o
    ˷e                     @   sD   d Z ddlZddlmZ dgZeddddZdd Zd	d
 ZdS )z'Distance measures approximated metrics.    N)py_random_statediameter   c                 C   s:   | st d|  dkrdS |  rt| |S t| |S )u  Returns a lower bound on the diameter of the graph G.

    The function computes a lower bound on the diameter (i.e., the maximum eccentricity)
    of a directed or undirected graph G. The procedure used varies depending on the graph
    being directed or not.

    If G is an `undirected` graph, then the function uses the `2-sweep` algorithm [1]_.
    The main idea is to pick the farthest node from a random node and return its eccentricity.

    Otherwise, if G is a `directed` graph, the function uses the `2-dSweep` algorithm [2]_,
    The procedure starts by selecting a random source node $s$ from which it performs a
    forward and a backward BFS. Let $a_1$ and $a_2$ be the farthest nodes in the forward and
    backward cases, respectively. Then, it computes the backward eccentricity of $a_1$ using
    a backward BFS and the forward eccentricity of $a_2$ using a forward BFS.
    Finally, it returns the best lower bound between the two.

    In both cases, the time complexity is linear with respect to the size of G.

    Parameters
    ----------
    G : NetworkX graph

    seed : integer, random_state, or None (default)
        Indicator of random number generation state.
        See :ref:`Randomness<randomness>`.

    Returns
    -------
    d : integer
       Lower Bound on the Diameter of G

    Raises
    ------
    NetworkXError
        If the graph is empty or
        If the graph is undirected and not connected or
        If the graph is directed and not strongly connected.

    See Also
    --------
    networkx.algorithms.distance_measures.diameter

    References
    ----------
    .. [1] Magnien, Clémence, Matthieu Latapy, and Michel Habib.
       *Fast computation of empirically tight bounds for the diameter of massive graphs.*
       Journal of Experimental Algorithmics (JEA), 2009.
       https://arxiv.org/pdf/0904.2728.pdf
    .. [2] Crescenzi, Pierluigi, Roberto Grossi, Leonardo Lanzi, and Andrea Marino.
       *On computing the diameter of real-world directed (weighted) graphs.*
       International Symposium on Experimental Algorithms. Springer, Berlin, Heidelberg, 2012.
       https://courses.cs.ut.ee/MTAT.03.238/2014_fall/uploads/Main/diameter.pdf
    z"Expected non-empty NetworkX graph!r   r   )nxNetworkXErrornumber_of_nodesis_directed_two_sweep_directed_two_sweep_undirected)Gseed r   j/var/www/ideatree/venv/lib/python3.10/site-packages/networkx/algorithms/approximation/distance_measures.pyr   	   s   8


c                 C   sJ   | t| }t| |}t|t| krtd|^ }}t| |S )aL  Helper function for finding a lower bound on the diameter
        for undirected Graphs.

        The idea is to pick the farthest node from a random node
        and return its eccentricity.

        ``G`` is a NetworkX undirected graph.

    .. note::

        ``seed`` is a random.Random or numpy.random.RandomState instance
    zGraph not connected.)choicelistr   shortest_path_lengthlenr   eccentricity)r   r   source	distances_noder   r   r   r
   M   s   

r
   c           
      C   s   |   }|t| }t| |}t||}t| }t||ks't||kr,td|^ }}|^ }}	tt||t| |	S )a   Helper function for finding a lower bound on the diameter
        for directed Graphs.

        It implements 2-dSweep, the directed version of the 2-sweep algorithm.
        The algorithm follows the following steps.
        1. Select a source node $s$ at random.
        2. Perform a forward BFS from $s$ to select a node $a_1$ at the maximum
        distance from the source, and compute $LB_1$, the backward eccentricity of $a_1$.
        3. Perform a backward BFS from $s$ to select a node $a_2$ at the maximum
        distance from the source, and compute $LB_2$, the forward eccentricity of $a_2$.
        4. Return the maximum between $LB_1$ and $LB_2$.

        ``G`` is a NetworkX directed graph.

    .. note::

        ``seed`` is a random.Random or numpy.random.RandomState instance
    zDiGraph not strongly connected.)	reverser   r   r   r   r   r   maxr   )
r   r   
G_reversedr   forward_distancesbackward_distancesnr   a_1a_2r   r   r   r	   g   s   


r	   )N)	__doc__networkxr   networkx.utils.decoratorsr   __all__r   r
   r	   r   r   r   r   <module>   s    C