ó |£*^c@sdZdddddgZddlZddlmZmZdd lmZd e d „Z d d „Z e Z d e d „Z d d„ZdS(s6 Computes minimum spanning tree of a weighted graph. t kruskal_msttminimum_spanning_edgestminimum_spanning_treetprim_mst_edgestprim_mstiÿÿÿÿN(theappoptheappush(tcounttweightc #sÅddlm}|jƒr.tjdƒ‚n|ƒ}t|jdtƒd‡fd†ƒ}x`|D]X\}}}||||kre|rŸ|||fVn ||fV|j||ƒqeqeWdS(sØGenerate edges in a minimum spanning forest of an undirected weighted graph. A minimum spanning tree is a subgraph of the graph (a tree) with the minimum sum of edge weights. A spanning forest is a union of the spanning trees for each connected component of the graph. Parameters ---------- G : NetworkX Graph weight : string Edge data key to use for weight (default 'weight'). data : bool, optional If True yield the edge data along with the edge. Returns ------- edges : iterator A generator that produces edges in the minimum spanning tree. The edges are three-tuples (u,v,w) where w is the weight. Examples -------- >>> G=nx.cycle_graph(4) >>> G.add_edge(0,3,weight=2) # assign weight 2 to edge 0-3 >>> mst=nx.minimum_spanning_edges(G,data=False) # a generator of MST edges >>> edgelist=list(mst) # make a list of the edges >>> print(sorted(edgelist)) [(0, 1), (1, 2), (2, 3)] Notes ----- Uses Kruskal's algorithm. If the graph edges do not have a weight attribute a default weight of 1 will be used. Modified code from David Eppstein, April 2006 http://www.ics.uci.edu/~eppstein/PADS/ iÿÿÿÿ(t UnionFinds6Mimimum spanning tree not defined for directed graphs.tdatatkeycs|djˆdƒS(Nii(tget(tt(R(sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/mst.pytOsN( tnetworkx.utilsR t is_directedtnxt NetworkXErrortsortedtedgestTruetunion( tGRR R tsubtreesRtutvtd((Rsk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/mst.pyRs1   ' cCs¾tjtj|d|dtƒƒ}t|ƒt|ƒkr}|jg|jƒjƒD]\}}|dkrU|^qUƒnx(|D] }|j|j ƒ|j|>> G=nx.cycle_graph(4) >>> G.add_edge(0,3,weight=2) # assign weight 2 to edge 0-3 >>> T=nx.minimum_spanning_tree(G) >>> print(sorted(T.edges(data=True))) [(0, 1, {}), (1, 2, {}), (2, 3, {})] Notes ----- Uses Kruskal's algorithm. If the graph edges do not have a weight attribute a default weight of 1 will be used. RR i( RtGraphRRtlentadd_nodes_fromtdegreetitemstnodetcopytgraph(RRtTtnR((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/mst.pyRYs&$A ccsž|jƒrtjdƒ‚nt}t}|jƒ}tƒ}xX|r™|jdƒ}g}|g} xP|j|ƒD]?\}} ||||| j |dƒt |ƒ|| fƒqvWxÚ|r•||ƒ\} } }} | | krìq¼n| j | ƒ|j | ƒx_|j| ƒD]N\} } | | kr|||| | j |dƒt |ƒ| | fƒqqW|r‡|| ||| fVq¼|| fVq¼WqBWdS(soGenerate edges in a minimum spanning forest of an undirected weighted graph. A minimum spanning tree is a subgraph of the graph (a tree) with the minimum sum of edge weights. A spanning forest is a union of the spanning trees for each connected component of the graph. Parameters ---------- G : NetworkX Graph weight : string Edge data key to use for weight (default 'weight'). data : bool, optional If True yield the edge data along with the edge. Returns ------- edges : iterator A generator that produces edges in the minimum spanning tree. The edges are three-tuples (u,v,w) where w is the weight. Examples -------- >>> G=nx.cycle_graph(4) >>> G.add_edge(0,3,weight=2) # assign weight 2 to edge 0-3 >>> mst=nx.prim_mst_edges(G,data=False) # a generator of MST edges >>> edgelist=list(mst) # make a list of the edges >>> print(sorted(edgelist)) [(0, 1), (1, 2), (2, 3)] Notes ----- Uses Prim's algorithm. If the graph edges do not have a weight attribute a default weight of 1 will be used. s6Mimimum spanning tree not defined for directed graphs.iiN( RRRRRtnodesRtpopRR tnexttappendtremove(RRR tpushR'R&tcRtfrontiertvisitedRtWt_tw((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/mst.pyRŒs2)      7     :cCs¾tjtj|d|dtƒƒ}t|ƒt|ƒkr}|jg|jƒjƒD]\}}|dkrU|^qUƒnx(|D] }|j|j ƒ|j|>> G=nx.cycle_graph(4) >>> G.add_edge(0,3,weight=2) # assign weight 2 to edge 0-3 >>> T=nx.prim_mst(G) >>> print(sorted(T.edges(data=True))) [(0, 1, {}), (1, 2, {}), (2, 3, {})] Notes ----- Uses Prim's algorithm. If the graph edges do not have a weight attribute a default weight of 1 will be used. RR i( RRRRRRRR R!R"R#(RRR$R%R((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/mst.pyRÕs'$A (t__doc__t__all__tnetworkxRtheapqRRt itertoolsRRRRRRR(((sk/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/mst.pyts   A 0I