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    """Implementation of gSpan."""
    from __future__ import absolute_import
    from __future__ import division
    from __future__ import print_function
    
    import collections
    import copy
    import itertools
    import time
    
    from .graph import AUTO_EDGE_ID
    from .graph import Graph
    from .graph import VACANT_GRAPH_ID
    from .graph import VACANT_VERTEX_LABEL
    
    
    def record_timestamp(func):
        """Record timestamp before and after call of `func`."""
    
        def deco(self):
            self.timestamps[func.__name__ + '_in'] = time.time()
            func(self)
            self.timestamps[func.__name__ + '_out'] = time.time()
    
        return deco
    
    
    class DFSedge(object):
        """DFSedge class."""
    
        def __init__(self, frm, to, vevlb):
            """Initialize DFSedge instance."""
            self.frm = frm
            self.to = to
            self.vevlb = vevlb
    
        def __eq__(self, other):
            """Check equivalence of DFSedge."""
            return (self.frm == other.frm and
                    self.to == other.to and
                    self.vevlb == other.vevlb)
    
        def __ne__(self, other):
            """Check if not equal."""
            return not self.__eq__(other)
    
        def __repr__(self):
            """Represent DFScode in string way."""
            return '(frm={}, to={}, vevlb={})'.format(
                self.frm, self.to, self.vevlb
            )
    
    
    class DFScode(list):
        """DFScode is a list of DFSedge."""
    
        def __init__(self):
            """Initialize DFScode."""
            super().__init__()
            self.rmpath = list()
    
        def __eq__(self, other):
            """Check equivalence of DFScode."""
            la, lb = len(self), len(other)
            if la != lb:
                return False
            for i in range(la):
                if self[i] != other[i]:
                    return False
            return True
    
        def __ne__(self, other):
            """Check if not equal."""
            return not self.__eq__(other)
    
        def __repr__(self):
            """Represent DFScode in string way."""
            return ''.join(['[', ','.join(
                [str(dfsedge) for dfsedge in self]), ']']
                           )
    
        def push_back(self, frm, to, vevlb):
            """Update DFScode by adding one edge."""
            self.append(DFSedge(frm, to, vevlb))
            return self
    
        def to_graph(self, gid=VACANT_GRAPH_ID, is_undirected=True):
            """Construct a graph according to the dfs code."""
            g = Graph(gid,
                      is_undirected=is_undirected,
                      eid_auto_increment=True)
            for dfsedge in self:
                frm, to, (vlb1, elb, vlb2) = dfsedge.frm, dfsedge.to, dfsedge.vevlb
                if vlb1 != VACANT_VERTEX_LABEL:
                    g.add_vertex(frm, vlb1)
                if vlb2 != VACANT_VERTEX_LABEL:
                    g.add_vertex(to, vlb2)
                g.add_edge(AUTO_EDGE_ID, frm, to, elb)
            return g
    
        def from_graph(self, g):
            """Build DFScode from graph `g`."""
            raise NotImplementedError('Not inplemented yet.')
    
        def build_rmpath(self):
            """Build right most path."""
            self.rmpath = list()
            old_frm = None
            for i in range(len(self) - 1, -1, -1):
                dfsedge = self[i]
                frm, to = dfsedge.frm, dfsedge.to
                if frm < to and (old_frm is None or to == old_frm):
                    self.rmpath.append(i)
                    old_frm = frm
            return self
    
        def get_num_vertices(self):
            """Return number of vertices in the corresponding graph."""
            return len(set(
                [dfsedge.frm for dfsedge in self] +
                [dfsedge.to for dfsedge in self]
            ))
    
    
    class PDFS(object):
        """PDFS class."""
    
        def __init__(self, gid=VACANT_GRAPH_ID, edge=None, prev=None):
            """Initialize PDFS instance."""
            self.gid = gid
            self.edge = edge
            self.prev = prev
    
    
    class Projected(list):
        """Projected is a list of PDFS.
    
        Each element of Projected is a projection one frequent graph in one
        original graph.
        """
    
        def __init__(self):
            """Initialize Projected instance."""
            super(Projected, self).__init__()
    
        def push_back(self, gid, edge, prev):
            """Update this Projected instance."""
            self.append(PDFS(gid, edge, prev))
            return self
    
    
    class History(object):
        """History class."""
    
        def __init__(self, g, pdfs):
            """Initialize History instance."""
            super(History, self).__init__()
            self.edges = list()
            self.vertices_used = collections.defaultdict(int)
            self.edges_used = collections.defaultdict(int)
            if pdfs is None:
                return
            while pdfs:
                e = pdfs.edge
                self.edges.append(e)
                (self.vertices_used[e.frm],
                 self.vertices_used[e.to],
                 self.edges_used[e.eid]) = 1, 1, 1
    
                pdfs = pdfs.prev
            self.edges = self.edges[::-1]
    
        def has_vertex(self, vid):
            """Check if the vertex with vid exists in the history."""
            return self.vertices_used[vid] == 1
    
        def has_edge(self, eid):
            """Check if the edge with eid exists in the history."""
            return self.edges_used[eid] == 1
    
    
    class gSpan(object):
        """`gSpan` algorithm."""
    
        def __init__(self,
                     task,
                     min_num_vertices=1,
                     max_num_vertices=float('inf'),
                     is_undirected=True,
                     verbose=False,
                     visualize=False,
                     where=False):
            """Initialize gSpan instance."""
            self._is_undirected = is_undirected
            self._task = task
            self._database = task.database
            self._min_num_vertices = min_num_vertices
            self._max_num_vertices = max_num_vertices
            self._DFScode = DFScode()
            self._support = 0
            self._frequent_size1_subgraphs = list()
            # Include subgraphs with
            # any num(but >= 2, <= max_num_vertices) of vertices.
            self._counter = itertools.count()
            self._verbose = verbose
            self._visualize = visualize
            self._where = where
            self.timestamps = dict()
            if self._max_num_vertices < self._min_num_vertices:
                print('Max number of vertices can not be smaller than '
                      'min number of that.\n'
                      'Set max_num_vertices = min_num_vertices.')
                self._max_num_vertices = self._min_num_vertices
    
        def time_stats(self):
            """Print stats of time."""
            func_names = ['run']
            time_deltas = collections.defaultdict(float)
            for fn in func_names:
                time_deltas[fn] = round(
                    self.timestamps[fn + '_out'] - self.timestamps[fn + '_in'],
                    2
                )
    
            print('Total:\t{} s'.format(time_deltas['run']))
    
            return self
    
        def _get_gid_subsets(self, projected):
            subsets = [[] for _ in self._task.gid_subsets]
            gids = set([g.gid for g in projected])
            for gid in gids:
                subsets[self._gid_subset_ids[gid]].append(gid)
            return subsets
    
        @record_timestamp
        def run(self):
            """Run the gSpan algorithm."""
            root = collections.defaultdict(Projected)
            gids = set([gid for gid_subset in self._task.gid_subsets for gid in gid_subset])
            self._gid_subset_ids = {}
            for i, gid_subset in enumerate(self._task.gid_subsets):
                for gid in gid_subset:
                    self._gid_subset_ids[gid] = i
    
            for gid in gids:
                g = self._database._graphs[gid]
                for vid, v in g.vertices.items():
                    edges = self._get_forward_root_edges(g, vid)
                    for e in edges:
                        root[(v.vlb, e.elb, g.vertices[e.to].vlb)].append(
                            PDFS(gid, e, None)
                        )
    
            for vevlb, projected in root.items():
                self._DFScode.append(DFSedge(0, 1, vevlb))
                self._subgraph_mining(projected)
                self._DFScode.pop()
    
        def _report(self, projected):
            self._frequent_subgraphs.append(copy.copy(self._DFScode))
            if self._DFScode.get_num_vertices() < self._min_num_vertices:
                return
            g = self._DFScode.to_graph(gid=next(self._counter),
                                       is_undirected=self._is_undirected)
            display_str = g.display()
            print('\nSupport: {}'.format(self._support))
    
            if self._visualize:
                g.plot()
            if self._where:
                print('where: {}'.format(list(set([p.gid for p in projected]))))
            print('\n-----------------\n')
    
        def print_results(self):
            for i, subgraph in enumerate(self._frequent_subgraphs):
                g = subgraph.to_graph(gid=next(self._counter),
                                      is_undirected=self._is_undirected)
                g.display()
                print(self._subgraph_occurrences[i])
    
        def _get_forward_root_edges(self, g, frm):
            result = []
            v_frm = g.vertices[frm]
            for to, e in v_frm.edges.items():
                if (not self._is_undirected) or v_frm.vlb <= g.vertices[to].vlb:
                    result.append(e)
            return result
    
        def _get_backward_edge(self, g, e1, e2, history):
            if self._is_undirected and e1 == e2:
                return None
            for to, e in g.vertices[e2.to].edges.items():
                if history.has_edge(e.eid) or e.to != e1.frm:
                    continue
                # if reture here, then self._DFScodep[0] != dfs_code_min[0]
                # should be checked in _is_min(). or:
                if self._is_undirected:
                    if e1.elb < e.elb or (
                            e1.elb == e.elb and
                            g.vertices[e1.to].vlb <= g.vertices[e2.to].vlb):
                        return e
                else:
                    if g.vertices[e1.frm].vlb < g.vertices[e2.to] or (
                            g.vertices[e1.frm].vlb == g.vertices[e2.to] and
                            e1.elb <= e.elb):
                        return e
                # if e1.elb < e.elb or (e1.elb == e.elb and
                #     g.vertices[e1.to].vlb <= g.vertices[e2.to].vlb):
                #     return e
            return None
    
        def _get_forward_pure_edges(self, g, rm_edge, min_vlb, history):
            result = []
            for to, e in g.vertices[rm_edge.to].edges.items():
                if min_vlb <= g.vertices[e.to].vlb and (
                        not history.has_vertex(e.to)):
                    result.append(e)
            return result
    
        def _get_forward_rmpath_edges(self, g, rm_edge, min_vlb, history):
            result = []
            to_vlb = g.vertices[rm_edge.to].vlb
            for to, e in g.vertices[rm_edge.frm].edges.items():
                new_to_vlb = g.vertices[to].vlb
                if (rm_edge.to == e.to or
                        min_vlb > new_to_vlb or
                        history.has_vertex(e.to)):
                    continue
                if rm_edge.elb < e.elb or (rm_edge.elb == e.elb and
                                           to_vlb <= new_to_vlb):
                    result.append(e)
            return result
    
        def _is_min(self):
            if self._verbose:
                print('is_min: checking {}'.format(self._DFScode))
            if len(self._DFScode) == 1:
                return True
            g = self._DFScode.to_graph(gid=VACANT_GRAPH_ID,
                                       is_undirected=self._is_undirected)
            dfs_code_min = DFScode()
            root = collections.defaultdict(Projected)
            for vid, v in g.vertices.items():
                edges = self._get_forward_root_edges(g, vid)
                for e in edges:
                    root[(v.vlb, e.elb, g.vertices[e.to].vlb)].append(
                        PDFS(g.gid, e, None))
            min_vevlb = min(root.keys())
            dfs_code_min.append(DFSedge(0, 1, min_vevlb))
    
            # No need to check if is min code because of pruning in get_*_edge*.
    
            def project_is_min(projected):
                dfs_code_min.build_rmpath()
                rmpath = dfs_code_min.rmpath
                min_vlb = dfs_code_min[0].vevlb[0]
                maxtoc = dfs_code_min[rmpath[0]].to
    
                backward_root = collections.defaultdict(Projected)
                flag, newto = False, 0,
                end = 0 if self._is_undirected else -1
                for i in range(len(rmpath) - 1, end, -1):
                    if flag:
                        break
                    for p in projected:
                        history = History(g, p)
                        e = self._get_backward_edge(g,
                                                    history.edges[rmpath[i]],
                                                    history.edges[rmpath[0]],
                                                    history)
                        if e is not None:
                            backward_root[e.elb].append(PDFS(g.gid, e, p))
                            newto = dfs_code_min[rmpath[i]].frm
                            flag = True
                if flag:
                    backward_min_elb = min(backward_root.keys())
                    dfs_code_min.append(DFSedge(
                        maxtoc, newto,
                        (VACANT_VERTEX_LABEL,
                         backward_min_elb,
                         VACANT_VERTEX_LABEL)
                    ))
                    idx = len(dfs_code_min) - 1
                    if self._DFScode[idx] != dfs_code_min[idx]:
                        return False
                    return project_is_min(backward_root[backward_min_elb])
    
                forward_root = collections.defaultdict(Projected)
                flag, newfrm = False, 0
                for p in projected:
                    history = History(g, p)
                    edges = self._get_forward_pure_edges(g,
                                                         history.edges[rmpath[0]],
                                                         min_vlb,
                                                         history)
                    if len(edges) > 0:
                        flag = True
                        newfrm = maxtoc
                        for e in edges:
                            forward_root[
                                (e.elb, g.vertices[e.to].vlb)
                            ].append(PDFS(g.gid, e, p))
                for rmpath_i in rmpath:
                    if flag:
                        break
                    for p in projected:
                        history = History(g, p)
                        edges = self._get_forward_rmpath_edges(g,
                                                               history.edges[
                                                                   rmpath_i],
                                                               min_vlb,
                                                               history)
                        if len(edges) > 0:
                            flag = True
                            newfrm = dfs_code_min[rmpath_i].frm
                            for e in edges:
                                forward_root[
                                    (e.elb, g.vertices[e.to].vlb)
                                ].append(PDFS(g.gid, e, p))
    
                if not flag:
                    return True
    
                forward_min_evlb = min(forward_root.keys())
                dfs_code_min.append(DFSedge(
                    newfrm, maxtoc + 1,
                    (VACANT_VERTEX_LABEL, forward_min_evlb[0], forward_min_evlb[1]))
                )
                idx = len(dfs_code_min) - 1
                if self._DFScode[idx] != dfs_code_min[idx]:
                    return False
                return project_is_min(forward_root[forward_min_evlb])
    
            res = project_is_min(root[min_vevlb])
            return res
    
        def _subgraph_mining(self, projected):
            gid_subsets = self._get_gid_subsets(projected)
            if self._task.prune(gid_subsets):
                return
            if not self._is_min():
                return
            self._task.store(repr(self._DFScode), gid_subsets)
    
            num_vertices = self._DFScode.get_num_vertices()
            self._DFScode.build_rmpath()
            rmpath = self._DFScode.rmpath
            maxtoc = self._DFScode[rmpath[0]].to
            min_vlb = self._DFScode[0].vevlb[0]
    
            forward_root = collections.defaultdict(Projected)
            backward_root = collections.defaultdict(Projected)
            for p in projected:
                g = self._database._graphs[p.gid]
                history = History(g, p)
                # backward
                for rmpath_i in rmpath[::-1]:
                    e = self._get_backward_edge(g,
                                                history.edges[rmpath_i],
                                                history.edges[rmpath[0]],
                                                history)
                    if e is not None:
                        backward_root[
                            (self._DFScode[rmpath_i].frm, e.elb)
                        ].append(PDFS(g.gid, e, p))
                # pure forward
                if num_vertices >= self._max_num_vertices:
                    continue
                edges = self._get_forward_pure_edges(g,
                                                     history.edges[rmpath[0]],
                                                     min_vlb,
                                                     history)
                for e in edges:
                    forward_root[
                        (maxtoc, e.elb, g.vertices[e.to].vlb)
                    ].append(PDFS(g.gid, e, p))
                # rmpath forward
                for rmpath_i in rmpath:
                    edges = self._get_forward_rmpath_edges(g,
                                                           history.edges[rmpath_i],
                                                           min_vlb,
                                                           history)
                    for e in edges:
                        forward_root[
                            (self._DFScode[rmpath_i].frm,
                             e.elb, g.vertices[e.to].vlb)
                        ].append(PDFS(g.gid, e, p))
    
            # backward
            for to, elb in backward_root:
                self._DFScode.append(DFSedge(
                    maxtoc, to,
                    (VACANT_VERTEX_LABEL, elb, VACANT_VERTEX_LABEL))
                )
                self._subgraph_mining(backward_root[(to, elb)])
                self._DFScode.pop()
            # forward
            # No need to check if num_vertices >= self._max_num_vertices.
            # Because forward_root has no element.
            for frm, elb, vlb2 in forward_root:
                self._DFScode.append(DFSedge(
                    frm, maxtoc + 1,
                    (VACANT_VERTEX_LABEL, elb, vlb2))
                )
                self._subgraph_mining(forward_root[(frm, elb, vlb2)])
                self._DFScode.pop()
    
            return self