wg$dZddlZddlmZddlmZddlmZddlZ ddl m Z m Z m Z ddlmZe Zd gZe j$d d Zd Zy) z0 Kanevsky all minimum node k cutsets algorithm. N) defaultdict) combinations) itemgetter)build_residual_network edmonds_karpshortest_augmenting_path)!build_auxiliary_node_connectivity all_node_cutsc # "#Ktj|stjdtj|dk(r dEd{yg}t |}|j "|j d}tj|j}t|d}d|d}|t}|turd|d <|tj|| }t|jtdd d|D chc]\} } |  } } } t!|| r|j#| | | D]} t%|| hz t%|| z } | D]h}|||| d ||d fi|}|j d}||k(s0|j'dD cgc]\}}} | ddk7s||fc} }}x}}|D chc] }|D]} |  c} }x}}|j'dD cgc]\}}} | d| dk(s| ddk(r||| f }}}} |j)|tj*|}tj,|}|j d}t/t0}|j3D]\} }||j#| |D chc]} ||  }} tj4|D]+}t%|j7|st%#|D]}#j9||t%}#D] } |j9|j| "#j9||| d #vs ||d #vrt%}#D] |j9#fd|D"t;"fd|Dr|D chc] \}} "|d}!}} t=|!|k(s| |!vs||!vr|!|vs|!|j#|!.|j?|| d ||d d|j?||d || d d|j?|| d ||d d|j?||d || d d|j?||d || d d|j?|| d ||d d|jA|ky7}cc} } wcc} }}wcc} }wcc} }}wcc} wcc} }ww)aReturns all minimum k cutsets of an undirected graph G. This implementation is based on Kanevsky's algorithm [1]_ for finding all minimum-size node cut-sets of an undirected graph G; ie the set (or sets) of nodes of cardinality equal to the node connectivity of G. Thus if removed, would break G into two or more connected components. Parameters ---------- G : NetworkX graph Undirected graph k : Integer Node connectivity of the input graph. If k is None, then it is computed. Default value: None. flow_func : function Function to perform the underlying flow computations. Default value is :func:`~networkx.algorithms.flow.edmonds_karp`. This function performs better in sparse graphs with right tailed degree distributions. :func:`~networkx.algorithms.flow.shortest_augmenting_path` will perform better in denser graphs. Returns ------- cuts : a generator of node cutsets Each node cutset has cardinality equal to the node connectivity of the input graph. Examples -------- >>> # A two-dimensional grid graph has 4 cutsets of cardinality 2 >>> G = nx.grid_2d_graph(5, 5) >>> cutsets = list(nx.all_node_cuts(G)) >>> len(cutsets) 4 >>> all(2 == len(cutset) for cutset in cutsets) True >>> nx.node_connectivity(G) 2 Notes ----- This implementation is based on the sequential algorithm for finding all minimum-size separating vertex sets in a graph [1]_. The main idea is to compute minimum cuts using local maximum flow computations among a set of nodes of highest degree and all other non-adjacent nodes in the Graph. Once we find a minimum cut, we add an edge between the high degree node and the target node of the local maximum flow computation to make sure that we will not find that minimum cut again. See also -------- node_connectivity edmonds_karp shortest_augmenting_path References ---------- .. [1] Kanevsky, A. (1993). Finding all minimum-size separating vertex sets in a graph. Networks 23(6), 533--541. http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract zInput graph is disconnected.r Nmappingcapacity)rresidualT two_phase) flow_func)keyreverseBA flow_value)dataflowrc30K|] }|vs|fyw)Nr ).0wSus n/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/connectivity/kcutsets.py z all_node_cuts..s%WAUVJq!f%Ws  c3FK|]\}}|d|dk7yw)idNr )rrrH_nodess rr z all_node_cuts..s,SDAq71:d+wqz$/??Ss!r")r)!nx is_connected NetworkXErrordensityr nodesgraphcopy_predrdefault_flow_funcrnode_connectivitysorteddegreer_is_separating_setappendsetedgesremove_edges_fromtransitive_closure condensationrlistitems antichainsissubsetupdateanylenadd_edgeadd_edges_from)$GkrseenHroriginal_H_predRkwargsndXx non_adjacentvrrrE1 flowed_edgesedgeVE1incident_nodessaturated_edges R_closureLcmapinv_cmapscc antichain S_ancestorscutset_node_cutr#rs$ ` @@rr r sbF ??1 =>>  zz!}  D *!,AggGggi Gii(Oq*-A$! 4F% ,,"{ y  i 8ahhjjmTJ2ANOtq!OAO!Q A \21v|c!A$i/ X 2A! |1-'!*Q/?J6JA.JQ-.GGG,>%%(1a!F)q.QF%\79'Gd$'GQ'G'GGn &'WW$W%7##!Aq}& 1Qz]a5G1I## ##O411!4 OOA&wwy)&t,"jjl,FAsSM((+,),,1tAw,,"$q!1$2Iy>2237 A(0#/0"%%K?#**9??1+=>?HH[)!!*Q'q0wqzl!4D4I  UFX %Woa6H%WWXSFSS =CDTQ 4 0DHD8})=AM$#4/"*N KK1I$2Z gaj\+ |1-= J gaj\+ |1-= J gaj\+ |1-= J gaj\+ |1-= J gaj\+ |1-= J gaj\+ |1-= J  1qX 2 \2C 6 P$%(H#-> Es}AS2 S B6S2 S A9S2 S2 S 2S 8 S2S S20#S B S2 S',C9S2%S, 7S2 S2C1S2 %S2ct|t|dz k(rytj||g}tj|ryy)z)Assumes that the input graph is connectedr TF)r=r$restricted_viewr%)r@cutrCs rr0r0s? 3x3q6A: 1c2&A q )NN)__doc__r* collectionsr itertoolsroperatorrnetworkxr$networkx.algorithms.flowrrrutilsr r,__all__ _dispatchabler r0r r`rrjs\ #" 5   F2F2Rr`