/brz/remove-bazaar

# Copyright (C) 2007, 2008, 2009 Canonical Ltd

#

# This program is free software; you can redistribute it and/or modify

# it under the terms of the GNU General Public License as published by

# the Free Software Foundation; either version 2 of the License, or

# (at your option) any later version.

#

# This program is distributed in the hope that it will be useful,

# but WITHOUT ANY WARRANTY; without even the implied warranty of

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

# GNU General Public License for more details.

#

# You should have received a copy of the GNU General Public License

# along with this program; if not, write to the Free Software

# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA

import time

from bzrlib import (

    debug,

    errors,

    osutils,

    revision,

    trace,

    tsort,

    )

from bzrlib.symbol_versioning import deprecated_function, deprecated_in

STEP_UNIQUE_SEARCHER_EVERY = 5

# DIAGRAM of terminology

#       A

#       /\

#      B  C

#      |  |\

#      D  E F

#      |\/| |

#      |/\|/

#      G  H

#

# In this diagram, relative to G and H:

# A, B, C, D, E are common ancestors.

# C, D and E are border ancestors, because each has a non-common descendant.

# D and E are least common ancestors because none of their descendants are

# common ancestors.

# C is not a least common ancestor because its descendant, E, is a common

# ancestor.

#

# The find_unique_lca algorithm will pick A in two steps:

# 1. find_lca('G', 'H') => ['D', 'E']

# 2. Since len(['D', 'E']) > 1, find_lca('D', 'E') => ['A']

class DictParentsProvider(object):

    """A parents provider for Graph objects."""

    def __init__(self, ancestry):

        self.ancestry = ancestry

    def __repr__(self):

        return 'DictParentsProvider(%r)' % self.ancestry

    def get_parent_map(self, keys):

        """See StackedParentsProvider.get_parent_map"""

        ancestry = self.ancestry

        return dict((k, ancestry[k]) for k in keys if k in ancestry)

@deprecated_function(deprecated_in((1, 16, 0)))

def _StackedParentsProvider(*args, **kwargs):

    return StackedParentsProvider(*args, **kwargs)

class StackedParentsProvider(object):

    """A parents provider which stacks (or unions) multiple providers.

    The providers are queries in the order of the provided parent_providers.

    """

    def __init__(self, parent_providers):

        self._parent_providers = parent_providers

    def __repr__(self):

        return "%s(%r)" % (self.__class__.__name__, self._parent_providers)

    def get_parent_map(self, keys):

        """Get a mapping of keys => parents

        A dictionary is returned with an entry for each key present in this

        source. If this source doesn't have information about a key, it should

        not include an entry.

        [NULL_REVISION] is used as the parent of the first user-committed

        revision.  Its parent list is empty.

        :param keys: An iterable returning keys to check (eg revision_ids)

        :return: A dictionary mapping each key to its parents

        """

        found = {}

        remaining = set(keys)

        for parents_provider in self._parent_providers:

            new_found = parents_provider.get_parent_map(remaining)

            found.update(new_found)

            remaining.difference_update(new_found)

            if not remaining:

                break

        return found

class CachingParentsProvider(object):

    """A parents provider which will cache the revision => parents as a dict.

    This is useful for providers which have an expensive look up.

    Either a ParentsProvider or a get_parent_map-like callback may be

    supplied.  If it provides extra un-asked-for parents, they will be cached,

    but filtered out of get_parent_map.

    The cache is enabled by default, but may be disabled and re-enabled.

    """

    def __init__(self, parent_provider=None, get_parent_map=None):

        """Constructor.

        :param parent_provider: The ParentProvider to use.  It or

            get_parent_map must be supplied.

        :param get_parent_map: The get_parent_map callback to use.  It or

            parent_provider must be supplied.

        """

        self._real_provider = parent_provider

        if get_parent_map is None:

            self._get_parent_map = self._real_provider.get_parent_map

        else:

            self._get_parent_map = get_parent_map

        self._cache = None

        self.enable_cache(True)

    def __repr__(self):

        return "%s(%r)" % (self.__class__.__name__, self._real_provider)

    def enable_cache(self, cache_misses=True):

        """Enable cache."""

        if self._cache is not None:

            raise AssertionError('Cache enabled when already enabled.')

        self._cache = {}

        self._cache_misses = cache_misses

        self.missing_keys = set()

    def disable_cache(self):

        """Disable and clear the cache."""

        self._cache = None

        self._cache_misses = None

        self.missing_keys = set()

    def get_cached_map(self):

        """Return any cached get_parent_map values."""

        if self._cache is None:

            return None

        return dict(self._cache)

    def get_parent_map(self, keys):

        """See StackedParentsProvider.get_parent_map."""

        cache = self._cache

        if cache is None:

            cache = self._get_parent_map(keys)

        else:

            needed_revisions = set(key for key in keys if key not in cache)

            # Do not ask for negatively cached keys

            needed_revisions.difference_update(self.missing_keys)

            if needed_revisions:

                parent_map = self._get_parent_map(needed_revisions)

                cache.update(parent_map)

                if self._cache_misses:

                    for key in needed_revisions:

                        if key not in parent_map:

                            self.note_missing_key(key)

        result = {}

        for key in keys:

            value = cache.get(key)

            if value is not None:

                result[key] = value

        return result

    def note_missing_key(self, key):

        """Note that key is a missing key."""

        if self._cache_misses:

            self.missing_keys.add(key)

class Graph(object):

    """Provide incremental access to revision graphs.

    This is the generic implementation; it is intended to be subclassed to

    specialize it for other repository types.

    """

    def __init__(self, parents_provider):

        """Construct a Graph that uses several graphs as its input

        This should not normally be invoked directly, because there may be

        specialized implementations for particular repository types.  See

        Repository.get_graph().

        :param parents_provider: An object providing a get_parent_map call

            conforming to the behavior of

            StackedParentsProvider.get_parent_map.

        """

        if getattr(parents_provider, 'get_parents', None) is not None:

            self.get_parents = parents_provider.get_parents

        if getattr(parents_provider, 'get_parent_map', None) is not None:

            self.get_parent_map = parents_provider.get_parent_map

        self._parents_provider = parents_provider

    def __repr__(self):

        return 'Graph(%r)' % self._parents_provider

    def find_lca(self, *revisions):

        """Determine the lowest common ancestors of the provided revisions

        A lowest common ancestor is a common ancestor none of whose

        descendants are common ancestors.  In graphs, unlike trees, there may

        be multiple lowest common ancestors.

        This algorithm has two phases.  Phase 1 identifies border ancestors,

        and phase 2 filters border ancestors to determine lowest common

        ancestors.

        In phase 1, border ancestors are identified, using a breadth-first

        search starting at the bottom of the graph.  Searches are stopped

        whenever a node or one of its descendants is determined to be common

        In phase 2, the border ancestors are filtered to find the least

        common ancestors.  This is done by searching the ancestries of each

        border ancestor.

        Phase 2 is perfomed on the principle that a border ancestor that is

        not an ancestor of any other border ancestor is a least common

        ancestor.

        Searches are stopped when they find a node that is determined to be a

        common ancestor of all border ancestors, because this shows that it

        cannot be a descendant of any border ancestor.

        The scaling of this operation should be proportional to

        1. The number of uncommon ancestors

        2. The number of border ancestors

        3. The length of the shortest path between a border ancestor and an

           ancestor of all border ancestors.

        """

        border_common, common, sides = self._find_border_ancestors(revisions)

        # We may have common ancestors that can be reached from each other.

        # - ask for the heads of them to filter it down to only ones that

        # cannot be reached from each other - phase 2.

        return self.heads(border_common)

    def find_difference(self, left_revision, right_revision):

        """Determine the graph difference between two revisions"""

        border, common, searchers = self._find_border_ancestors(

            [left_revision, right_revision])

        self._search_for_extra_common(common, searchers)

        left = searchers[0].seen

        right = searchers[1].seen

        return (left.difference(right), right.difference(left))

    def find_distance_to_null(self, target_revision_id, known_revision_ids):

        """Find the left-hand distance to the NULL_REVISION.

        (This can also be considered the revno of a branch at

        target_revision_id.)

        :param target_revision_id: A revision_id which we would like to know

            the revno for.

        :param known_revision_ids: [(revision_id, revno)] A list of known

            revno, revision_id tuples. We'll use this to seed the search.

        """

        # Map from revision_ids to a known value for their revno

        known_revnos = dict(known_revision_ids)

        cur_tip = target_revision_id

        num_steps = 0

        NULL_REVISION = revision.NULL_REVISION

        known_revnos[NULL_REVISION] = 0

        searching_known_tips = list(known_revnos.keys())

        unknown_searched = {}

        while cur_tip not in known_revnos:

            unknown_searched[cur_tip] = num_steps

            num_steps += 1

            to_search = set([cur_tip])

            to_search.update(searching_known_tips)

            parent_map = self.get_parent_map(to_search)

            parents = parent_map.get(cur_tip, None)

            if not parents: # An empty list or None is a ghost

                raise errors.GhostRevisionsHaveNoRevno(target_revision_id,

                                                       cur_tip)

            cur_tip = parents[0]

            next_known_tips = []

            for revision_id in searching_known_tips:

                parents = parent_map.get(revision_id, None)

                if not parents:

                    continue

                next = parents[0]

                next_revno = known_revnos[revision_id] - 1

                if next in unknown_searched:

                    # We have enough information to return a value right now

                    return next_revno + unknown_searched[next]

                if next in known_revnos:

                    continue

                known_revnos[next] = next_revno

                next_known_tips.append(next)

            searching_known_tips = next_known_tips

        # We reached a known revision, so just add in how many steps it took to

        # get there.

        return known_revnos[cur_tip] + num_steps

    def find_unique_ancestors(self, unique_revision, common_revisions):

        """Find the unique ancestors for a revision versus others.

        This returns the ancestry of unique_revision, excluding all revisions

        in the ancestry of common_revisions. If unique_revision is in the

        ancestry, then the empty set will be returned.

        :param unique_revision: The revision_id whose ancestry we are

            interested in.

            XXX: Would this API be better if we allowed multiple revisions on

                 to be searched here?

        :param common_revisions: Revision_ids of ancestries to exclude.

        :return: A set of revisions in the ancestry of unique_revision

        """

        if unique_revision in common_revisions:

            return set()

        # Algorithm description

        # 1) Walk backwards from the unique node and all common nodes.

        # 2) When a node is seen by both sides, stop searching it in the unique

        #    walker, include it in the common walker.

        # 3) Stop searching when there are no nodes left for the unique walker.

        #    At this point, you have a maximal set of unique nodes. Some of

        #    them may actually be common, and you haven't reached them yet.

        # 4) Start new searchers for the unique nodes, seeded with the

        #    information you have so far.

        # 5) Continue searching, stopping the common searches when the search

        #    tip is an ancestor of all unique nodes.

        # 6) Aggregate together unique searchers when they are searching the

        #    same tips. When all unique searchers are searching the same node,

        #    stop move it to a single 'all_unique_searcher'.

        # 7) The 'all_unique_searcher' represents the very 'tip' of searching.

        #    Most of the time this produces very little important information.

        #    So don't step it as quickly as the other searchers.

        # 8) Search is done when all common searchers have completed.

        unique_searcher, common_searcher = self._find_initial_unique_nodes(

            [unique_revision], common_revisions)

        unique_nodes = unique_searcher.seen.difference(common_searcher.seen)

        if not unique_nodes:

            return unique_nodes

        (all_unique_searcher,

         unique_tip_searchers) = self._make_unique_searchers(unique_nodes,

                                    unique_searcher, common_searcher)

        self._refine_unique_nodes(unique_searcher, all_unique_searcher,

                                  unique_tip_searchers, common_searcher)

        true_unique_nodes = unique_nodes.difference(common_searcher.seen)

        if 'graph' in debug.debug_flags:

            trace.mutter('Found %d truly unique nodes out of %d',

                         len(true_unique_nodes), len(unique_nodes))

        return true_unique_nodes

    def _find_initial_unique_nodes(self, unique_revisions, common_revisions):

        """Steps 1-3 of find_unique_ancestors.

        Find the maximal set of unique nodes. Some of these might actually

        still be common, but we are sure that there are no other unique nodes.

        :return: (unique_searcher, common_searcher)

        """

        unique_searcher = self._make_breadth_first_searcher(unique_revisions)

        # we know that unique_revisions aren't in common_revisions, so skip

        # past them.

        unique_searcher.next()

        common_searcher = self._make_breadth_first_searcher(common_revisions)

        # As long as we are still finding unique nodes, keep searching

        while unique_searcher._next_query:

            next_unique_nodes = set(unique_searcher.step())

            next_common_nodes = set(common_searcher.step())

            # Check if either searcher encounters new nodes seen by the other

            # side.

            unique_are_common_nodes = next_unique_nodes.intersection(

                common_searcher.seen)

            unique_are_common_nodes.update(

                next_common_nodes.intersection(unique_searcher.seen))

            if unique_are_common_nodes:

                ancestors = unique_searcher.find_seen_ancestors(

                                unique_are_common_nodes)

                # TODO: This is a bit overboard, we only really care about

                #       the ancestors of the tips because the rest we

                #       already know. This is *correct* but causes us to

                #       search too much ancestry.

                ancestors.update(common_searcher.find_seen_ancestors(ancestors))

                unique_searcher.stop_searching_any(ancestors)

                common_searcher.start_searching(ancestors)

        return unique_searcher, common_searcher

    def _make_unique_searchers(self, unique_nodes, unique_searcher,

                               common_searcher):

        """Create a searcher for all the unique search tips (step 4).

        As a side effect, the common_searcher will stop searching any nodes

        that are ancestors of the unique searcher tips.

        :return: (all_unique_searcher, unique_tip_searchers)

        """

        unique_tips = self._remove_simple_descendants(unique_nodes,

                        self.get_parent_map(unique_nodes))

        if len(unique_tips) == 1:

            unique_tip_searchers = []

            ancestor_all_unique = unique_searcher.find_seen_ancestors(unique_tips)

        else:

            unique_tip_searchers = []

            for tip in unique_tips:

                revs_to_search = unique_searcher.find_seen_ancestors([tip])

                revs_to_search.update(

                    common_searcher.find_seen_ancestors(revs_to_search))

                searcher = self._make_breadth_first_searcher(revs_to_search)

                # We don't care about the starting nodes.

                searcher._label = tip

                searcher.step()

                unique_tip_searchers.append(searcher)

            ancestor_all_unique = None

            for searcher in unique_tip_searchers:

                if ancestor_all_unique is None:

                    ancestor_all_unique = set(searcher.seen)

                else:

                    ancestor_all_unique = ancestor_all_unique.intersection(

                                                searcher.seen)

        # Collapse all the common nodes into a single searcher

        all_unique_searcher = self._make_breadth_first_searcher(

                                ancestor_all_unique)

        if ancestor_all_unique:

            # We've seen these nodes in all the searchers, so we'll just go to

            # the next

            all_unique_searcher.step()

            # Stop any search tips that are already known as ancestors of the

            # unique nodes

            stopped_common = common_searcher.stop_searching_any(

                common_searcher.find_seen_ancestors(ancestor_all_unique))

            total_stopped = 0

            for searcher in unique_tip_searchers:

                total_stopped += len(searcher.stop_searching_any(

                    searcher.find_seen_ancestors(ancestor_all_unique)))

        if 'graph' in debug.debug_flags:

            trace.mutter('For %d unique nodes, created %d + 1 unique searchers'

                         ' (%d stopped search tips, %d common ancestors'

                         ' (%d stopped common)',

                         len(unique_nodes), len(unique_tip_searchers),

                         total_stopped, len(ancestor_all_unique),

                         len(stopped_common))

        return all_unique_searcher, unique_tip_searchers

    def _step_unique_and_common_searchers(self, common_searcher,

                                          unique_tip_searchers,

                                          unique_searcher):

        """Step all the searchers"""

        newly_seen_common = set(common_searcher.step())

        newly_seen_unique = set()

        for searcher in unique_tip_searchers:

            next = set(searcher.step())

            next.update(unique_searcher.find_seen_ancestors(next))

            next.update(common_searcher.find_seen_ancestors(next))

            for alt_searcher in unique_tip_searchers:

                if alt_searcher is searcher:

                    continue

                next.update(alt_searcher.find_seen_ancestors(next))

            searcher.start_searching(next)

            newly_seen_unique.update(next)

        return newly_seen_common, newly_seen_unique

    def _find_nodes_common_to_all_unique(self, unique_tip_searchers,

                                         all_unique_searcher,

                                         newly_seen_unique, step_all_unique):

        """Find nodes that are common to all unique_tip_searchers.

        If it is time, step the all_unique_searcher, and add its nodes to the

        result.

        """

        common_to_all_unique_nodes = newly_seen_unique.copy()

        for searcher in unique_tip_searchers:

            common_to_all_unique_nodes.intersection_update(searcher.seen)

        common_to_all_unique_nodes.intersection_update(

                                    all_unique_searcher.seen)

        # Step all-unique less frequently than the other searchers.

        # In the common case, we don't need to spider out far here, so

        # avoid doing extra work.

        if step_all_unique:

            tstart = time.clock()

            nodes = all_unique_searcher.step()

            common_to_all_unique_nodes.update(nodes)

            if 'graph' in debug.debug_flags:

                tdelta = time.clock() - tstart

                trace.mutter('all_unique_searcher step() took %.3fs'

                             'for %d nodes (%d total), iteration: %s',

                             tdelta, len(nodes), len(all_unique_searcher.seen),

                             all_unique_searcher._iterations)

        return common_to_all_unique_nodes

    def _collapse_unique_searchers(self, unique_tip_searchers,

                                   common_to_all_unique_nodes):

        """Combine searchers that are searching the same tips.

        When two searchers are searching the same tips, we can stop one of the

        searchers. We also know that the maximal set of common ancestors is the

        intersection of the two original searchers.

        :return: A list of searchers that are searching unique nodes.

        """

        # Filter out searchers that don't actually search different

        # nodes. We already have the ancestry intersection for them

        unique_search_tips = {}

        for searcher in unique_tip_searchers:

            stopped = searcher.stop_searching_any(common_to_all_unique_nodes)

            will_search_set = frozenset(searcher._next_query)

            if not will_search_set:

                if 'graph' in debug.debug_flags:

                    trace.mutter('Unique searcher %s was stopped.'

                                 ' (%s iterations) %d nodes stopped',

                                 searcher._label,

                                 searcher._iterations,

                                 len(stopped))

            elif will_search_set not in unique_search_tips:

                # This searcher is searching a unique set of nodes, let it

                unique_search_tips[will_search_set] = [searcher]

            else:

                unique_search_tips[will_search_set].append(searcher)

        # TODO: it might be possible to collapse searchers faster when they

        #       only have *some* search tips in common.

        next_unique_searchers = []

        for searchers in unique_search_tips.itervalues():

            if len(searchers) == 1:

                # Searching unique tips, go for it

                next_unique_searchers.append(searchers[0])

            else:

                # These searchers have started searching the same tips, we

                # don't need them to cover the same ground. The

                # intersection of their ancestry won't change, so create a

                # new searcher, combining their histories.

                next_searcher = searchers[0]

                for searcher in searchers[1:]:

                    next_searcher.seen.intersection_update(searcher.seen)

                if 'graph' in debug.debug_flags:

                    trace.mutter('Combining %d searchers into a single'

                                 ' searcher searching %d nodes with'

                                 ' %d ancestry',

                                 len(searchers),

                                 len(next_searcher._next_query),

                                 len(next_searcher.seen))

                next_unique_searchers.append(next_searcher)

        return next_unique_searchers

    def _refine_unique_nodes(self, unique_searcher, all_unique_searcher,

                             unique_tip_searchers, common_searcher):

        """Steps 5-8 of find_unique_ancestors.

        This function returns when common_searcher has stopped searching for

        more nodes.

        """

        # We step the ancestor_all_unique searcher only every

        # STEP_UNIQUE_SEARCHER_EVERY steps.

        step_all_unique_counter = 0

        # While we still have common nodes to search

        while common_searcher._next_query:

            (newly_seen_common,

             newly_seen_unique) = self._step_unique_and_common_searchers(

                common_searcher, unique_tip_searchers, unique_searcher)

            # These nodes are common ancestors of all unique nodes

            common_to_all_unique_nodes = self._find_nodes_common_to_all_unique(

                unique_tip_searchers, all_unique_searcher, newly_seen_unique,

                step_all_unique_counter==0)

            step_all_unique_counter = ((step_all_unique_counter + 1)

                                       % STEP_UNIQUE_SEARCHER_EVERY)

            if newly_seen_common:

                # If a 'common' node is an ancestor of all unique searchers, we

                # can stop searching it.

                common_searcher.stop_searching_any(

                    all_unique_searcher.seen.intersection(newly_seen_common))

            if common_to_all_unique_nodes:

                common_to_all_unique_nodes.update(

                    common_searcher.find_seen_ancestors(

                        common_to_all_unique_nodes))

                # The all_unique searcher can start searching the common nodes

                # but everyone else can stop.

                # This is the sort of thing where we would like to not have it

                # start_searching all of the nodes, but only mark all of them

                # as seen, and have it search only the actual tips. Otherwise

                # it is another get_parent_map() traversal for it to figure out

                # what we already should know.

                all_unique_searcher.start_searching(common_to_all_unique_nodes)

                common_searcher.stop_searching_any(common_to_all_unique_nodes)

            next_unique_searchers = self._collapse_unique_searchers(

                unique_tip_searchers, common_to_all_unique_nodes)

            if len(unique_tip_searchers) != len(next_unique_searchers):

                if 'graph' in debug.debug_flags:

                    trace.mutter('Collapsed %d unique searchers => %d'

                                 ' at %s iterations',

                                 len(unique_tip_searchers),

                                 len(next_unique_searchers),

                                 all_unique_searcher._iterations)

            unique_tip_searchers = next_unique_searchers

    def get_parent_map(self, revisions):

        """Get a map of key:parent_list for revisions.

        This implementation delegates to get_parents, for old parent_providers

        that do not supply get_parent_map.

        """

        result = {}

        for rev, parents in self.get_parents(revisions):

            if parents is not None:

                result[rev] = parents

        return result

    def _make_breadth_first_searcher(self, revisions):

        return _BreadthFirstSearcher(revisions, self)

    def _find_border_ancestors(self, revisions):

        """Find common ancestors with at least one uncommon descendant.

        Border ancestors are identified using a breadth-first

        search starting at the bottom of the graph.  Searches are stopped

        whenever a node or one of its descendants is determined to be common.

        This will scale with the number of uncommon ancestors.

        As well as the border ancestors, a set of seen common ancestors and a

        list of sets of seen ancestors for each input revision is returned.

        This allows calculation of graph difference from the results of this

        operation.

        """

        if None in revisions:

            raise errors.InvalidRevisionId(None, self)

        common_ancestors = set()

        searchers = [self._make_breadth_first_searcher([r])

                     for r in revisions]

        active_searchers = searchers[:]

        border_ancestors = set()

        while True:

            newly_seen = set()

            for searcher in searchers:

                new_ancestors = searcher.step()

                if new_ancestors:

                    newly_seen.update(new_ancestors)

            new_common = set()

            for revision in newly_seen:

                if revision in common_ancestors:

                    # Not a border ancestor because it was seen as common

                    # already

                    new_common.add(revision)

                    continue

                for searcher in searchers:

                    if revision not in searcher.seen:

                        break

                else:

                    # This is a border because it is a first common that we see

                    # after walking for a while.

                    border_ancestors.add(revision)

                    new_common.add(revision)

            if new_common:

                for searcher in searchers:

                    new_common.update(searcher.find_seen_ancestors(new_common))

                for searcher in searchers:

                    searcher.start_searching(new_common)

                common_ancestors.update(new_common)

            # Figure out what the searchers will be searching next, and if

            # there is only 1 set being searched, then we are done searching,

            # since all searchers would have to be searching the same data,

            # thus it *must* be in common.

            unique_search_sets = set()

            for searcher in searchers:

                will_search_set = frozenset(searcher._next_query)

                if will_search_set not in unique_search_sets:

                    # This searcher is searching a unique set of nodes, let it

                    unique_search_sets.add(will_search_set)

            if len(unique_search_sets) == 1:

                nodes = unique_search_sets.pop()

                uncommon_nodes = nodes.difference(common_ancestors)

                if uncommon_nodes:

                    raise AssertionError("Somehow we ended up converging"

                                         " without actually marking them as"

                                         " in common."

                                         "\nStart_nodes: %s"

                                         "\nuncommon_nodes: %s"

                                         % (revisions, uncommon_nodes))

                break

        return border_ancestors, common_ancestors, searchers

    def heads(self, keys):

        """Return the heads from amongst keys.

        This is done by searching the ancestries of each key.  Any key that is

        reachable from another key is not returned; all the others are.

        This operation scales with the relative depth between any two keys. If

        any two keys are completely disconnected all ancestry of both sides

        will be retrieved.

        :param keys: An iterable of keys.

        :return: A set of the heads. Note that as a set there is no ordering

            information. Callers will need to filter their input to create

            order if they need it.

        """

        candidate_heads = set(keys)