U
    ¹mœd`  ã                   @   sp   d Z ddlmZ ddlmZ ddlmZ ddlZddl	m
Z
 dgZdZd	ZdZd
ZdZdZdd„ Zddd„ZdS )z=Lukes Algorithm for exact optimal weighted tree partitioning.é    )Údeepcopy)Ú	lru_cache)ÚchoiceN)Únot_implemented_forÚlukes_partitioningÚweightg      ð?é   Z
partitionsi   c                 c   s2   | |kst ‚t|| d ƒD ]}|| | fV  qd S )Nr   )ÚAssertionErrorÚrange)ÚnZmin_size_of_first_partÚp1© r   ú\/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/networkx/algorithms/community/lukes.pyÚ_split_n_from   s    r   c              	      sš  t  | ¡st  d¡‚nXt  | ¡rTdd„ |  ¡ D ƒ}t|ƒdksBt‚|d }t| ƒ}ntt	| j
ƒƒ}t  | |¡}ˆdks~ˆdkr¼t| ƒ‰ˆdkr t  ˆtt¡ t‰ˆdkrÀt  ˆtt¡ t‰n| ‰t  ˆˆ¡ ¡ }|D ]}t|tƒsÔtdˆ› d�ƒ‚qÔtd	ƒd
d„ ƒ‰ td	ƒ‡ fdd„ƒ}ttƒ‡‡fdd„ƒ‰‡fdd„‰ttƒ‡‡fdd„ƒ‰dd„ ‰‡‡‡fdd„}	tˆ |ƒƒ‰ˆD ]N}
i |j
|
 t< ˆj
|
 ˆ }|
hg|j
|
 t |< |
hg|j
|
 t d< �qx‡fdd„|j
D ƒD ]8}i |j
| t< ˆj
| ˆ }|hg|j
| t |< �qÜ||ƒ}ˆj
| ˆ }d}d}i }t  ||¡}|D �]}t||d ƒD ]Æ}t||ƒD ]´\}}||j
| t  ¡ k�sj||j
| t  ¡ k�r¦�qj|j
| t | }|j
| t | }|	|||||ƒ\}}|| ¡ k�sþ|| d |k �r
||f||< ||k�rj|}|}�qj�q\|  ¡ D ] \}\}}||j
| t |< �q,| !¡  �qH||j
| t d< | "|¡ ||k�r|j
| t d S �qdS )u  Optimal partitioning of a weighted tree using the Lukes algorithm.

    This algorithm partitions a connected, acyclic graph featuring integer
    node weights and float edge weights. The resulting clusters are such
    that the total weight of the nodes in each cluster does not exceed
    max_size and that the weight of the edges that are cut by the partition
    is minimum. The algorithm is based on LUKES[1].

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

    max_size : int
        Maximum weight a partition can have in terms of sum of
        node_weight for all nodes in the partition

    edge_weight : key
        Edge data key to use as weight. If None, the weights are all
        set to one.

    node_weight : key
        Node data key to use as weight. If None, the weights are all
        set to one. The data must be int.

    Returns
    -------
    partition : list
        A list of sets of nodes representing the clusters of the
        partition.

    Raises
    ------
    NotATree
        If G is not a tree.
    TypeError
        If any of the values of node_weight is not int.

    References
    ----------
    .. Lukes, J. A. (1974).
       "Efficient Algorithm for the Partitioning of Trees."
       IBM Journal of Research and Development, 18(3), 217â€“224.

    z&lukes_partitioning works only on treesc                 S   s   g | ]\}}|d kr|‘qS )r   r   )Ú.0r   Údr   r   r   Ú
<listcomp>N   s      z&lukes_partitioning.<locals>.<listcomp>r   r   Nz9lukes_partitioning needs integer values for node_weight (ú)Z
undirectedc                 s   s"   | j D ]}t | |¡s|V  qd S ©N)ÚnodesÚnxÚdescendants)ÚgrÚxr   r   r   Ú_leavesu   s    
z#lukes_partitioning.<locals>._leavesc                    sJ   t ˆ| ƒƒ‰ t | jƒˆ  D ]*}t‡ fdd„t | |¡D ƒƒr|  S qd S )Nc                 3   s   | ]}|ˆ kV  qd S r   r   ©r   r   ©Ztleavesr   r   Ú	<genexpr>€   s     zGlukes_partitioning.<locals>._a_parent_of_leaves_only.<locals>.<genexpr>)Úsetr   Úallr   r   )r   r   )r   r   r   Ú_a_parent_of_leaves_only|   s    z4lukes_partitioning.<locals>._a_parent_of_leaves_onlyc                    s,   ‡ fdd„ˆj D ƒ}t‡‡fdd„|D ƒƒS )Nc                    s(   g | ] }|d  ˆ kr|d ˆ kr|‘qS )r   r   r   ©r   Úe©Úclusterr   r   r   …   s       zAlukes_partitioning.<locals>._value_of_cluster.<locals>.<listcomp>c                 3   s   | ]}ˆj | ˆ  V  qd S r   )Úedgesr!   ©Úedge_weightÚsafe_Gr   r   r   †   s     z@lukes_partitioning.<locals>._value_of_cluster.<locals>.<genexpr>)r%   Úsum)r$   Zvalid_edgesr&   r#   r   Ú_value_of_clusterƒ   s    z-lukes_partitioning.<locals>._value_of_clusterc                    s   t ‡ fdd„| D ƒƒS )Nc                 3   s   | ]}ˆ t |ƒƒV  qd S r   )Ú	frozenset©r   Úc©r*   r   r   r   ‰   s     zBlukes_partitioning.<locals>._value_of_partition.<locals>.<genexpr>©r)   )Ú	partitionr.   r   r   Ú_value_of_partitionˆ   s    z/lukes_partitioning.<locals>._value_of_partitionc                    s   t ‡ ‡fdd„| D ƒƒS )Nc                 3   s   | ]}ˆj | ˆ  V  qd S r   )r   )r   r   ©Únode_weightr(   r   r   r   �   s     zAlukes_partitioning.<locals>._weight_of_cluster.<locals>.<genexpr>r/   r#   r2   r   r   Ú_weight_of_cluster‹   s    z.lukes_partitioning.<locals>._weight_of_clusterc                    s*   ‡ fdd„| D ƒ}t |ƒdks"t‚|d S )Nc                    s   g | ]}ˆ |kr|‘qS r   r   r,   ©Únoder   r   r   �   s      z6lukes_partitioning.<locals>._pivot.<locals>.<listcomp>r   r   )Úlenr	   )r0   r6   Úccxr   r5   r   Ú_pivot�   s    z"lukes_partitioning.<locals>._pivotc           
         sŒ   ˆ| |ƒ‰ˆ||ƒ‰ ˆ  ˆ ¡}ˆt|ƒƒ|krttt‡fdd„| ƒƒ}tt‡ fdd„|ƒƒ}|g| | }|ˆ|ƒfS | | }	|	ˆ|	ƒfS d S )Nc                    s   | ˆ kS r   r   ©r   )r8   r   r   Ú<lambda>œ   ó    zClukes_partitioning.<locals>._concatenate_or_merge.<locals>.<lambda>c                    s   | ˆ kS r   r   r:   )Úccir   r   r;   �   r<   )Úunionr+   ÚlistÚfilter)
Zpartition_1Zpartition_2r   ÚiZ
ref_weightZ	merged_xiZcp1Zcp2Zoption_2Zoption_1)r9   r1   r4   )r=   r8   r   Ú_concatenate_or_merge”   s    


z1lukes_partitioning.<locals>._concatenate_or_mergec                    s   g | ]}|ˆ kr|‘qS r   r   r   )Úleavesr   r   r   ­   s      )#r   Zis_treeZNotATreeZis_directedZ	in_degreer7   r	   r   r   r?   r   Zdfs_treeZset_edge_attributesÚD_EDGE_VALUEÚD_EDGE_WZset_node_attributesÚD_NODE_VALUEÚD_NODE_WZget_node_attributesÚvaluesÚ
isinstanceÚintÚ	TypeErrorr   r   ÚCLUSTER_EVAL_CACHE_SIZEr   ÚPKEYr   r
   r   ÚkeysÚitemsÚclearZremove_nodes_from)ÚGÚmax_sizer3   r'   ÚrootZt_GZ
all_n_attrr   r    rB   ÚlvZslotÚinnerZx_nodeZweight_of_xZ
best_valueZbest_partitionZ	bp_bufferZx_descendantsZi_nodeÚjÚaÚbZpart1Zpart2ÚpartÚvalueÚwZbest_part_for_vlZvlr   )	r   r9   r*   r1   r4   r'   rC   r3   r(   r   r      s”    .




ÿ


ÿþ 


)NN)Ú__doc__Úcopyr   Ú	functoolsr   Úrandomr   Znetworkxr   Znetworkx.utilsr   Ú__all__rE   rD   rG   rF   rM   rL   r   r   r   r   r   r   Ú<module>   s   