 For disconnected graphs you can compute the average shortest path length for each component: >>> G=nx.Graph([(1,2),(3,4)]) >>> for g in nx.connected_component_subgraphs(G): ... print(nx.average_shortest_path_length(g)) 1.0 1.0 sGraph is not connected.gR iN( t is_directedRtis_weakly_connectedRt is_connectedRRtsumtvaluesRR(R R tavgtnodet path_lengthtn((sb/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/generic.pyRs*     c cs^|dk r-tj||d|\}}ntj||}||krZtjn|dgg}d}x|dkrY||\}} ||krgt||d D]\} } | ^qVnt||| kr4|d7}|t|kr|j||| dgqV||| dg||>> G=nx.Graph() >>> G.add_path([0,1,2]) >>> G.add_path([0,10,2]) >>> print([p for p in nx.all_shortest_paths(G,source=0,target=2)]) [[0, 1, 2], [0, 10, 2]] Notes ----- There may be many shortest paths between the source and target. See Also -------- shortest_path() single_source_shortest_path() all_pairs_shortest_path() R iiN(RRt!dijkstra_predecessor_and_distancet predecessorRtreversedRtappend( R R R R tpredtdisttstackttopR$tiRR&((sb/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/generic.pyRs$) !  / ( t__doc__tnetworkxRtjoint __author__t__all__RRRRRR(((sb/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/generic.pyt s     T[ =