3 Mdsa@sHdZddlZddlmZddlZddlmZddlm Z m Z ddd d d d d gZ ddhZ ddddZ edZedd/ddZddZddZd0ddZedd1ddZGdd d ejZd!d"ZGd#d d Zd2d%d Zd3d&d Zd4d'd Zd5d(d Zd)Zed*Zejd+dd,e_ejd-dd,e_ejd+d.d,e_ejd-d.d,e_dS)6u Algorithms for finding optimum branchings and spanning arborescences. This implementation is based on: J. Edmonds, Optimum branchings, J. Res. Natl. Bur. Standards 71B (1967), 233–240. URL: http://archive.org/details/jresv71Bn4p233 N) itemgetter)py_random_state)is_arborescence is_branchingbranching_weightgreedy_branchingmaximum_branchingminimum_branchingmaximum_spanning_arborescenceminimum_spanning_arborescenceEdmondsmaxmin branching arborescence)rrzspanning arborescenceinfcsdjfddt|DS)Ncsg|]}jtjqS)choicestring ascii_letters).0n)seedrU/var/www/html/virt/lib/python3.6/site-packages/networkx/algorithms/tree/branchings.py ?sz!random_string..)joinrange)Lrr)rr random_string=sr!cCs| S)Nr)weightrrr _min_weightBsr#cCs|S)Nr)r"rrr _max_weightFsr$r"cs tfdd|jddDS)z3 Returns the total weight of a branching. c3s|]}|djVqdS)N)get)redge)attrdefaultrr Osz#branching_weight..T)data)sumedges)Gr(r)r)r(r)rrJsc s(|tkrtjd|dkr d}nd}dkr6t|dfdd|jdd D}y|jtd d d |d Wn&tk r|jtd |d YnXtj}|j |tj j }xrt |D]f\} \} } } || || krqq|j | d krqqi} dk r| | <|j| | f| |j| | qW|S)a7 Returns a branching obtained through a greedy algorithm. This algorithm is wrong, and cannot give a proper optimal branching. However, we include it for pedagogical reasons, as it can be helpful to see what its outputs are. The output is a branching, and possibly, a spanning arborescence. However, it is not guaranteed to be optimal in either case. Parameters ---------- G : DiGraph The directed graph to scan. attr : str The attribute to use as weights. If None, then each edge will be treated equally with a weight of 1. default : float When `attr` is not None, then if an edge does not have that attribute, `default` specifies what value it should take. kind : str The type of optimum to search for: 'min' or 'max' greedy branching. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- B : directed graph The greedily obtained branching. zUnknown value for `kind`.rFTN)rcs$g|]\}}}|||jfqSr)r&)ruvr+)r(r)rrrsz$greedy_branching..)r+r%rr)keyreverse)KINDSnxNetworkXExceptionr!r-sortr TypeErrorZDiGraphadd_nodes_fromutils UnionFind enumerateZ in_degreeadd_edgeunion)r.r(r)kindrr3r-Bufir0r1wr+r)r(r)rrRs4"     csReZdZdZdfdd ZddZddZd d Zd d Zd dZ ddZ Z S)MultiDiGraph_EdgeKeya MultiDiGraph which assigns unique keys to every edge. Adds a dictionary edge_index which maps edge keys to (u, v, data) tuples. This is not a complete implementation. For Edmonds algorithm, we only use add_node and add_edge, so that is all that is implemented here. During additions, any specified keys are ignored---this means that you also cannot update edge attributes through add_node and add_edge. Why do we need this? Edmonds algorithm requires that we track edges, even as we change the head and tail of an edge, and even changing the weight of edges. We must reliably track edges across graph mutations. Nc s*t}|jfd|i|||_i|_dS)Nincoming_graph_data)super__init___cls edge_index)selfrEr(cls) __class__rrrGszMultiDiGraph_EdgeKey.__init__cCspt}x |j|jD]}|j|qWx |j|jD]}|j|q8Wx|D] }|j|=qPW|jj|dS)N)setpredvaluesupdatesuccrIrH remove_node)rJrkeysZkeydictr2rrrrRs  z MultiDiGraph_EdgeKey.remove_nodecCsx|D]}|j|qWdS)N)rR)rJZnbunchrrrrremove_nodes_froms z&MultiDiGraph_EdgeKey.remove_nodes_fromc Ks|||}}}||jkrJ|j|\}} } ||ks:|| krJtd|d|jj|||f||||j|||f|j|<dS)z' Key is now required. zKey z is already in use.N)rI ExceptionrHr=rQ) rJZ u_for_edgeZ v_for_edgeZ key_for_edger(r0r1r2uuvv_rrrr=s zMultiDiGraph_EdgeKey.add_edgecKs,x&|D]\}}}}|j|||f|qWdS)N)r=)rJZ ebunch_to_addr(r0r1kdrrradd_edges_fromsz#MultiDiGraph_EdgeKey.add_edges_fromcCsdy|j|\}}}Wn2tk rF}ztd||WYdd}~XnX|j|=|jj|||dS)NzInvalid edge key )rIKeyErrorrHZ remove_edge)rJr2r0r1rXerrrremove_edge_with_keys "z)MultiDiGraph_EdgeKey.remove_edge_with_keycCstdS)N)NotImplementedError)rJZebunchrrrremove_edges_fromsz&MultiDiGraph_EdgeKey.remove_edges_from)N) __name__ __module__ __qualname____doc__rGrRrTr=r[r^r` __classcell__rr)rLrrDs  rDcsBtj||fddfddtddD}|fS)z Returns the edge keys of the unique path between u and v. This is not a generic function. G must be a branching and an instance of MultiDiGraph_EdgeKey. cs$||j}t|}|dS)Nr)rSlist)rBrWrS)r.nodesrr first_keyszget_path..first_keycsg|]\}}||qSrr)rrBrW)rhrrrszget_path..rN)r5Z shortest_pathr<)r.r0r1r-r)r.rhrgrget_pathsric@s,eZdZdZdddZddZdd d ZdS)r zW Edmonds algorithm for finding optimal branchings and spanning arborescences. NcCs&||_d|_g|_t|dd|_dS)NT)rz_{0}) G_originalstorer-r!template)rJr.rrrrrGszEdmonds.__init__cCs0|tkrtjd||_||_||_||_|dkr>t|_}n t |_}|dkrZt |d}||_ dt |d|_ t |_}xtt|jjddD]^\} \} } } ||| j||i} |rx$| jD]\}}||kr|| |<qW|j| | | f| qWd|_t |_i|j_g|_g|_tjj|_g|_g|_dS)NzUnknown value for `kind`.r)rZ candidate_T)r+r)r4r5r6r(r)r?styler#transr$r!_attrcandidate_attrrDr.r<rjr-r&itemsr=levelr@rIgraphs branchingsr:r;rAcircuitsminedge_circuit)rJr(r)r?rmpreserve_attrsrrnr.r2r0r1r+rZZd_kZd_vrrr_inits:     "   z Edmonds._initr"rrrFc(s`|j||||||j}|j|j}t} ttj} |jj } fdd} x`y t | } Wn|t k rt t |kst t |rt|st |jr|jjj|jj|j|jjg|jjdPYn X| | krq\| j| |j| | | \}}|dkrq\q\|d}|||| krXt|| |\}}|j|dnd\}}|jdkr||dkr|d}nd}|r\|i}|j|| |df|d|| |d|j<|j|| |dk r\t}d}i}x@|D]8}|j|\}} }|}||| <||kr|}|}qW|jj||jj||jrN|jjj|jj|j|jj |j!}j|g}xj"ddd D]\}} }}||kr| |krqn|j}|j|| ||fnJ| |kr|}|||| 7}|j}||<|j||||fnqqWj#||j#|| j$t|xZ|D]R\}} }}j|| |f||j|krD||j=|j|| |f||j|| qDWttj} |j!d 7_!q\W|j%j&}d d }t|j|j!j} x|j!dkr|j!d 8_!|jj |j!}!|j|j!}"||j|j!d |!| \}#}$| j'|"|#rh|j|j!}|dkr\t(| j)|nX|j|j!j|$d }%x2|"D]"}$j|$\}} }| |%krPqWt(d | j)|$qW| |_"|j*|j%x| D]z}$|jdj|$\}} }&|j+|j,|&|j+i}|rFx0|&j-D]$\}}'||j+|jgkr|'||<qW|j|| f|qW|S)a Returns a branching from G. Parameters ---------- attr : str The edge attribute used to in determining optimality. default : float The value of the edge attribute used if an edge does not have the attribute `attr`. kind : {'min', 'max'} The type of optimum to search for, either 'min' or 'max'. style : {'branching', 'arborescence'} If 'branching', then an optimal branching is found. If `style` is 'arborescence', then a branching is found, such that if the branching is also an arborescence, then the branching is an optimal spanning arborescences. A given graph G need not have an optimal spanning arborescence. preserve_attrs : bool If True, preserve the other edge attributes of the original graph (that are not the one passed to `attr`) seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- H : (multi)digraph The branching. csTd}t }x@j|dddD],\}}}}|}||kr|}||||f}qW||fS)zO Find the edge directed toward v with maximal weight. NT)r+rS)INFZin_edges)r1r'r"r0rXr2r+Z new_weight)r.r(rr desired_edgesz*Edmonds.find_optimum..desired_edgeNrr%rFT)r+rSrcSsZ||krt|dx>|j|D],}x&|j||D]}||kr6d|fSq6Wq"WdSdS)z Returns True if `u` is a root node in G. Node `u` will be a root node if its in-degree, restricted to the specified edges, is equal to 0. z not in GFTN)TN)rUrN)r.r0Zedgekeysr1edgekeyrrris_root&sz%Edmonds.find_optimum..is_rootz+Couldn't find edge incoming to merged node.)NN).rxrAr.r@rMiterrfrgrorNnext StopIterationlenAssertionErrorrrkrsappendcopyrtrurvaddadd_noderirmr=rpr>ryrIrlformatrrr-rTdifference_updaterjrLrPrUremover9r(rnrq)(rJr(r)r?rmrwrrAr@DrgZG_predrzr1r'r"r0ZQ_nodesZQ_edgesZ acceptableddZ minweightZminedgeZQ_incoming_weightZedge_keyr+rCnew_nodeZ new_edgesr2Hr|r-Z merged_nodeZcircuitZisrootr{targetrZvaluer)r.r(r find_optimumTs(                                 zEdmonds.find_optimum)N)r"rrrFN)rarbrcrdrGrxrrrrrr s CFcCs t|}|j||dd|d}|S)Nrr)r?rmrw)r r)r.r(r)rwedr@rrrr scCs t|}|j||dd|d}|S)Nrr)r?rmrw)r r)r.r(r)rwrr@rrrr scCs8t|}|j||dd|d}t|s4d}tjj||S)Nrr)r?rmrwz&No maximum spanning arborescence in G.)r rrr5 exceptionr6)r.r(r)rwrr@msgrrrr s cCs8t|}|j||dd|d}t|s4d}tjj||S)Nrr)r?rmrwz&No minimum spanning arborescence in G.)r rrr5rr6)r.r(r)rwrr@rrrrr s a Returns a {kind} {style} from G. Parameters ---------- G : (multi)digraph-like The graph to be searched. attr : str The edge attribute used to in determining optimality. default : float The value of the edge attribute used if an edge does not have the attribute `attr`. preserve_attrs : bool If True, preserve the other attributes of the original graph (that are not passed to `attr`) Returns ------- B : (multi)digraph-like A {kind} {style}. zV Raises ------ NetworkXException If the graph does not contain a {kind} {style}. maximum)r?rmZminimumzspanning arborescence)rN)r"r)r"rrN)r"rF)r"rF)r"rF)r"rF) rdroperatorrZnetworkxr5Znetworkx.utilsrZ recognitionrr__all__r4STYLESfloatryr!r#r$rrZ MultiDiGraphrDrir r r r r Zdocstring_branchingZdocstring_arborescencerrrrr sZ     OG