two version of R2R are hereHEADmaster

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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/lowest_common_ancestors.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/lowest_common_ancestors.py
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+"""Algorithms for finding the lowest common ancestor of trees and DAGs."""
+
+from collections import defaultdict
+from collections.abc import Mapping, Set
+from itertools import combinations_with_replacement
+
+import networkx as nx
+from networkx.utils import UnionFind, arbitrary_element, not_implemented_for
+
+__all__ = [
+    "all_pairs_lowest_common_ancestor",
+    "tree_all_pairs_lowest_common_ancestor",
+    "lowest_common_ancestor",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def all_pairs_lowest_common_ancestor(G, pairs=None):
+    """Return the lowest common ancestor of all pairs or the provided pairs
+
+    Parameters
+    ----------
+    G : NetworkX directed graph
+
+    pairs : iterable of pairs of nodes, optional (default: all pairs)
+        The pairs of nodes of interest.
+        If None, will find the LCA of all pairs of nodes.
+
+    Yields
+    ------
+    ((node1, node2), lca) : 2-tuple
+        Where lca is least common ancestor of node1 and node2.
+        Note that for the default case, the order of the node pair is not considered,
+        e.g. you will not get both ``(a, b)`` and ``(b, a)``
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If `G` is null.
+    NetworkXError
+        If `G` is not a DAG.
+
+    Examples
+    --------
+    The default behavior is to yield the lowest common ancestor for all
+    possible combinations of nodes in `G`, including self-pairings:
+
+    >>> G = nx.DiGraph([(0, 1), (0, 3), (1, 2)])
+    >>> dict(nx.all_pairs_lowest_common_ancestor(G))
+    {(0, 0): 0, (0, 1): 0, (0, 3): 0, (0, 2): 0, (1, 1): 1, (1, 3): 0, (1, 2): 1, (3, 3): 3, (3, 2): 0, (2, 2): 2}
+
+    The pairs argument can be used to limit the output to only the
+    specified node pairings:
+
+    >>> dict(nx.all_pairs_lowest_common_ancestor(G, pairs=[(1, 2), (2, 3)]))
+    {(1, 2): 1, (2, 3): 0}
+
+    Notes
+    -----
+    Only defined on non-null directed acyclic graphs.
+
+    See Also
+    --------
+    lowest_common_ancestor
+    """
+    if not nx.is_directed_acyclic_graph(G):
+        raise nx.NetworkXError("LCA only defined on directed acyclic graphs.")
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept("LCA meaningless on null graphs.")
+
+    if pairs is None:
+        pairs = combinations_with_replacement(G, 2)
+    else:
+        # Convert iterator to iterable, if necessary. Trim duplicates.
+        pairs = dict.fromkeys(pairs)
+        # Verify that each of the nodes in the provided pairs is in G
+        nodeset = set(G)
+        for pair in pairs:
+            if set(pair) - nodeset:
+                raise nx.NodeNotFound(
+                    f"Node(s) {set(pair) - nodeset} from pair {pair} not in G."
+                )
+
+    # Once input validation is done, construct the generator
+    def generate_lca_from_pairs(G, pairs):
+        ancestor_cache = {}
+
+        for v, w in pairs:
+            if v not in ancestor_cache:
+                ancestor_cache[v] = nx.ancestors(G, v)
+                ancestor_cache[v].add(v)
+            if w not in ancestor_cache:
+                ancestor_cache[w] = nx.ancestors(G, w)
+                ancestor_cache[w].add(w)
+
+            common_ancestors = ancestor_cache[v] & ancestor_cache[w]
+
+            if common_ancestors:
+                common_ancestor = next(iter(common_ancestors))
+                while True:
+                    successor = None
+                    for lower_ancestor in G.successors(common_ancestor):
+                        if lower_ancestor in common_ancestors:
+                            successor = lower_ancestor
+                            break
+                    if successor is None:
+                        break
+                    common_ancestor = successor
+                yield ((v, w), common_ancestor)
+
+    return generate_lca_from_pairs(G, pairs)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def lowest_common_ancestor(G, node1, node2, default=None):
+    """Compute the lowest common ancestor of the given pair of nodes.
+
+    Parameters
+    ----------
+    G : NetworkX directed graph
+
+    node1, node2 : nodes in the graph.
+
+    default : object
+        Returned if no common ancestor between `node1` and `node2`
+
+    Returns
+    -------
+    The lowest common ancestor of node1 and node2,
+    or default if they have no common ancestors.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> nx.add_path(G, (0, 1, 2, 3))
+    >>> nx.add_path(G, (0, 4, 3))
+    >>> nx.lowest_common_ancestor(G, 2, 4)
+    0
+
+    See Also
+    --------
+    all_pairs_lowest_common_ancestor"""
+
+    ans = list(all_pairs_lowest_common_ancestor(G, pairs=[(node1, node2)]))
+    if ans:
+        assert len(ans) == 1
+        return ans[0][1]
+    return default
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def tree_all_pairs_lowest_common_ancestor(G, root=None, pairs=None):
+    r"""Yield the lowest common ancestor for sets of pairs in a tree.
+
+    Parameters
+    ----------
+    G : NetworkX directed graph (must be a tree)
+
+    root : node, optional (default: None)
+        The root of the subtree to operate on.
+        If None, assume the entire graph has exactly one source and use that.
+
+    pairs : iterable or iterator of pairs of nodes, optional (default: None)
+        The pairs of interest. If None, Defaults to all pairs of nodes
+        under `root` that have a lowest common ancestor.
+
+    Returns
+    -------
+    lcas : generator of tuples `((u, v), lca)` where `u` and `v` are nodes
+        in `pairs` and `lca` is their lowest common ancestor.
+
+    Examples
+    --------
+    >>> import pprint
+    >>> G = nx.DiGraph([(1, 3), (2, 4), (1, 2)])
+    >>> pprint.pprint(dict(nx.tree_all_pairs_lowest_common_ancestor(G)))
+    {(1, 1): 1,
+     (2, 1): 1,
+     (2, 2): 2,
+     (3, 1): 1,
+     (3, 2): 1,
+     (3, 3): 3,
+     (3, 4): 1,
+     (4, 1): 1,
+     (4, 2): 2,
+     (4, 4): 4}
+
+    We can also use `pairs` argument to specify the pairs of nodes for which we
+    want to compute lowest common ancestors. Here is an example:
+
+    >>> dict(nx.tree_all_pairs_lowest_common_ancestor(G, pairs=[(1, 4), (2, 3)]))
+    {(2, 3): 1, (1, 4): 1}
+
+    Notes
+    -----
+    Only defined on non-null trees represented with directed edges from
+    parents to children. Uses Tarjan's off-line lowest-common-ancestors
+    algorithm. Runs in time $O(4 \times (V + E + P))$ time, where 4 is the largest
+    value of the inverse Ackermann function likely to ever come up in actual
+    use, and $P$ is the number of pairs requested (or $V^2$ if all are needed).
+
+    Tarjan, R. E. (1979), "Applications of path compression on balanced trees",
+    Journal of the ACM 26 (4): 690-715, doi:10.1145/322154.322161.
+
+    See Also
+    --------
+    all_pairs_lowest_common_ancestor: similar routine for general DAGs
+    lowest_common_ancestor: just a single pair for general DAGs
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept("LCA meaningless on null graphs.")
+
+    # Index pairs of interest for efficient lookup from either side.
+    if pairs is not None:
+        pair_dict = defaultdict(set)
+        # See note on all_pairs_lowest_common_ancestor.
+        if not isinstance(pairs, Mapping | Set):
+            pairs = set(pairs)
+        for u, v in pairs:
+            for n in (u, v):
+                if n not in G:
+                    msg = f"The node {str(n)} is not in the digraph."
+                    raise nx.NodeNotFound(msg)
+            pair_dict[u].add(v)
+            pair_dict[v].add(u)
+
+    # If root is not specified, find the exactly one node with in degree 0 and
+    # use it. Raise an error if none are found, or more than one is. Also check
+    # for any nodes with in degree larger than 1, which would imply G is not a
+    # tree.
+    if root is None:
+        for n, deg in G.in_degree:
+            if deg == 0:
+                if root is not None:
+                    msg = "No root specified and tree has multiple sources."
+                    raise nx.NetworkXError(msg)
+                root = n
+            # checking deg>1 is not sufficient for MultiDiGraphs
+            elif deg > 1 and len(G.pred[n]) > 1:
+                msg = "Tree LCA only defined on trees; use DAG routine."
+                raise nx.NetworkXError(msg)
+    if root is None:
+        raise nx.NetworkXError("Graph contains a cycle.")
+
+    # Iterative implementation of Tarjan's offline lca algorithm
+    # as described in CLRS on page 521 (2nd edition)/page 584 (3rd edition)
+    uf = UnionFind()
+    ancestors = {}
+    for node in G:
+        ancestors[node] = uf[node]
+
+    colors = defaultdict(bool)
+    for node in nx.dfs_postorder_nodes(G, root):
+        colors[node] = True
+        for v in pair_dict[node] if pairs is not None else G:
+            if colors[v]:
+                # If the user requested both directions of a pair, give it.
+                # Otherwise, just give one.
+                if pairs is not None and (node, v) in pairs:
+                    yield (node, v), ancestors[uf[v]]
+                if pairs is None or (v, node) in pairs:
+                    yield (v, node), ancestors[uf[v]]
+        if node != root:
+            parent = arbitrary_element(G.pred[node])
+            uf.union(parent, node)
+            ancestors[uf[parent]] = parent