ó ,µ[c@s‹dZddlmZddlmZddlmZddddd gZd „Zd „Zd „Z d „Z d„Z e dd„Z dS(s;Functions for computing and verifying matchings in a graph.iÿÿÿÿ(tCounter(t combinations(trepeatt is_matchingtis_maximal_matchingtis_perfect_matchingtmax_weight_matchingtmaximal_matchingcCs‡tƒ}tƒ}xn|jƒD]`\}}||kr||kr||kr|j||fƒ|j|ƒ|j|ƒqqW|S(sûFind 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. 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. (tsettedgestadd(tGtmatchingtnodestutv((s;lib/python2.7/site-packages/networkx/algorithms/matching.pyRs  $ cCs)td„ttt|jƒƒƒDƒƒS(sConverts 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``. css!|]\}}||fVqdS(N((t.0RR((s;lib/python2.7/site-packages/networkx/algorithms/matching.pys Js(Rtmapt frozensettitems(R ((s;lib/python2.7/site-packages/networkx/algorithms/matching.pytmatching_dict_to_set9scCs;t|tƒrt|ƒ}ntd„t|dƒDƒƒS(sÈDecides whether the given set or dictionary represents a valid matching in ``G``. A *matching* in a graph is a set of edges in which no two distinct edges share a common endpoint. 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. css7|]-\}}tt|ƒt|ƒ@ƒdkVqdS(iN(tlenR(Rte1te2((s;lib/python2.7/site-packages/networkx/algorithms/matching.pys isi(t isinstancetdictRtallR(R R ((s;lib/python2.7/site-packages/networkx/algorithms/matching.pyRMs csˆtˆtƒrtˆƒ‰ntˆˆƒs1tStttˆjƒƒƒ}tttˆƒƒ}||}t ‡‡fd†|DƒƒS(sóDecides whether the given set or dictionary represents a valid maximal matching in ``G``. A *maximal matching* in a graph is a matching in which adding any edge would cause the set to no longer be a valid matching. 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 maximal matching in the graph. c3s&|]}tˆˆ|hBƒ VqdS(N(R(Rte(R R (s;lib/python2.7/site-packages/networkx/algorithms/matching.pys –s( RRRRtFalseRRRR R(R R t all_edgest matched_edgestunmatched_edges((R R s;lib/python2.7/site-packages/networkx/algorithms/matching.pyRms cs`t|tƒrt|ƒ}nt||ƒs1tStt|dƒƒ‰t‡fd†|DƒƒS(sÎDecides whether the given set represents a valid perfect matching in ``G``. A *perfect matching* in a graph is a matching in which exactly one edge is incident upon each vertex. 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. 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