two version of R2R are hereHEADmaster

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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/generic.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/shortest_paths/generic.py
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+"""
+Compute the shortest paths and path lengths between nodes in the graph.
+
+These algorithms work with undirected and directed graphs.
+
+"""
+
+import warnings
+
+import networkx as nx
+
+__all__ = [
+    "shortest_path",
+    "all_shortest_paths",
+    "single_source_all_shortest_paths",
+    "all_pairs_all_shortest_paths",
+    "shortest_path_length",
+    "average_shortest_path_length",
+    "has_path",
+]
+
+
+@nx._dispatchable
+def has_path(G, source, target):
+    """Returns *True* if *G* has a path from *source* to *target*.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node
+       Starting node for path
+
+    target : node
+       Ending node for path
+    """
+    try:
+        nx.shortest_path(G, source, target)
+    except nx.NetworkXNoPath:
+        return False
+    return True
+
+
+@nx._dispatchable(edge_attrs="weight")
+def shortest_path(G, source=None, target=None, weight=None, method="dijkstra"):
+    """Compute shortest paths in the graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+        Starting node for path. If not specified, compute shortest
+        paths for each possible starting node.
+
+    target : node, optional
+        Ending node for path. If not specified, compute shortest
+        paths to all possible nodes.
+
+    weight : None, string or function, optional (default = None)
+        If None, every edge has weight/distance/cost 1.
+        If a string, use this edge attribute as the edge weight.
+        Any edge attribute not present defaults to 1.
+        If this is a function, the weight of an edge is the value
+        returned by the function. The function must accept exactly
+        three positional arguments: the two endpoints of an edge and
+        the dictionary of edge attributes for that edge.
+        The function must return a number.
+
+    method : string, optional (default = 'dijkstra')
+        The algorithm to use to compute the path.
+        Supported options: 'dijkstra', 'bellman-ford'.
+        Other inputs produce a ValueError.
+        If `weight` is None, unweighted graph methods are used, and this
+        suggestion is ignored.
+
+    Returns
+    -------
+    path: list or dictionary
+        All returned paths include both the source and target in the path.
+
+        If the source and target are both specified, return a single list
+        of nodes in a shortest path from the source to the target.
+
+        If only the source is specified, return a dictionary keyed by
+        targets with a list of nodes in a shortest path from the source
+        to one of the targets.
+
+        If only the target is specified, return a dictionary keyed by
+        sources with a list of nodes in a shortest path from one of the
+        sources to the target.
+
+        If neither the source nor target are specified return a dictionary
+        of dictionaries with path[source][target]=[list of nodes in path].
+
+    Raises
+    ------
+    NodeNotFound
+        If `source` is not in `G`.
+
+    ValueError
+        If `method` is not among the supported options.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> print(nx.shortest_path(G, source=0, target=4))
+    [0, 1, 2, 3, 4]
+    >>> p = nx.shortest_path(G, source=0)  # target not specified
+    >>> p[3]  # shortest path from source=0 to target=3
+    [0, 1, 2, 3]
+    >>> p = nx.shortest_path(G, target=4)  # source not specified
+    >>> p[1]  # shortest path from source=1 to target=4
+    [1, 2, 3, 4]
+    >>> p = dict(nx.shortest_path(G))  # source, target not specified
+    >>> p[2][4]  # shortest path from source=2 to target=4
+    [2, 3, 4]
+
+    Notes
+    -----
+    There may be more than one shortest path between a source and target.
+    This returns only one of them.
+
+    See Also
+    --------
+    all_pairs_shortest_path
+    all_pairs_dijkstra_path
+    all_pairs_bellman_ford_path
+    single_source_shortest_path
+    single_source_dijkstra_path
+    single_source_bellman_ford_path
+    """
+    if method not in ("dijkstra", "bellman-ford"):
+        # so we don't need to check in each branch later
+        raise ValueError(f"method not supported: {method}")
+    method = "unweighted" if weight is None else method
+    if source is None:
+        if target is None:
+            warnings.warn(
+                (
+                    "\n\nshortest_path will return an iterator that yields\n"
+                    "(node, path) pairs instead of a dictionary when source\n"
+                    "and target are unspecified beginning in version 3.5\n\n"
+                    "To keep the current behavior, use:\n\n"
+                    "\tdict(nx.shortest_path(G))"
+                ),
+                FutureWarning,
+                stacklevel=3,
+            )
+
+            # Find paths between all pairs.
+            if method == "unweighted":
+                paths = dict(nx.all_pairs_shortest_path(G))
+            elif method == "dijkstra":
+                paths = dict(nx.all_pairs_dijkstra_path(G, weight=weight))
+            else:  # method == 'bellman-ford':
+                paths = dict(nx.all_pairs_bellman_ford_path(G, weight=weight))
+        else:
+            # Find paths from all nodes co-accessible to the target.
+            if G.is_directed():
+                G = G.reverse(copy=False)
+            if method == "unweighted":
+                paths = nx.single_source_shortest_path(G, target)
+            elif method == "dijkstra":
+                paths = nx.single_source_dijkstra_path(G, target, weight=weight)
+            else:  # method == 'bellman-ford':
+                paths = nx.single_source_bellman_ford_path(G, target, weight=weight)
+            # Now flip the paths so they go from a source to the target.
+            for target in paths:
+                paths[target] = list(reversed(paths[target]))
+    else:
+        if target is None:
+            # Find paths to all nodes accessible from the source.
+            if method == "unweighted":
+                paths = nx.single_source_shortest_path(G, source)
+            elif method == "dijkstra":
+                paths = nx.single_source_dijkstra_path(G, source, weight=weight)
+            else:  # method == 'bellman-ford':
+                paths = nx.single_source_bellman_ford_path(G, source, weight=weight)
+        else:
+            # Find shortest source-target path.
+            if method == "unweighted":
+                paths = nx.bidirectional_shortest_path(G, source, target)
+            elif method == "dijkstra":
+                _, paths = nx.bidirectional_dijkstra(G, source, target, weight)
+            else:  # method == 'bellman-ford':
+                paths = nx.bellman_ford_path(G, source, target, weight)
+    return paths
+
+
+@nx._dispatchable(edge_attrs="weight")
+def shortest_path_length(G, source=None, target=None, weight=None, method="dijkstra"):
+    """Compute shortest path lengths in the graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node, optional
+        Starting node for path.
+        If not specified, compute shortest path lengths using all nodes as
+        source nodes.
+
+    target : node, optional
+        Ending node for path.
+        If not specified, compute shortest path lengths using all nodes as
+        target nodes.
+
+    weight : None, string or function, optional (default = None)
+        If None, every edge has weight/distance/cost 1.
+        If a string, use this edge attribute as the edge weight.
+        Any edge attribute not present defaults to 1.
+        If this is a function, the weight of an edge is the value
+        returned by the function. The function must accept exactly
+        three positional arguments: the two endpoints of an edge and
+        the dictionary of edge attributes for that edge.
+        The function must return a number.
+
+    method : string, optional (default = 'dijkstra')
+        The algorithm to use to compute the path length.
+        Supported options: 'dijkstra', 'bellman-ford'.
+        Other inputs produce a ValueError.
+        If `weight` is None, unweighted graph methods are used, and this
+        suggestion is ignored.
+
+    Returns
+    -------
+    length: number or iterator
+        If the source and target are both specified, return the length of
+        the shortest path from the source to the target.
+
+        If only the source is specified, return a dict keyed by target
+        to the shortest path length from the source to that target.
+
+        If only the target is specified, return a dict keyed by source
+        to the shortest path length from that source to the target.
+
+        If neither the source nor target are specified, return an iterator
+        over (source, dictionary) where dictionary is keyed by target to
+        shortest path length from source to that target.
+
+    Raises
+    ------
+    NodeNotFound
+        If `source` is not in `G`.
+
+    NetworkXNoPath
+        If no path exists between source and target.
+
+    ValueError
+        If `method` is not among the supported options.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> nx.shortest_path_length(G, source=0, target=4)
+    4
+    >>> p = nx.shortest_path_length(G, source=0)  # target not specified
+    >>> p[4]
+    4
+    >>> p = nx.shortest_path_length(G, target=4)  # source not specified
+    >>> p[0]
+    4
+    >>> p = dict(nx.shortest_path_length(G))  # source,target not specified
+    >>> p[0][4]
+    4
+
+    Notes
+    -----
+    The length of the path is always 1 less than the number of nodes involved
+    in the path since the length measures the number of edges followed.
+
+    For digraphs this returns the shortest directed path length. To find path
+    lengths in the reverse direction use G.reverse(copy=False) first to flip
+    the edge orientation.
+
+    See Also
+    --------
+    all_pairs_shortest_path_length
+    all_pairs_dijkstra_path_length
+    all_pairs_bellman_ford_path_length
+    single_source_shortest_path_length
+    single_source_dijkstra_path_length
+    single_source_bellman_ford_path_length
+    """
+    if method not in ("dijkstra", "bellman-ford"):
+        # so we don't need to check in each branch later
+        raise ValueError(f"method not supported: {method}")
+    method = "unweighted" if weight is None else method
+    if source is None:
+        if target is None:
+            # Find paths between all pairs.
+            if method == "unweighted":
+                paths = nx.all_pairs_shortest_path_length(G)
+            elif method == "dijkstra":
+                paths = nx.all_pairs_dijkstra_path_length(G, weight=weight)
+            else:  # method == 'bellman-ford':
+                paths = nx.all_pairs_bellman_ford_path_length(G, weight=weight)
+        else:
+            # Find paths from all nodes co-accessible to the target.
+            if G.is_directed():
+                G = G.reverse(copy=False)
+            if method == "unweighted":
+                path_length = nx.single_source_shortest_path_length
+                paths = path_length(G, target)
+            elif method == "dijkstra":
+                path_length = nx.single_source_dijkstra_path_length
+                paths = path_length(G, target, weight=weight)
+            else:  # method == 'bellman-ford':
+                path_length = nx.single_source_bellman_ford_path_length
+                paths = path_length(G, target, weight=weight)
+    else:
+        if target is None:
+            # Find paths to all nodes accessible from the source.
+            if method == "unweighted":
+                paths = nx.single_source_shortest_path_length(G, source)
+            elif method == "dijkstra":
+                path_length = nx.single_source_dijkstra_path_length
+                paths = path_length(G, source, weight=weight)
+            else:  # method == 'bellman-ford':
+                path_length = nx.single_source_bellman_ford_path_length
+                paths = path_length(G, source, weight=weight)
+        else:
+            # Find shortest source-target path.
+            if method == "unweighted":
+                p = nx.bidirectional_shortest_path(G, source, target)
+                paths = len(p) - 1
+            elif method == "dijkstra":
+                paths = nx.dijkstra_path_length(G, source, target, weight)
+            else:  # method == 'bellman-ford':
+                paths = nx.bellman_ford_path_length(G, source, target, weight)
+    return paths
+
+
+@nx._dispatchable(edge_attrs="weight")
+def average_shortest_path_length(G, weight=None, method=None):
+    r"""Returns the average shortest path length.
+
+    The average shortest path length is
+
+    .. math::
+
+       a =\sum_{\substack{s,t \in V \\ s\neq t}} \frac{d(s, t)}{n(n-1)}
+
+    where `V` is the set of nodes in `G`,
+    `d(s, t)` is the shortest path from `s` to `t`,
+    and `n` is the number of nodes in `G`.
+
+    .. versionchanged:: 3.0
+       An exception is raised for directed graphs that are not strongly
+       connected.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    weight : None, string or function, optional (default = None)
+        If None, every edge has weight/distance/cost 1.
+        If a string, use this edge attribute as the edge weight.
+        Any edge attribute not present defaults to 1.
+        If this is a function, the weight of an edge is the value
+        returned by the function. The function must accept exactly
+        three positional arguments: the two endpoints of an edge and
+        the dictionary of edge attributes for that edge.
+        The function must return a number.
+
+    method : string, optional (default = 'unweighted' or 'dijkstra')
+        The algorithm to use to compute the path lengths.
+        Supported options are 'unweighted', 'dijkstra', 'bellman-ford',
+        'floyd-warshall' and 'floyd-warshall-numpy'.
+        Other method values produce a ValueError.
+        The default method is 'unweighted' if `weight` is None,
+        otherwise the default method is 'dijkstra'.
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If `G` is the null graph (that is, the graph on zero nodes).
+
+    NetworkXError
+        If `G` is not connected (or not strongly connected, in the case
+        of a directed graph).
+
+    ValueError
+        If `method` is not among the supported options.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(5)
+    >>> nx.average_shortest_path_length(G)
+    2.0
+
+    For disconnected graphs, you can compute the average shortest path
+    length for each component
+
+    >>> G = nx.Graph([(1, 2), (3, 4)])
+    >>> for C in (G.subgraph(c).copy() for c in nx.connected_components(G)):
+    ...     print(nx.average_shortest_path_length(C))
+    1.0
+    1.0
+
+    """
+    single_source_methods = ["unweighted", "dijkstra", "bellman-ford"]
+    all_pairs_methods = ["floyd-warshall", "floyd-warshall-numpy"]
+    supported_methods = single_source_methods + all_pairs_methods
+
+    if method is None:
+        method = "unweighted" if weight is None else "dijkstra"
+    if method not in supported_methods:
+        raise ValueError(f"method not supported: {method}")
+
+    n = len(G)
+    # For the special case of the null graph, raise an exception, since
+    # there are no paths in the null graph.
+    if n == 0:
+        msg = (
+            "the null graph has no paths, thus there is no average "
+            "shortest path length"
+        )
+        raise nx.NetworkXPointlessConcept(msg)
+    # For the special case of the trivial graph, return zero immediately.
+    if n == 1:
+        return 0
+    # Shortest path length is undefined if the graph is not strongly connected.
+    if G.is_directed() and not nx.is_strongly_connected(G):
+        raise nx.NetworkXError("Graph is not strongly connected.")
+    # Shortest path length is undefined if the graph is not connected.
+    if not G.is_directed() and not nx.is_connected(G):
+        raise nx.NetworkXError("Graph is not connected.")
+
+    # Compute all-pairs shortest paths.
+    def path_length(v):
+        if method == "unweighted":
+            return nx.single_source_shortest_path_length(G, v)
+        elif method == "dijkstra":
+            return nx.single_source_dijkstra_path_length(G, v, weight=weight)
+        elif method == "bellman-ford":
+            return nx.single_source_bellman_ford_path_length(G, v, weight=weight)
+
+    if method in single_source_methods:
+        # Sum the distances for each (ordered) pair of source and target node.
+        s = sum(l for u in G for l in path_length(u).values())
+    else:
+        if method == "floyd-warshall":
+            all_pairs = nx.floyd_warshall(G, weight=weight)
+            s = sum(sum(t.values()) for t in all_pairs.values())
+        elif method == "floyd-warshall-numpy":
+            s = float(nx.floyd_warshall_numpy(G, weight=weight).sum())
+    return s / (n * (n - 1))
+
+
+@nx._dispatchable(edge_attrs="weight")
+def all_shortest_paths(G, source, target, weight=None, method="dijkstra"):
+    """Compute all shortest simple paths in the graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node
+       Starting node for path.
+
+    target : node
+       Ending node for path.
+
+    weight : None, string or function, optional (default = None)
+        If None, every edge has weight/distance/cost 1.
+        If a string, use this edge attribute as the edge weight.
+        Any edge attribute not present defaults to 1.
+        If this is a function, the weight of an edge is the value
+        returned by the function. The function must accept exactly
+        three positional arguments: the two endpoints of an edge and
+        the dictionary of edge attributes for that edge.
+        The function must return a number.
+
+    method : string, optional (default = 'dijkstra')
+       The algorithm to use to compute the path lengths.
+       Supported options: 'dijkstra', 'bellman-ford'.
+       Other inputs produce a ValueError.
+       If `weight` is None, unweighted graph methods are used, and this
+       suggestion is ignored.
+
+    Returns
+    -------
+    paths : generator of lists
+        A generator of all paths between source and target.
+
+    Raises
+    ------
+    ValueError
+        If `method` is not among the supported options.
+
+    NetworkXNoPath
+        If `target` cannot be reached from `source`.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_path(G, [0, 1, 2])
+    >>> nx.add_path(G, [0, 10, 2])
+    >>> print([p for p in nx.all_shortest_paths(G, source=0, target=2)])
+    [[0, 1, 2], [0, 10, 2]]
+
+    Notes
+    -----
+    There may be many shortest paths between the source and target.  If G
+    contains zero-weight cycles, this function will not produce all shortest
+    paths because doing so would produce infinitely many paths of unbounded
+    length -- instead, we only produce the shortest simple paths.
+
+    See Also
+    --------
+    shortest_path
+    single_source_shortest_path
+    all_pairs_shortest_path
+    """
+    method = "unweighted" if weight is None else method
+    if method == "unweighted":
+        pred = nx.predecessor(G, source)
+    elif method == "dijkstra":
+        pred, dist = nx.dijkstra_predecessor_and_distance(G, source, weight=weight)
+    elif method == "bellman-ford":
+        pred, dist = nx.bellman_ford_predecessor_and_distance(G, source, weight=weight)
+    else:
+        raise ValueError(f"method not supported: {method}")
+
+    return _build_paths_from_predecessors({source}, target, pred)
+
+
+@nx._dispatchable(edge_attrs="weight")
+def single_source_all_shortest_paths(G, source, weight=None, method="dijkstra"):
+    """Compute all shortest simple paths from the given source in the graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    source : node
+       Starting node for path.
+
+    weight : None, string or function, optional (default = None)
+        If None, every edge has weight/distance/cost 1.
+        If a string, use this edge attribute as the edge weight.
+        Any edge attribute not present defaults to 1.
+        If this is a function, the weight of an edge is the value
+        returned by the function. The function must accept exactly
+        three positional arguments: the two endpoints of an edge and
+        the dictionary of edge attributes for that edge.
+        The function must return a number.
+
+    method : string, optional (default = 'dijkstra')
+       The algorithm to use to compute the path lengths.
+       Supported options: 'dijkstra', 'bellman-ford'.
+       Other inputs produce a ValueError.
+       If `weight` is None, unweighted graph methods are used, and this
+       suggestion is ignored.
+
+    Returns
+    -------
+    paths : generator of dictionary
+        A generator of all paths between source and all nodes in the graph.
+
+    Raises
+    ------
+    ValueError
+        If `method` is not among the supported options.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_path(G, [0, 1, 2, 3, 0])
+    >>> dict(nx.single_source_all_shortest_paths(G, source=0))
+    {0: [[0]], 1: [[0, 1]], 2: [[0, 1, 2], [0, 3, 2]], 3: [[0, 3]]}
+
+    Notes
+    -----
+    There may be many shortest paths between the source and target.  If G
+    contains zero-weight cycles, this function will not produce all shortest
+    paths because doing so would produce infinitely many paths of unbounded
+    length -- instead, we only produce the shortest simple paths.
+
+    See Also
+    --------
+    shortest_path
+    all_shortest_paths
+    single_source_shortest_path
+    all_pairs_shortest_path
+    all_pairs_all_shortest_paths
+    """
+    method = "unweighted" if weight is None else method
+    if method == "unweighted":
+        pred = nx.predecessor(G, source)
+    elif method == "dijkstra":
+        pred, dist = nx.dijkstra_predecessor_and_distance(G, source, weight=weight)
+    elif method == "bellman-ford":
+        pred, dist = nx.bellman_ford_predecessor_and_distance(G, source, weight=weight)
+    else:
+        raise ValueError(f"method not supported: {method}")
+    for n in G:
+        try:
+            yield n, list(_build_paths_from_predecessors({source}, n, pred))
+        except nx.NetworkXNoPath:
+            pass
+
+
+@nx._dispatchable(edge_attrs="weight")
+def all_pairs_all_shortest_paths(G, weight=None, method="dijkstra"):
+    """Compute all shortest paths between all nodes.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    weight : None, string or function, optional (default = None)
+        If None, every edge has weight/distance/cost 1.
+        If a string, use this edge attribute as the edge weight.
+        Any edge attribute not present defaults to 1.
+        If this is a function, the weight of an edge is the value
+        returned by the function. The function must accept exactly
+        three positional arguments: the two endpoints of an edge and
+        the dictionary of edge attributes for that edge.
+        The function must return a number.
+
+    method : string, optional (default = 'dijkstra')
+       The algorithm to use to compute the path lengths.
+       Supported options: 'dijkstra', 'bellman-ford'.
+       Other inputs produce a ValueError.
+       If `weight` is None, unweighted graph methods are used, and this
+       suggestion is ignored.
+
+    Returns
+    -------
+    paths : generator of dictionary
+        Dictionary of arrays, keyed by source and target, of all shortest paths.
+
+    Raises
+    ------
+    ValueError
+        If `method` is not among the supported options.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(4)
+    >>> dict(nx.all_pairs_all_shortest_paths(G))[0][2]
+    [[0, 1, 2], [0, 3, 2]]
+    >>> dict(nx.all_pairs_all_shortest_paths(G))[0][3]
+    [[0, 3]]
+
+    Notes
+    -----
+    There may be multiple shortest paths with equal lengths. Unlike
+    all_pairs_shortest_path, this method returns all shortest paths.
+
+    See Also
+    --------
+    all_pairs_shortest_path
+    single_source_all_shortest_paths
+    """
+    for n in G:
+        yield (
+            n,
+            dict(single_source_all_shortest_paths(G, n, weight=weight, method=method)),
+        )
+
+
+def _build_paths_from_predecessors(sources, target, pred):
+    """Compute all simple paths to target, given the predecessors found in
+    pred, terminating when any source in sources is found.
+
+    Parameters
+    ----------
+    sources : set
+       Starting nodes for path.
+
+    target : node
+       Ending node for path.
+
+    pred : dict
+       A dictionary of predecessor lists, keyed by node
+
+    Returns
+    -------
+    paths : generator of lists
+        A generator of all paths between source and target.
+
+    Raises
+    ------
+    NetworkXNoPath
+        If `target` cannot be reached from `source`.
+
+    Notes
+    -----
+    There may be many paths between the sources and target.  If there are
+    cycles among the predecessors, this function will not produce all
+    possible paths because doing so would produce infinitely many paths
+    of unbounded length -- instead, we only produce simple paths.
+
+    See Also
+    --------
+    shortest_path
+    single_source_shortest_path
+    all_pairs_shortest_path
+    all_shortest_paths
+    bellman_ford_path
+    """
+    if target not in pred:
+        raise nx.NetworkXNoPath(f"Target {target} cannot be reached from given sources")
+
+    seen = {target}
+    stack = [[target, 0]]
+    top = 0
+    while top >= 0:
+        node, i = stack[top]
+        if node in sources:
+            yield [p for p, n in reversed(stack[: top + 1])]
+        if len(pred[node]) > i:
+            stack[top][1] = i + 1
+            next = pred[node][i]
+            if next in seen:
+                continue
+            else:
+                seen.add(next)
+            top += 1
+            if top == len(stack):
+                stack.append([next, 0])
+            else:
+                stack[top][:] = [next, 0]
+        else:
+            seen.discard(node)
+            top -= 1