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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/traversal/depth_first_search.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/traversal/depth_first_search.py
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+"""Basic algorithms for depth-first searching the nodes of a graph."""
+
+from collections import defaultdict
+
+import networkx as nx
+
+__all__ = [
+    "dfs_edges",
+    "dfs_tree",
+    "dfs_predecessors",
+    "dfs_successors",
+    "dfs_preorder_nodes",
+    "dfs_postorder_nodes",
+    "dfs_labeled_edges",
+]
+
+
+@nx._dispatchable
+def dfs_edges(G, source=None, depth_limit=None, *, sort_neighbors=None):
+    """Iterate over edges in a depth-first-search (DFS).
+
+    Perform a depth-first-search over the nodes of `G` and yield
+    the edges in order. This may not generate all edges in `G`
+    (see `~networkx.algorithms.traversal.edgedfs.edge_dfs`).
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+       Specify starting node for depth-first search and yield edges in
+       the component reachable from source.
+
+    depth_limit : int, optional (default=len(G))
+       Specify the maximum search depth.
+
+    sort_neighbors : function (default=None)
+        A function that takes an iterator over nodes as the input, and
+        returns an iterable of the same nodes with a custom ordering.
+        For example, `sorted` will sort the nodes in increasing order.
+
+    Yields
+    ------
+    edge: 2-tuple of nodes
+       Yields edges resulting from the depth-first-search.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> list(nx.dfs_edges(G, source=0))
+    [(0, 1), (1, 2), (2, 3), (3, 4)]
+    >>> list(nx.dfs_edges(G, source=0, depth_limit=2))
+    [(0, 1), (1, 2)]
+
+    Notes
+    -----
+    If a source is not specified then a source is chosen arbitrarily and
+    repeatedly until all components in the graph are searched.
+
+    The implementation of this function is adapted from David Eppstein's
+    depth-first search function in PADS [1]_, with modifications
+    to allow depth limits based on the Wikipedia article
+    "Depth-limited search" [2]_.
+
+    See Also
+    --------
+    dfs_preorder_nodes
+    dfs_postorder_nodes
+    dfs_labeled_edges
+    :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs`
+    :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_edges`
+
+    References
+    ----------
+    .. [1] http://www.ics.uci.edu/~eppstein/PADS
+    .. [2] https://en.wikipedia.org/wiki/Depth-limited_search
+    """
+    if source is None:
+        # edges for all components
+        nodes = G
+    else:
+        # edges for components with source
+        nodes = [source]
+    if depth_limit is None:
+        depth_limit = len(G)
+
+    get_children = (
+        G.neighbors
+        if sort_neighbors is None
+        else lambda n: iter(sort_neighbors(G.neighbors(n)))
+    )
+
+    visited = set()
+    for start in nodes:
+        if start in visited:
+            continue
+        visited.add(start)
+        stack = [(start, get_children(start))]
+        depth_now = 1
+        while stack:
+            parent, children = stack[-1]
+            for child in children:
+                if child not in visited:
+                    yield parent, child
+                    visited.add(child)
+                    if depth_now < depth_limit:
+                        stack.append((child, get_children(child)))
+                        depth_now += 1
+                        break
+            else:
+                stack.pop()
+                depth_now -= 1
+
+
+@nx._dispatchable(returns_graph=True)
+def dfs_tree(G, source=None, depth_limit=None, *, sort_neighbors=None):
+    """Returns oriented tree constructed from a depth-first-search from source.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+       Specify starting node for depth-first search.
+
+    depth_limit : int, optional (default=len(G))
+       Specify the maximum search depth.
+
+    sort_neighbors : function (default=None)
+        A function that takes an iterator over nodes as the input, and
+        returns an iterable of the same nodes with a custom ordering.
+        For example, `sorted` will sort the nodes in increasing order.
+
+    Returns
+    -------
+    T : NetworkX DiGraph
+       An oriented tree
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> T = nx.dfs_tree(G, source=0, depth_limit=2)
+    >>> list(T.edges())
+    [(0, 1), (1, 2)]
+    >>> T = nx.dfs_tree(G, source=0)
+    >>> list(T.edges())
+    [(0, 1), (1, 2), (2, 3), (3, 4)]
+
+    See Also
+    --------
+    dfs_preorder_nodes
+    dfs_postorder_nodes
+    dfs_labeled_edges
+    :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs`
+    :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree`
+    """
+    T = nx.DiGraph()
+    if source is None:
+        T.add_nodes_from(G)
+    else:
+        T.add_node(source)
+    T.add_edges_from(dfs_edges(G, source, depth_limit, sort_neighbors=sort_neighbors))
+    return T
+
+
+@nx._dispatchable
+def dfs_predecessors(G, source=None, depth_limit=None, *, sort_neighbors=None):
+    """Returns dictionary of predecessors in depth-first-search from source.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+       Specify starting node for depth-first search.
+       Note that you will get predecessors for all nodes in the
+       component containing `source`. This input only specifies
+       where the DFS starts.
+
+    depth_limit : int, optional (default=len(G))
+       Specify the maximum search depth.
+
+    sort_neighbors : function (default=None)
+        A function that takes an iterator over nodes as the input, and
+        returns an iterable of the same nodes with a custom ordering.
+        For example, `sorted` will sort the nodes in increasing order.
+
+    Returns
+    -------
+    pred: dict
+       A dictionary with nodes as keys and predecessor nodes as values.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> nx.dfs_predecessors(G, source=0)
+    {1: 0, 2: 1, 3: 2}
+    >>> nx.dfs_predecessors(G, source=0, depth_limit=2)
+    {1: 0, 2: 1}
+
+    Notes
+    -----
+    If a source is not specified then a source is chosen arbitrarily and
+    repeatedly until all components in the graph are searched.
+
+    The implementation of this function is adapted from David Eppstein's
+    depth-first search function in `PADS`_, with modifications
+    to allow depth limits based on the Wikipedia article
+    "`Depth-limited search`_".
+
+    .. _PADS: http://www.ics.uci.edu/~eppstein/PADS
+    .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search
+
+    See Also
+    --------
+    dfs_preorder_nodes
+    dfs_postorder_nodes
+    dfs_labeled_edges
+    :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs`
+    :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree`
+    """
+    return {
+        t: s
+        for s, t in dfs_edges(G, source, depth_limit, sort_neighbors=sort_neighbors)
+    }
+
+
+@nx._dispatchable
+def dfs_successors(G, source=None, depth_limit=None, *, sort_neighbors=None):
+    """Returns dictionary of successors in depth-first-search from source.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+       Specify starting node for depth-first search.
+       Note that you will get successors for all nodes in the
+       component containing `source`. This input only specifies
+       where the DFS starts.
+
+    depth_limit : int, optional (default=len(G))
+       Specify the maximum search depth.
+
+    sort_neighbors : function (default=None)
+        A function that takes an iterator over nodes as the input, and
+        returns an iterable of the same nodes with a custom ordering.
+        For example, `sorted` will sort the nodes in increasing order.
+
+    Returns
+    -------
+    succ: dict
+       A dictionary with nodes as keys and list of successor nodes as values.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> nx.dfs_successors(G, source=0)
+    {0: [1], 1: [2], 2: [3], 3: [4]}
+    >>> nx.dfs_successors(G, source=0, depth_limit=2)
+    {0: [1], 1: [2]}
+
+    Notes
+    -----
+    If a source is not specified then a source is chosen arbitrarily and
+    repeatedly until all components in the graph are searched.
+
+    The implementation of this function is adapted from David Eppstein's
+    depth-first search function in `PADS`_, with modifications
+    to allow depth limits based on the Wikipedia article
+    "`Depth-limited search`_".
+
+    .. _PADS: http://www.ics.uci.edu/~eppstein/PADS
+    .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search
+
+    See Also
+    --------
+    dfs_preorder_nodes
+    dfs_postorder_nodes
+    dfs_labeled_edges
+    :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs`
+    :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree`
+    """
+    d = defaultdict(list)
+    for s, t in dfs_edges(
+        G,
+        source=source,
+        depth_limit=depth_limit,
+        sort_neighbors=sort_neighbors,
+    ):
+        d[s].append(t)
+    return dict(d)
+
+
+@nx._dispatchable
+def dfs_postorder_nodes(G, source=None, depth_limit=None, *, sort_neighbors=None):
+    """Generate nodes in a depth-first-search post-ordering starting at source.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+       Specify starting node for depth-first search.
+
+    depth_limit : int, optional (default=len(G))
+       Specify the maximum search depth.
+
+    sort_neighbors : function (default=None)
+        A function that takes an iterator over nodes as the input, and
+        returns an iterable of the same nodes with a custom ordering.
+        For example, `sorted` will sort the nodes in increasing order.
+
+    Returns
+    -------
+    nodes: generator
+       A generator of nodes in a depth-first-search post-ordering.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> list(nx.dfs_postorder_nodes(G, source=0))
+    [4, 3, 2, 1, 0]
+    >>> list(nx.dfs_postorder_nodes(G, source=0, depth_limit=2))
+    [1, 0]
+
+    Notes
+    -----
+    If a source is not specified then a source is chosen arbitrarily and
+    repeatedly until all components in the graph are searched.
+
+    The implementation of this function is adapted from David Eppstein's
+    depth-first search function in `PADS`_, with modifications
+    to allow depth limits based on the Wikipedia article
+    "`Depth-limited search`_".
+
+    .. _PADS: http://www.ics.uci.edu/~eppstein/PADS
+    .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search
+
+    See Also
+    --------
+    dfs_edges
+    dfs_preorder_nodes
+    dfs_labeled_edges
+    :func:`~networkx.algorithms.traversal.edgedfs.edge_dfs`
+    :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_tree`
+    """
+    edges = nx.dfs_labeled_edges(
+        G, source=source, depth_limit=depth_limit, sort_neighbors=sort_neighbors
+    )
+    return (v for u, v, d in edges if d == "reverse")
+
+
+@nx._dispatchable
+def dfs_preorder_nodes(G, source=None, depth_limit=None, *, sort_neighbors=None):
+    """Generate nodes in a depth-first-search pre-ordering starting at source.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+       Specify starting node for depth-first search and return nodes in
+       the component reachable from source.
+
+    depth_limit : int, optional (default=len(G))
+       Specify the maximum search depth.
+
+    sort_neighbors : function (default=None)
+        A function that takes an iterator over nodes as the input, and
+        returns an iterable of the same nodes with a custom ordering.
+        For example, `sorted` will sort the nodes in increasing order.
+
+    Returns
+    -------
+    nodes: generator
+       A generator of nodes in a depth-first-search pre-ordering.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> list(nx.dfs_preorder_nodes(G, source=0))
+    [0, 1, 2, 3, 4]
+    >>> list(nx.dfs_preorder_nodes(G, source=0, depth_limit=2))
+    [0, 1, 2]
+
+    Notes
+    -----
+    If a source is not specified then a source is chosen arbitrarily and
+    repeatedly until all components in the graph are searched.
+
+    The implementation of this function is adapted from David Eppstein's
+    depth-first search function in `PADS`_, with modifications
+    to allow depth limits based on the Wikipedia article
+    "`Depth-limited search`_".
+
+    .. _PADS: http://www.ics.uci.edu/~eppstein/PADS
+    .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search
+
+    See Also
+    --------
+    dfs_edges
+    dfs_postorder_nodes
+    dfs_labeled_edges
+    :func:`~networkx.algorithms.traversal.breadth_first_search.bfs_edges`
+    """
+    edges = nx.dfs_labeled_edges(
+        G, source=source, depth_limit=depth_limit, sort_neighbors=sort_neighbors
+    )
+    return (v for u, v, d in edges if d == "forward")
+
+
+@nx._dispatchable
+def dfs_labeled_edges(G, source=None, depth_limit=None, *, sort_neighbors=None):
+    """Iterate over edges in a depth-first-search (DFS) labeled by type.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+       Specify starting node for depth-first search and return edges in
+       the component reachable from source.
+
+    depth_limit : int, optional (default=len(G))
+       Specify the maximum search depth.
+
+    sort_neighbors : function (default=None)
+        A function that takes an iterator over nodes as the input, and
+        returns an iterable of the same nodes with a custom ordering.
+        For example, `sorted` will sort the nodes in increasing order.
+
+    Returns
+    -------
+    edges: generator
+       A generator of triples of the form (*u*, *v*, *d*), where (*u*,
+       *v*) is the edge being explored in the depth-first search and *d*
+       is one of the strings 'forward', 'nontree', 'reverse', or 'reverse-depth_limit'.
+       A 'forward' edge is one in which *u* has been visited but *v* has
+       not. A 'nontree' edge is one in which both *u* and *v* have been
+       visited but the edge is not in the DFS tree. A 'reverse' edge is
+       one in which both *u* and *v* have been visited and the edge is in
+       the DFS tree. When the `depth_limit` is reached via a 'forward' edge,
+       a 'reverse' edge is immediately generated rather than the subtree
+       being explored. To indicate this flavor of 'reverse' edge, the string
+       yielded is 'reverse-depth_limit'.
+
+    Examples
+    --------
+
+    The labels reveal the complete transcript of the depth-first search
+    algorithm in more detail than, for example, :func:`dfs_edges`::
+
+        >>> from pprint import pprint
+        >>>
+        >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 1)])
+        >>> pprint(list(nx.dfs_labeled_edges(G, source=0)))
+        [(0, 0, 'forward'),
+         (0, 1, 'forward'),
+         (1, 2, 'forward'),
+         (2, 1, 'nontree'),
+         (1, 2, 'reverse'),
+         (0, 1, 'reverse'),
+         (0, 0, 'reverse')]
+
+    Notes
+    -----
+    If a source is not specified then a source is chosen arbitrarily and
+    repeatedly until all components in the graph are searched.
+
+    The implementation of this function is adapted from David Eppstein's
+    depth-first search function in `PADS`_, with modifications
+    to allow depth limits based on the Wikipedia article
+    "`Depth-limited search`_".
+
+    .. _PADS: http://www.ics.uci.edu/~eppstein/PADS
+    .. _Depth-limited search: https://en.wikipedia.org/wiki/Depth-limited_search
+
+    See Also
+    --------
+    dfs_edges
+    dfs_preorder_nodes
+    dfs_postorder_nodes
+    """
+    # Based on http://www.ics.uci.edu/~eppstein/PADS/DFS.py
+    # by D. Eppstein, July 2004.
+    if source is None:
+        # edges for all components
+        nodes = G
+    else:
+        # edges for components with source
+        nodes = [source]
+    if depth_limit is None:
+        depth_limit = len(G)
+
+    get_children = (
+        G.neighbors
+        if sort_neighbors is None
+        else lambda n: iter(sort_neighbors(G.neighbors(n)))
+    )
+
+    visited = set()
+    for start in nodes:
+        if start in visited:
+            continue
+        yield start, start, "forward"
+        visited.add(start)
+        stack = [(start, get_children(start))]
+        depth_now = 1
+        while stack:
+            parent, children = stack[-1]
+            for child in children:
+                if child in visited:
+                    yield parent, child, "nontree"
+                else:
+                    yield parent, child, "forward"
+                    visited.add(child)
+                    if depth_now < depth_limit:
+                        stack.append((child, iter(get_children(child))))
+                        depth_now += 1
+                        break
+                    else:
+                        yield parent, child, "reverse-depth_limit"
+            else:
+                stack.pop()
+                depth_now -= 1
+                if stack:
+                    yield stack[-1][0], parent, "reverse"
+        yield start, start, "reverse"