wgdZddlmZddlmZmZddlZddlm Z gdZ e de dejd Z d Z ejd Zejd Zejd Ze de dejdddZe de dejdddZy)z;Functions for computing and verifying matchings in a graph.)Counter) combinationsrepeatN)not_implemented_for) is_matchingis_maximal_matchingis_perfect_matchingmax_weight_matchingmin_weight_matchingmaximal_matching multigraphdirectedct}t}|jD]9}|\}}||vs ||vs||k7s|j||j|;|S)aFind a maximal matching in the graph. A matching is a subset of edges in which no node occurs more than once. A maximal matching cannot add more edges and still be a matching. Parameters ---------- G : NetworkX graph Undirected graph Returns ------- matching : set A maximal matching of the graph. Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5)]) >>> sorted(nx.maximal_matching(G)) [(1, 2), (3, 5)] Notes ----- The algorithm greedily selects a maximal matching M of the graph G (i.e. no superset of M exists). It runs in $O(|E|)$ time. )setedgesaddupdateGmatchingnodesedgeuvs a/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/matching.pyr r sd<uH EE 1 E>auna LL  LL   Oct}|jD]@}|\}}||f|vs||vr||k(rtjd||j |B|S)a?Converts matching dict format to matching set format Converts a dictionary representing a matching (as returned by :func:`max_weight_matching`) to a set representing a matching (as returned by :func:`maximal_matching`). In the definition of maximal matching adopted by NetworkX, self-loops are not allowed, so the provided dictionary is expected to never have any mapping from a key to itself. However, the dictionary is expected to have mirrored key/value pairs, for example, key ``u`` with value ``v`` and key ``v`` with value ``u``. z%Selfloops cannot appear in matchings )ritemsnx NetworkXErrorr)rrrrrs rmatching_dict_to_setr!=sp EE 1 q6U?dem  6""%J4&#QR R $  Lrc`t|tr t|}t}|D]}t |dk7rt j d||\}}||vs||vrt j d|d||k(ry|j||sy||vs||vry|j|y)aReturn True if ``matching`` is a valid matching of ``G`` A *matching* in a graph is a set of edges in which no two distinct edges share a common endpoint. Each node is incident to at most one edge in the matching. The edges are said to be independent. Parameters ---------- G : NetworkX graph matching : dict or set A dictionary or set representing a matching. If a dictionary, it must have ``matching[u] == v`` and ``matching[v] == u`` for each edge ``(u, v)`` in the matching. If a set, it must have elements of the form ``(u, v)``, where ``(u, v)`` is an edge in the matching. Returns ------- bool Whether the given set or dictionary represents a valid matching in the graph. Raises ------ NetworkXError If the proposed matching has an edge to a node not in G. Or if the matching is not a collection of 2-tuple edges. Examples -------- >>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5)]) >>> nx.is_maximal_matching(G, {1: 3, 2: 4}) # using dict to represent matching True >>> nx.is_matching(G, {(1, 3), (2, 4)}) # using set to represent matching True matching has non-2-tuple edge matching contains edge  with node not in GFT isinstancedictr!rlenrr has_edgerrs rrrVsR(D!'1 EE  t9>""%CD6#JK K1 A:!""%>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (3, 4), (3, 5)]) >>> nx.is_maximal_matching(G, {(1, 2), (3, 4)}) True r#r$r%r&FT) r(r)r!rr*rr r+rrr)rrrrrrrs rrrs>(D!'1 EE EE t9>""%CD6#JK K1 A:!""%>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (2, 4), (3, 5), (4, 5), (4, 6)]) >>> my_match = {1: 2, 3: 5, 4: 6} >>> nx.is_perfect_matching(G, my_match) True r#r$r%r&Fr'rs rr r s@(D!'1 EE  t9>""%CD6#JK K1 A:!""%z&min_weight_matching..;s2wq!Q2sc36K|]\}}}|||z fywr6r7)r8rrr: max_weights rr;z&min_weight_matching..=s" ;1aaJN # ;sr.)r*rr maxrGraphadd_weighted_edges_from)rr.G_edgesInvGrr=s @rr r sf 177|q"1T&IIgg61g-GS2'222J 88:D ;7 ;E  v 6 tD HHrc   !"#$%&'()*GddGfddt$$s tSd}d}jdD]P\}}}|jd}||k7r||kDr|}|xr(t t |j d dd v}Ri(i&i'tt$$%tt$td "tt$$ itt$t|#i!ig)#fd * %&'()f d  %&'(fd}  !"%&'()*f d}  !"%&'(f d}  "(fd %&'(fd} !"#$(fd} &j'jj!D] }d |_ jg)d d $D]&}|(vs&j%||dd (d} )rk|sh)j}&%|dk(sJj|D]0}||k(r %|}%|}||k(r||fvr*||}|dkrdx||f<||f<||fvr~&j| |d|^&j|dk(r%| ||}|ur | |||| ||d}n&j|&|dk(sJd&|<||f'|<&j|dk(r%j| *|ks||f|<&j| j| *|ks*||f|<3)r|sh|rnqd}d x}x}}sd}t#j}j!D]E}&j%|j|**|}|dk(s||ks=|}d}|}G"D]b}"| &j|dk(sj|0*|}|r|dzdk(sJ|dz}n|dz }|dk(s||ksZ|}d}|}d!D]4}"| &j|dk(s|dk(s !||ks,!|}d}|}6|dk(r)sJd}t#dt#j}$D]L}&j%|dk(r#|xx|zcc<(&j%|dk(s@#|xx|z cc<N!D]L}"| &j|dk(r!|xx|z cc<+&j|dk(s@!|xx|zcc<N|dk(rn~|dk(r2|\}}&%|dk(sJdx||f<||f<)j%|nE|dk(r2|\}}dx||f<||f<&%|dk(sJ)j%|n|dk(r | |d(D]}((||k(rJ|snRt!j'D]4}|!vr"|&j|dk(s#!|dk(s,| |d6|r| t)(S)aCompute a maximum-weighted matching of G. A matching is a subset of edges in which no node occurs more than once. The weight of a matching is the sum of the weights of its edges. A maximal matching cannot add more edges and still be a matching. The cardinality of a matching is the number of matched edges. Parameters ---------- G : NetworkX graph Undirected graph maxcardinality: bool, optional (default=False) If maxcardinality is True, compute the maximum-cardinality matching with maximum weight among all maximum-cardinality matchings. weight: string, optional (default='weight') Edge data key corresponding to the edge weight. If key not found, uses 1 as weight. Returns ------- matching : set A maximal matching of the graph. Examples -------- >>> G = nx.Graph() >>> edges = [(1, 2, 6), (1, 3, 2), (2, 3, 1), (2, 4, 7), (3, 5, 9), (4, 5, 3)] >>> G.add_weighted_edges_from(edges) >>> sorted(nx.max_weight_matching(G)) [(2, 4), (5, 3)] Notes ----- If G has edges with weight attributes the edge data are used as weight values else the weights are assumed to be 1. This function takes time O(number_of_nodes ** 3). If all edge weights are integers, the algorithm uses only integer computations. If floating point weights are used, the algorithm could return a slightly suboptimal matching due to numeric precision errors. This method is based on the "blossom" method for finding augmenting paths and the "primal-dual" method for finding a matching of maximum weight, both methods invented by Jack Edmonds [1]_. Bipartite graphs can also be matched using the functions present in :mod:`networkx.algorithms.bipartite.matching`. References ---------- .. 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