human
Complete the below
@not_implemented_for('multigraph', 'undirected')
def all_pairs_lowest_common_ancestor(G, pairs=None):

    ''''Compute the lowest common ancestor for pairs of nodes.
    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.
    Returns
    An iterator over ((node1, node2), lca) where (node1, node2) are
    the pairs specified and lca is a lowest common ancestor of the pair.
    Note that for the default of all pairs in G, we consider
    unordered pairs, e.g. you will not get both (b, a) and (a, b).
    Notes
    Only defined on non-null directed acyclic graphs.
    Uses the O(n^3) ancestor-list algorithm from:
    M. A. Bender, M. Farach-Colton, G. Pemmasani, S. Skiena, P. Sumazin.
    "Lowest common ancestors in trees and directed acyclic graphs."
    Journal of Algorithms, 57(2): 75-94, 2005.
    See Also
    tree_all_pairs_lowest_common_ancestor
    lowest_common_ancestor'
    '''
 Give me a Python program to find the LCA of all pairs of nodes?
assistant
#Here is Python program to find the LCA of all pairs of nodes.
    if (not nx.is_directed_acyclic_graph(G)):
        raise nx.NetworkXError('LCA    only    defined    on    directed    acyclic    graphs.')
    elif (len(G) == 0):
        raise nx.NetworkXPointlessConcept('LCA    meaningless    on    null    graphs.')
    elif (None in G):
        raise nx.NetworkXError('None    is    not    a    valid    node.')
    if ((not isinstance(pairs, (Mapping, Set))) and (pairs is not None)):
        pairs = set(pairs)
    sources = [n for (n, deg) in G.in_degree if (deg == 0)]
    if (len(sources) == 1):
        root = sources[0]
        super_root = None
    else:
        G = G.copy()
        super_root = root = generate_unique_node()
        for source in sources:
            G.add_edge(root, source)
    spanning_tree = nx.dfs_tree(G, root)
    dag = nx.DiGraph(((u, v) for (u, v) in G.edges if ((u not in spanning_tree) or (v not in spanning_tree[u]))))
    spanning_tree.add_nodes_from(G)
    dag.add_nodes_from(G)
    counter = count()
    root_distance = {root: next(counter)}
    for edge in nx.bfs_edges(spanning_tree, root):
        for node in edge:
            if (node not in root_distance):
                root_distance[node] = next(counter)
    euler_tour_pos = {}
    for node in nx.depth_first_search.dfs_preorder_nodes(G, root):
        if (node not in euler_tour_pos):
            euler_tour_pos[node] = next(counter)
    pairset = set()
    if (pairs is not None):
        pairset = set(chain.from_iterable(pairs))
    for n in pairset:
        if (n not in G):
            msg = ('The    node    %s    is    not    in    the    digraph.' % str(n))
            raise nx.NodeNotFound(msg)
    ancestors = {}
    for v in dag:
        if ((pairs is None) or (v in pairset)):
            my_ancestors = nx.dag.ancestors(dag, v)
            my_ancestors.add(v)
            ancestors[v] = sorted(my_ancestors, key=euler_tour_pos.get)
    def _compute_dag_lca_from_tree_values(tree_lca, dry_run):
        "Iterate    through    the    in-order    merge    for    each    pair    of   ...