\c@sdZdZddddddgZdd lZd d Zd d Zd Zd Z d dZ d dZ d d d dZ d S(s1 Shortest path algorithms for unweighted graphs. sAric Hagberg (hagberg@lanl.gov)tbidirectional_shortest_pathtsingle_source_shortest_patht"single_source_shortest_path_lengthtall_pairs_shortest_pathtall_pairs_shortest_path_lengtht predecessoriNcCsi}d}id|6}xw|r|}i}x8|D]0}||kr5|||<|j||q5q5W|dk r||krPn|d}qW|S(sCompute the shortest path lengths from source to all reachable nodes. Parameters ---------- G : NetworkX graph source : node Starting node for path cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- lengths : dictionary Dictionary of shortest path lengths keyed by target. Examples -------- >>> G=nx.path_graph(5) >>> length=nx.single_source_shortest_path_length(G,0) >>> length[4] 4 >>> print(length) {0: 0, 1: 1, 2: 2, 3: 3, 4: 4} See Also -------- shortest_path_length iiN(tupdatetNone(tGtsourcetcutofftseentlevelt nextlevelt thisleveltv((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/unweighted.pyRs     cCs4i}x'|D]}t||d|||>> G=nx.path_graph(5) >>> length=nx.all_pairs_shortest_path_length(G) >>> print(length[1][4]) 3 >>> length[1] {0: 1, 1: 0, 2: 1, 3: 2, 4: 3} R (R(RR tpathstn((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/unweighted.pyREs cCst|||}|\}}}g}x'|dk rP|j|||}q*W||d}x*|dk r|jd|||}qbW|S(s'Return a list of nodes in a shortest path between source and target. Parameters ---------- G : NetworkX graph source : node label starting node for path target : node label ending node for path Returns ------- path: list List of nodes in a path from source to target. Raises ------ NetworkXNoPath If no path exists between source and target. See Also -------- shortest_path Notes ----- This algorithm is used by shortest_path(G,source,target). iN(t_bidirectional_pred_succRtappendtinsert(RR ttargettresultstpredtsucctwtpath((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/unweighted.pyRjs  c Cs||kr'id|6id|6|fS|jrH|j}|j}n|j}|j}id|6}id|6}|g}|g}x|r|rt|t|kr#|} g}x| D]\} xS|| D]E} | |kr|j| | || >> G=nx.path_graph(5) >>> path=nx.single_source_shortest_path(G,0) >>> path[4] [0, 1, 2, 3, 4] Notes ----- The shortest path is not necessarily unique. So there can be multiple paths between the source and each target node, all of which have the same 'shortest' length. For each target node, this function returns only one of those paths. See Also -------- shortest_path iiN(R( RR R R R RRRR((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/unweighted.pyRs"%      cCs4i}x'|D]}t||d|||>> G=nx.path_graph(5) >>> path=nx.all_pairs_shortest_path(G) >>> print(path[0][4]) [0, 1, 2, 3, 4] See Also -------- floyd_warshall() R (R(RR RR((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/unweighted.pyRs c CsLd}|g}i||6}ig|6}x|r|d}|} g}xz| D]r} xi|| D]]} | |kr| g|| <||| <|j| q`|| |kr`|| j| q`q`WqOW|r,||kr,Pq,q,W|dk r4|r||krgdfS||||fS||kr)gS||Sn|rD||fS|SdS(s Returns dictionary of predecessors for the path from source to all nodes in G. Parameters ---------- G : NetworkX graph source : node label Starting node for path target : node label, optional Ending node for path. If provided only predecessors between source and target are returned cutoff : integer, optional Depth to stop the search. Only paths of length <= cutoff are returned. Returns ------- pred : dictionary Dictionary, keyed by node, of predecessors in the shortest path. Examples -------- >>> G=nx.path_graph(4) >>> print(G.nodes()) [0, 1, 2, 3] >>> nx.predecessor(G,0) {0: [], 1: [0], 2: [1], 3: [2]} iiiN(RR( RR RR t return_seenR R R RRRR((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/unweighted.pyR's:!              ( t__doc__t __author__t__all__tnetworkxR RRRRRRRR(((se/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/shortest_paths/unweighted.pyts   . % 1 2 7 #