o ]Zh@spdZddlmZddlZddlmZddlmZm Z m Z dgZ ddZ e d e d ej d d dddZdS)uBFunctions for computing the Kernighan–Lin bipartition algorithm.)countN) is_partition) BinaryHeapnot_implemented_forpy_random_statekernighan_lin_bisectionc #sttf\}}ttD]\}}}tfdd|D}|||r+|n| qfdd}d} d} |rn|rr|\}}||||\} } ||| | || 7} | d7} | | || ffV|rp|s@dSdSdSdS)z This is a modified form of Kernighan-Lin, which moves single nodes at a time, alternating between sides to keep the bisection balanced. We keep two min-heaps of swap costs to make optimal-next-move selection fast. c3s&|]\}}|r |n| VqdS)N).0vw)siderZ/var/www/auris/lib/python3.10/site-packages/networkx/algorithms/community/kernighan_lin.py s$z'_kernighan_lin_sweep..cs\|D]'\}}|}||}|dur+|d||ur | n|7}|||dqdS)NT)getinsert)Zcosts_xxyr Zcosts_yZcost_ycostsedgesr rr _update_costss  z+_kernighan_lin_sweep.._update_costsrN)rziprsumrpop) rr Zcosts0Zcosts1uZside_uZedges_uZcost_uriZtotcostr Zcost_vrrr _kernighan_lin_sweep s"     rZdirectedweight)Z edge_attrs c st}t}||ddt|D|dur+dg|ddg|dd}n7z|\}} WnttfyE} ztd| d} ~ wwt|| fsRtddg|}|D]} d|| <qY rrfd d |D} n fd d |D} t |D],} tt | |}t |\}}}|dkrn|d|D]\}}\}}d||<d||<qqd d t ||D}dd t ||D} || fS)uPartition a graph into two blocks using the Kernighan–Lin algorithm. This algorithm partitions a network into two sets by iteratively swapping pairs of nodes to reduce the edge cut between the two sets. The pairs are chosen according to a modified form of Kernighan-Lin [1]_, which moves node individually, alternating between sides to keep the bisection balanced. Parameters ---------- G : NetworkX graph Graph must be undirected. partition : tuple Pair of iterables containing an initial partition. If not specified, a random balanced partition is used. max_iter : int Maximum number of times to attempt swaps to find an improvement before giving up. weight : key Edge data key to use as weight. If None, the weights are all set to one. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Only used if partition is None Returns ------- partition : tuple A pair of sets of nodes representing the bipartition. Raises ------ NetworkXError If partition is not a valid partition of the nodes of the graph. References ---------- .. [1] Kernighan, B. W.; Lin, Shen (1970). "An efficient heuristic procedure for partitioning graphs." *Bell Systems Technical Journal* 49: 291--307. Oxford University Press 2011. cSsi|]\}}||qSrr)r rr rrr csz+kernighan_lin_bisection..Nrrrzpartition must be two setszpartition invalidc(g|]}fdd|DqS)cs2g|]\}}|tfdd|DfqS)c3s|] }|dVqdS)rNr)r e)r rr rusz@kernighan_lin_bisection....)rvalues)r rdindexr rr ts 6kernighan_lin_bisection...itemsr r Gr)r rr r*ss  z+kernighan_lin_bisection..cr#)cs$g|]\}}||dfqSrr$)r rr%r(rr r*|s$r+r,r.r/rr r*{scSh|] \}}|dkr|qS)rrr rsrrr z*kernighan_lin_bisection..cSr2r1rr3rrr r5r6)lenlistshuffle enumerate TypeError ValueErrornxZ NetworkXErrorrZ is_multigraphrangerminr)r0 partitionZmax_iterr seednlabelsr ABerrarrrZmin_costZmin_i_rr rr/r r+sH5 "      )Nr!r N)__doc__ itertoolsrZnetworkxr=Z-networkx.algorithms.community.community_utilsrZnetworkx.utilsrrr__all__rZ _dispatchablerrrrr s