wgdZddlmZddlZddlmZddlmZm Z m Z dgZ dZ e de d ejd d d Zy)uBFunctions for computing the Kernighan–Lin bipartition algorithm.)countN) is_partition) BinaryHeapnot_implemented_forpy_random_statekernighan_lin_bisectionc# Kttfx\}} ttD]4\}}}tfd|D} |j ||r|n| 6 fd}d} d} |rX|rU|j \}}||||j \} } ||| | || zz } | dz } | | || ff|r|rSyyyyw)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. c38K|]\}}|r|n| yw)N).0vwsides p/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/community/kernighan_lin.py z'_kernighan_lin_sweep..s">da$q'Qr)>sc|D]C\}}|}|j|}|"|d||ur| n|zz }|j||dEy)NT)getinsert) costs_xxyrcosts_ycost_ycostsedgesrs r _update_costsz+_kernighan_lin_sweep.._update_costssd!H 0DAqDGnG[[^F!!W%7rQ??q&$/  0rN)rziprsumrpop)rrcosts0costs1uside_uedges_ucost_uritotcostr cost_vrs`` @r_kernighan_lin_sweepr, s (\:<77NFFU!%'47?67>g>> f Q&vg>?0 AG VJJL 6fa JJL 6fa 6F?" Qq1a&   V&V&s CC Cdirectedweight) edge_attrsct|}t|}|j|t|Dcic]\}}|| } }}|dg|dzzdg|dzdzzz} n> |\} } t|| | fst jddg|z} | D] }d| | |< |jr]|Dcgc]M}||jDcgc],\}}| |tfd|jDf.c}}O}}}}nL|Dcgc]=}||jDcgc]\}}| ||jdfc}}?}}}}t|D]H}tt|| }t!|\}}}|dk\rn|d|D]\}}\}}d| |<d| |<Jt#|| Dchc] \}}|dk(s |} }}t#|| Dchc] \}}|dk(s |} }}| | fScc}}w#tt f$r} t jd| d} ~ wwxYwcc}}wcc}}}wcc}}wcc}}}wcc}}wcc}}w)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. Nrrrzpartition must be two setszpartition invalidc3BK|]}|jdyw)rN)r)r er/s rrz*kernighan_lin_bisection..usDAquuVQ/Ds)lenlistshuffle enumerate TypeError ValueErrornx NetworkXErrorr is_multigraphitemsr!valuesrranger,minr )G partitionmax_iterr/seednlabelsr)r indexrABerrar%drr3rmin_costmin_i_ss ` rrr+sj AA !WFLL'/ 0daQT 0E 0sa1f~A!| 44 JDAqA1v&""#67 7sQw ADqN      aDJJL Aqq3DDDE   NT  HIadjjl CdaeAhfa( ) C  8_)%67 Z% q= !&5M LAq&1aDGDG  64(3tq!AF3A364(3tq!AF3A3 a4KQ 1:& J""#?@c I J   D  43se G9!G?4H21H,H2H?,!H9 H?< I I I .I ?H)H$$H),H29H?)N r/N)__doc__ itertoolsrnetworkxr:-networkx.algorithms.community.community_utilsrnetworkx.utilsrrr__all__r, _dispatchablerr rrrYsaHFKK $ %!>Z X&]'!]r