ó ú£Õ\c @s dZdjdddgƒZddddd d d d d ddg ZddlZddlZddlmZdd„Z dd„Z ddd„Z ddd„Z dddd„Zddd„Zddd„Zddd„Zdd„Zdd„Zdd„ZdS(s. Shortest path algorithms for weighed graphs. s sAric Hagberg s'Loïc Séguin-C. s Dan Schult t dijkstra_pathtdijkstra_path_lengthtbidirectional_dijkstratsingle_source_dijkstratsingle_source_dijkstra_patht"single_source_dijkstra_path_lengthtall_pairs_dijkstra_pathtall_pairs_dijkstra_path_lengtht!dijkstra_predecessor_and_distancet bellman_fordtnegative_edge_cycleiÿÿÿÿN(tgenerate_unique_nodetweightcCs^t||d|d|ƒ\}}y ||SWn*tk rYtjd||fƒ‚nXdS(sReturns the shortest path from source to target in a weighted graph G. Parameters ---------- G : NetworkX graph source : node Starting node target : node Ending node weight: string, optional (default='weight') Edge data key corresponding to the edge weight Returns ------- path : list List of nodes in a shortest path. Raises ------ NetworkXNoPath If no path exists between source and target. Examples -------- >>> G=nx.path_graph(5) >>> print(nx.dijkstra_path(G,0,4)) [0, 1, 2, 3, 4] Notes ------ Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. See Also -------- bidirectional_dijkstra() ttargetR snode %s not reachable from %sN(RtKeyErrortnxtNetworkXNoPath(tGtsourceR R tlengthtpath((sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyRs )  cCsRt||d|ƒ}y ||SWn*tk rMtjd||fƒ‚nXdS(s.Returns the shortest path length from source to target in a weighted graph. Parameters ---------- G : NetworkX graph source : node label starting node for path target : node label ending node for path weight: string, optional (default='weight') Edge data key corresponding to the edge weight Returns ------- length : number Shortest path length. Raises ------ NetworkXNoPath If no path exists between source and target. Examples -------- >>> G=nx.path_graph(5) >>> print(nx.dijkstra_path_length(G,0,4)) 4 Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. See Also -------- bidirectional_dijkstra() R snode %s not reachable from %sN(RRRR(RRR R R((sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyROs *  cCst||d|ƒ\}}|S(s\Compute shortest path between source and all other reachable nodes for a weighted graph. Parameters ---------- G : NetworkX graph source : node Starting node for path. weight: string, optional (default='weight') Edge data key corresponding to the edge weight cutoff : integer or float, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- paths : dictionary Dictionary of shortest path lengths keyed by target. Examples -------- >>> G=nx.path_graph(5) >>> path=nx.single_source_dijkstra_path(G,0) >>> path[4] [0, 1, 2, 3, 4] Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. See Also -------- single_source_dijkstra() R (R(RRtcutoffR RR((sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyR€s'cs»i}id|6}g}tj|d|fƒx…|r¶tj|ƒ\}}||kr_q2n|||<|jƒrÛg} xs||jƒD]H\} } t‡fd†| jƒDƒƒ} | j| i| ˆ6fƒqŒWnt||jƒƒ} x¿| D]·\} } ||| jˆdƒ}|dk r?||kr?qøq?n| |krp||| kr¯t ddƒ‚q¯qø| |ksŒ||| krø||| >> G=nx.path_graph(5) >>> length=nx.single_source_dijkstra_path_length(G,0) >>> length[4] 4 >>> print(length) {0: 0, 1: 1, 2: 2, 3: 3, 4: 4} Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. See Also -------- single_source_dijkstra() ic3s'|]\}}|jˆdƒVqdS(iN(tget(t.0tktdd(R (sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pys ãsisContradictory paths found:snegative weights?N( theapqtheappushtheappopt is_multigraphtitemstmintappendtiterRtNonet ValueError(RRRR tdisttseentfringetdtvtedatatwtkeydatat minweighttedgedatatvw_dist((R sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyR«s:*     !     !cs||kr'id|6i|g|6fSi}i|g|6}id|6}g}tj|d|fƒxª|rtj|ƒ\} } | |kr–qin| || <| |kr°Pn|jƒr"g} xs|| jƒD]H\} } t‡fd†| jƒDƒƒ}| j| i|ˆ6fƒqÓWnt|| jƒƒ} xÔ| D]Ì\} }|| |jˆdƒ}|dk r†||kr†q?q†n| |kr·||| kr t ddƒ‚q q?| |ksÓ||| kr?||| >> G=nx.path_graph(5) >>> length,path=nx.single_source_dijkstra(G,0) >>> print(length[4]) 4 >>> print(length) {0: 0, 1: 1, 2: 2, 3: 3, 4: 4} >>> path[4] [0, 1, 2, 3, 4] Notes --------- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. Based on the Python cookbook recipe (119466) at http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/119466 This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems). See Also -------- single_source_dijkstra_path() single_source_dijkstra_path_length() ic3s'|]\}}|jˆdƒVqdS(iN(R(RRR(R (sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pys AsisContradictory paths found:snegative weights?N( RRRRRRR R!RR"R#(RRR RR R$tpathsR%R&R'R(R)R*R+R,R-R.((R sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyRøsF6       !      cstj}tj}i}ig|6}id|6}g} || d|fƒx°| rý|| ƒ\} } | |krxqNn| || <|jƒrôg} xs|| jƒD]H\} }t‡fd†|jƒDƒƒ}| j| i|ˆ6fƒq¥Wnt|| jƒƒ} xí| D]å\} }|| |jˆdƒ}|dk rX||krXqqXn| |kr‰||| kröt ddƒ‚qöq| |ks¥||| krÒ||| <|| || fƒ| g|| „sisContradictory paths found:snegative weights?N( RRRRRRR R!RR"R#(RRRR tpushtpopR$tpredR%R&R'R(R)R*R+R,R-R.((R sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyRWsF        !     cCs:i}x-|D]%}t||d|d|ƒ||>> G=nx.path_graph(5) >>> length=nx.all_pairs_dijkstra_path_length(G) >>> print(length[1][4]) 3 >>> length[1] {0: 1, 1: 0, 2: 1, 3: 2, 4: 3} Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. The dictionary returned only has keys for reachable node pairs. RR (R(RRR R/tn((sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyR›s " cCs:i}x-|D]%}t||d|d|ƒ||>> G=nx.path_graph(5) >>> path=nx.all_pairs_dijkstra_path(G) >>> print(path[0][4]) [0, 1, 2, 3, 4] Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. See Also -------- floyd_warshall() RR (R(RRR R/R3((sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyRÃs # csU||krtd|ƒ‚nt|ƒ}id|6}id|6}|dkr[||fS|jƒry‡fd†}n‡fd†}xÀt|ƒD]£}t}xŠt|jƒƒD]v\} } xg|| jƒD]U\} } | || ƒ} | |ks || | krÑ| || <| || >> import networkx as nx >>> G = nx.path_graph(5, create_using = nx.DiGraph()) >>> pred, dist = nx.bellman_ford(G, 0) >>> pred {0: None, 1: 0, 2: 1, 3: 2, 4: 3} >>> dist {0: 0, 1: 1, 2: 2, 3: 3, 4: 4} >>> from nose.tools import assert_raises >>> G = nx.cycle_graph(5, create_using = nx.DiGraph()) >>> G[1][2]['weight'] = -7 >>> assert_raises(nx.NetworkXUnbounded, nx.bellman_ford, G, 0) Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. The dictionaries returned only have keys for nodes reachable from the source. In the case where the (di)graph is not connected, if a component not containing the source contains a negative cost (di)cycle, it will not be detected. s!Node %s is not found in the graphiics/tg|jƒD]}|jˆdƒ^qƒS(Ni(RtvaluesR(t edge_dictteattr(R (sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyt get_weight5scs|jˆdƒS(Ni(R(R5(R (sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyR78ssNegative cost cycle detected.N( RtlenR"RtrangetTruetlistRtFalseRtNetworkXUnbounded(RRR t numb_nodesR$R2R7tit no_changestutdist_uR(tedicttdist_v((R sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyR ìs.>         cCsytƒ}|jg|D]}||f^qƒyt|||ƒWn"tjk rg|j|ƒtSX|j|ƒtS(s®Return True if there exists a negative edge cycle anywhere in G. Parameters ---------- G : NetworkX graph weight: string, optional (default='weight') Edge data key corresponding to the edge weight Returns ------- negative_cycle : bool True if a negative edge cycle exists, otherwise False. Examples -------- >>> import networkx as nx >>> G = nx.cycle_graph(5, create_using = nx.DiGraph()) >>> print(nx.negative_edge_cycle(G)) False >>> G[1][2]['weight'] = -7 >>> print(nx.negative_edge_cycle(G)) True Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. This algorithm uses bellman_ford() but finds negative cycles on any component by first adding a new node connected to every node, and starting bellman_ford on that node. It then removes that extra node. (R tadd_edges_fromR RR=t remove_nodeR:R<(RR tnewnodeR3((sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyR Ks# &  csž||krd|gfSiig}i|g|6i|g|6g}ggg}id|6id|6g}tj|dd|fƒtj|dd|fƒ|jƒrÀ|j|jg}n|j|jg}g} d} x |dr€|dr€d| } tj|| ƒ\} } | || kr.qán| || | <| |d| krZ| | fSx || | ƒD]}| dkrå|jƒr¶t‡fd†|| |j ƒDƒƒ}n|| |j ˆdƒ}|| | |}ne|jƒrt‡fd†||| j ƒDƒƒ}n||| j ˆdƒ}|| | |}||| kr€||| |kryt dƒ‚qyqk||| ks¤||| |krk||| |>> G=nx.path_graph(5) >>> length,path=nx.bidirectional_dijkstra(G,0,4) >>> print(length) 4 >>> print(path) [0, 1, 2, 3, 4] Notes ----- Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed. In practice bidirectional Dijkstra is much more than twice as fast as ordinary Dijkstra. Ordinary Dijkstra expands nodes in a sphere-like manner from the source. The radius of this sphere will eventually be the length of the shortest path. Bidirectional Dijkstra will expand nodes from both the source and the target, making two spheres of half this radius. Volume of the first sphere is pi*r*r while the others are 2*pi*r/2*r/2, making up half the volume. This algorithm is not guaranteed to work if edge weights are negative or are floating point numbers (overflows and roundoff errors can cause problems). See Also -------- shortest_path shortest_path_length iic3s'|]\}}|jˆdƒVqdS(iN(R(RRR(R (sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pys Þsc3s'|]\}}|jˆdƒVqdS(iN(R(RRR(R (sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pys åss,Contradictory paths found: negative weights?sNo path between %s and %s.N(RRt is_directedtsuccessors_itertpredecessors_itertneighbors_iterRRRRRR#treverseRR(RRR R tdistsR/R&R%tneighst finalpathtdirR$R(t finaldistR*R,tvwLengtht totaldisttrevpath((R sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyRzs`?          $  '(t__doc__tjoint __author__t__all__RtnetworkxRtnetworkx.utilsR RRR"RRRRRRR R R(((sc/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/weighted.pyts8      1 1+ L_D() _ /