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a ^�h� � @ s d Z ddlmZ ddlmZ dd� Zdd� Zd d � Zd d � Zd d� Z dd� Z dd� Z dd� Z dd� Z dd� Zd�dd�Zd d � Zd d � Zd d!� Zd"d#� Zd$d%� Zd&d'� Zd(d)� Zd*d+� Zd,d-� Zd.d/� Zd0d1� Zd2d3� Zd�d5d6�Z d7d8� Z d9d:� Z d;d<� Z d=d>� Z d?d@� Z!dAdB� Z"dCdD� Z#dEdF� Z$dGdH� Z%dIdJ� Z&dKdL� Z'dMdN� Z(dOdP� Z)dQdR� Z*dSdT� Z+dUdV� Z,dWdX� Z-dYdZ� Z.d[d\� Z/d]d^� Z0d_d`� Z1dadb� Z2dcdd� Z3dedf� Z4dgdh� Z5didj� Z6dkdl� Z7dmdn� Z8dodp� Z9dqdr� Z:dsdt� Z;dudv� Z<dwdx� Z=dydz� Z>d{d|� Z?d}d~� Z@dd�� ZAd4S )�z� Implementing planarity testing as per "The Hopcroft-Tarjan Planarity Algorithm" by William Kocay Location: http://www.combinatorialmath.ca/G&G/articles/planarity.pdf � )�deque� )�#depth_first_search_with_parent_datac C s8 t | �}t| |�}t|�}t| |�}t|� t|�}|S )z%Determines whether a graph is planar.)�__calculate_adjacency_lists�__setup_dfs_data�__sort_adjacency_lists�__branch_point_dfs�__embed_branch)�graph�adj�dfs_dataZ is_planar� r ��/root/rpmbuild/BUILDROOT/imh-python39-modules-3.9.7-92.el8.x86_64/opt/imh-python/lib/python3.9/site-packages/pygraph/functions/planarity/kocay_algorithm.py�kocay_planarity_test s r c C sJ t | |�}| |d< ||d< t|�\}}||d< ||d< t|�}||d< |S )z-Sets up the dfs_data object, for consistency.r r �lowpoint_1_lookup�lowpoint_2_lookup� edge_weights)�__get_dfs_data�__low_point_dfs�__calculate_edge_weights)r r r �L1�L2r r r r r - s r c C s t | �\}}||fS )z)Calculates the L1 and L2 for each vertex.)�__get_all_lowpoints)r r r r r r r > s r c C s0 | d }i }|� � D ]}t|| �}|||< q|S )z@Calculates the weight of each edge, for embedding-order sorting.r )�get_all_edge_ids� __edge_weight)r r �weights�edge_idZ edge_weightr r r r D s r c s� i }| d }| d }| d }t |�� �D ]~\}}i �i � |D ]8}| d �||�}|| �|< || dkrldnd� |< q<t|� fdd �d �} | j�fd d �d � | ||< q(|S ) z<Sorts the adjacency list representation by the edge weights.r r � edge_lookupr �backedge� r c s � | S �Nr ��n)� frond_lookupr r �<lambda>a � z(__sort_adjacency_lists.<locals>.<lambda>��keyc s � | S r r r! )�node_weight_lookupr r r$ d r% )�list�items� get_first_edge_id_by_node_ids�sorted�sort) r Znew_adjacency_lists�adjacency_listsr r Znode_idZadj_list�node_br �new_listr )r# r( r r P s r c C sT | d d }i }d||< i }|||< i }d||< t ||||| � || d< || d< dS )zUDFS that calculates the b(u) and N(u) lookups, and also reorders the adjacency lists.�orderingr r � N_u_lookup� b_u_lookupN)� __branch_point_dfs_recursive)r �u�large_n�stem�br r r r l s r c s � d � d }t �|� ���d dkr0�d7 �d}d}� ��fdd�� d � D �D ]�}||�< t|� ��krVd||< t �|� �d dkr�|}qV|� } t|� �} | | k r�d||< n^| dk�r|| } || dkr�|| d ||< n.� d ��t|� ���rd||< n |� ||< || d dkrV|} �q0qV|dk�rb� d � �|� � d � �d|� n0|dk�r�� d � �|� � d � �d|� d} � d � D ]v}t|� ��k�r�||< | �r�|� ||< n(t �|� �d dk�r�d||< nd||< ||�< t||||� � d } �q�d S ) z[A recursive implementation of the BranchPtDFS function, as defined on page 14 of the paper.r r r r c s g | ]}t �|� ��kr|�qS r )�wt)�.0�v�r Zlarge_wr5 r r � <listcomp>� r% z0__branch_point_dfs_recursive.<locals>.<listcomp>r TFN)r9 �ar Zadjacentr �remove�insertr4 ) r5 r6 r8 r7 r Z first_vertexZv_IZv_IIr; Zb_uZl2_vZxnode� first_timer r< r r4 { sZ " r4 c C s� | d d }g | d< g | d< i | d< | d � � }d|f}d|f}d|d�}d|d�}| d �|� | d �|� ||g| d d< d| d d < d| d d < d| d d < t|| �}| S ) zUBuilds the combinatorial embedding of the graph. Returns whether the graph is planar.r1 r �LF�RF�FGr �r5 r; ��x�y�m�l�r)� num_nodes�append�__embed_branch_recursive)r r5 r" Zf0Zg0ZL0ZR0� nonplanarr r r r � s" r c C s� |d | D ]�}d}t ||�| krdt||�| krLt| ||�}|sLd}| S t||�}|r�| S q t| ||�r t| ||�}|s�d}| S q q d}|S )zbA recursive implementation of the EmbedBranch function, as defined on pages 8 and 22 of the paper.r TF)r> r8 �__insert_branchrN �is_frond� __embed_frond)r5 r r; rO � successfulr r r rN � s& rN c C sN t ||�}t| |�}t||�}t| ||�}|s2dS t| | |dd�}|sJdS dS )zkEmbeds a branch Bu(v) (as described on page 22 of the paper). Returns whether the embedding was successful.FT)�as_branch_marker)r �DrR )r5 r; r �w�d_u�d_wrS r r r rP s rP Fc C s� t | |�}t ||�}t|�}|rR|d9 }|d dkrBt|||� n t|||� dS |d }|d d }t|�} t|�} t||�} t||�} d} d}d}|| kr�|| kr�d} n0|| kr�|| kr�d}n|| kr�|| kr�d}ndS || k�rP|| k�rPt|||� |d d d7 < |d d }|d �� }||d �}|d d �}||g|d |< dS || k�rv|| k �rvt ||| |||�S || k �r�|| k�r�t ||| |||�S || k �r�|| k �r�|| k �r|| k �r|| k�r�|| k�r�dS t ||� t|�} t|�} |d d }t||�} t||�} �q�d} d}d}|| k�r@|| k�r@d}n|| k�rX|| k�rXd}|| k�r~|| k �r~t ||| |||�S || k �r�|| k�r�t ||| |||�S ndS dS ) zUEmbeds a frond uw into either LF or RF. Returns whether the embedding was successful.����last_inserted_siderB TrD rI Fr r rE r rF ) rU �abs�__insert_frond_RF�__insert_frond_LF�lw�rwr5 �fn_xrL �__do_case_5_work�__do_case_6_work� switch_sides)Znode_uZnode_wr rT rW rX �comp_d_wrB rI �l_w�r_w�u_m�x_m�case_1�case_2�case_3r" �Lm�Rmr r r rR sz rR c C s� |rdS t | �}t| ||� |d d }t||�}||d k rF| |d< ||d krZ||d< |r�| |d< t|d |�} || k r�t|� |d d }t|d |�} qtdS )zsEncapsulates the work that will be done for case 5 of __embed_frond, since it gets used in more than one place.FrD rI r5 r; r T)r[ r] �Lr` �merge_Fm) rX rW ri rj rk r rd rI rl �x_m1r r r ra � s$ ra c C s� |rdS t | �}t| ||� |d d }t||�}||d k rF| |d< ||d krZ||d< |r�| |d< t|d |�} || k r�t|� |d d }t|d |�} qtdS )zsEncapsulates the work that will be done for case 6 of __embed_frond, since it gets used in more than one place.FrD rI rG rH r T)r[ r\ �Rr5 ro ) rX rW ri rj rk r rd rI rm �u_m1r r r rb � s$ rb c C s2 |d � | |f� |d d d7 < d|d< dS )zQEncapsulates the process of inserting a frond uw into the right side frond group.rC rD rK r rZ N�rM �rX rW r r r r r\ � s r\ c C s2 |d � | |f� |d d d7 < d|d< dS )zPEncapsulates the process of inserting a frond uw into the left side frond group.rB rD rJ r rZ Nrs rt r r r r] � s r] c C s� | d }|d }|| }||d }|d d |d d k rP|d d |d d< |d d |d d kr||d d |d d< |d d |d d k r�|d d |d d< |d d |d d kr�|d d |d d< ||= |d d8 < d S ) z7Merges Fm-1 and Fm, as defined on page 19 of the paper.rD rI r r r5 r; rG rH Nr )r rD rI ZFGmZFGm1r r r ro � s ro c C s� |d d }t ||�}| |kr�t|�}t |d |�}||kr`t|� |d d }t |d |�}q4|d d |d d< t||�}t|d �d }|d | d }||kr�|d8 }|dk r�d}q�|d | d }q�||d d< n�t|�} t|d |�} | | k�r t|� |d d }t|d |�} q�|d d |d d< t ||�}t|d �d } |d | d } | |k�r�| d8 } |d | d } �q^| |d d< |d d }|d } |d }t ||�}t||�}t||�}t||�}d}t| �d }d}t|�d }||k �r.| | }||d k�r"|d8 }�q.n|d7 }�q�||k �rh| | }||d k �rX|d8 }n |d7 }�qh�q.||k �r�|| }||d k�r�|d8 }�q�n|d7 }�qh||k �r�|| }||d k �r�|d8 }n |d7 }�qܐq�| ||d � }|||d � }| ||d �= |||d �= |}|D ]}| �||� |d7 }�q |}|D ]}|�||� |d7 }�qD|d | d }|d | d }t |�} t |�} | |d | d< | |d | d< t|� d S ) z7Switches Lm and Rm, as defined on page 20 of the paper.rD rI r rK rJ rC r rB N) r5 r^ ro r` �lenr_ r; rH r@ �__convert_RF_dict_to_LF�__convert_LF_dict_to_RF) rW r rI rg re rr rh rK Zg_rrf rp rJ Zf_lrB rC Zv_mZy_mZfirst_left_indexZlast_left_indexZfirst_right_indexZlast_right_index�frondZLF_sliceZRF_slice�irG Zold_rmZold_lmZ converted_rmZ converted_lmr r r rc s� rc c C s | d | d d�}|S )z\Converts a right-side encoded frond dict into a left-side encoded frond dict. x -> u, y -> vrG rH rE r �rG Znew_xr r r rv � s rv c C s | d | d d�}|S )z\Converts a left-side encoded frond dict into a right-side encoded frond dict. u -> x, v -> yr5 r; rF r rz r r r rw � s rw c C s, |d d }|d | \}}t | ||||�S )z[Checks to see if the frond xy will conflict with a frond on the left side of the embedding.rD rJ rB ��__check_conflict_fronds)rG rH r rJ rV �zr r r �__check_left_side_conflict� s r~ c C s, |d d }|d | \}}t | ||||�S )z\Checks to see if the frond xy will conflict with a frond on the right side of the embedding.rD rK rC r{ )rG rH r rK rV r} r r r �__check_right_side_conflict� s r c C s� | dk r0|dk r0| |ks ||kr0| |kr,dS dS t | |�t ||�kr`| |kr`||kr`||kr`dS | dk sp|dk r�| dk r�t| �}|}|} |}n t|�}|}t | |�|kr�||k r�| |ft|||�v r�dS dS dS )zgChecks a pair of fronds to see if they conflict. Returns True if a conflict was found, False otherwise.r TF)r8 r[ �__dfsify_branch_uv)rG rH rV r} r r5 �tr r r r| � s( ,�r| c C sx t | ||�}g }|D ]^}|d �|�}|d \}}t||�} t||�} | | k rX| } | } n| } | } | | f} |�| � q|S )zSHelper function to convert the output of Bu(v) from edge ids to dfs-ordered fronds.r �vertices)�B�get_edgerU rM )r5 r; r Zbuvr0 r �edge�j�kZd_xZd_yZsmallerZlargerrx r r r r� � s r� Nc C s� t | |d�\}}}ttt|ttdt|�d �����}tttttdt|�d ��|���}i }| �� D ]L}| �|�} | d \} } || } || } | | ks�| | kr�d||< qfd||< qfi }||d< ||d< ||d< ||d < ||d < ||d < |S ) a7 Internal function that calculates the depth-first search of the graph. Returns a dictionary with the following data: * 'ordering': A dfs-ordering list of nodes * 'ordering_lookup': A lookup dict mapping nodes to dfs-ordering * 'node_lookup': A lookup dict mapping dfs-ordering to nodes * 'edge_lookup': A lookup dict mapping edges as tree-edges or back-edges * 'parent_lookup': A lookup dict mapping nodes to their parent node * 'children_lookup': A lookup dict mapping nodes to their children )r. r r� z tree-edger r1 �ordering_lookup� node_lookupr � parent_lookup�children_lookup)r �dictr) �zip�rangeru r r� )r r r1 r� r� r� r� r r r� Znode_ar/ Zparent_aZparent_br r r r r � s( $$ r c C s( i }| � � D ]}| �|�}|||< q |S )z�Builds an adjacency list representation for the graph, since we can't guarantee that the internal representation of the graph is stored that way.)Zget_all_node_ids� neighbors)r r �noder� r r r r s r c C s@ i }i }| d }|D ]"}t || �\}}|||< |||< q||fS )z2Calculates the lowpoints for each node in a graph.r1 )�__get_lowpoints)r r r r1 r� Zlow_1Zlow_2r r r r s r c s> |d � t | |�}t|� fdd�d�}|d }|d }||fS )z6Calculates the lowpoints for a single node in a graph.r� c s � | S r r )r> �r� r r r$ * r% z!__get_lowpoints.<locals>.<lambda>r& r r )�Tr, )r� r Zt_uZ sorted_t_uZ lowpoint_1Z lowpoint_2r r� r r� $ s r� c C s� |d }|d }|� | �}|d \}}t||�}t||�}t||�} t| |�} || dkrj||k rjd| S t|||�r~d| S t|||�r�d| d S d|�� d S dS )z.Calculates the edge weight used to sort edges.r r r� r r r N)r� rU r �is_type_I_branch�is_type_II_branchrL ) r r r r r� r5 r; rW �d_vZlp_1Zd_lp_1r r r r 1 s r c C s. | d d }i }t || �||< t||| � |S )z!Calculates the b(u) lookup table.r1 r )rU � __calculate_bu_dfs_recursively)r r5 r8 r r r �__calculate_bu_dfsG s r� c C sX d}|d | D ]B}t ||�| krN|r4|| ||< nt| |�||< t|||� d}qdS )z6Calculates the b(u) lookup table with a recursive DFS.Tr FN)r> rU r� )r5 r8 r rA r; r r r r� P s r� c C s( | t ||�krdS | t||�kr$dS dS )z2Determines whether a branch uv is a type I branch.FT�r> r �r5 r; r r r r r� ] s r� c C s( | t ||�krdS | t||�k r$dS dS )z3Determines whether a branch uv is a type II branch.FTr� r� r r r r� f s r� c C s t | |�rdS dS )z/Determines if v is a leaf (has no descendants).TF)�S�r; r r r r �is_leafo s r� c C sD t | |�}t ||�}|d �| |�}|d | dkr@||k r@dS dS )z2Determines if the edge uv is a frond ("backedge").r r r TF)rU r+ )r5 r; r rW r� r r r r rQ t s rQ c C s� g }t � }|d }| }|| }t||�}|D ] }t||�} | |kr,|�|� q,t|�dkr�|�� }|�|� || }t||�}|D ] }t||�} | |kr�|�|� q�qN|S )z Gets the descendants of a node.r� r )r rU rM ru �pop) r� r Zlist_of_descendants�stackr� Z current_node�childrenZdfs_current_noder" Z dfs_childr r r �__get_descendants| s( r� c C s | d d S )z-Returns the frond at the top of the LF stack.rB rY r �r r r r �__top_frond_left� s r� c C s | d d S )z-Returns the frond at the top of the RF stack.rC rY r r� r r r �__top_frond_right� s r� c C s |d | S )zThe adjacency function.r r �r5 r r r r �A� s r� c C s |d | S )zThe ancestor function.r� r r� r r r r> � s r> c C s |d | S )zThe DFS-numbering function.r� r r� r r r rU � s rU c C s t | |�S )z The set of all descendants of u.)r� r� r r r r� � s r� c C s t | |�}| |vr |�| � |S )z.The set of all descendants of u, with u added.)r� rM )r5 r Zs_ur r r �S_star� s r� c s t t� fdd�t| � �D ���S )zCT(u) consists of all vertices adjacent to u or any descendant of u.c s g | ]}t |� �D ]}|�qqS r )r� )r: r; rV r� r r r= � r% zT.<locals>.<listcomp>)r) �setr� r� r r� r r� � s r� c s2 t |� �| krdS tt� fdd�t|� �D ���S )zhThe branch at u containing v is the set of all edges incident on v or any descendant of v, if a(v) == u.Nc s( g | ] }� d � |�d D ]}|�qqS )r �edges)Zget_node)r: rV r r� r r r= � r% zB.<locals>.<listcomp>)r> r) r� r� r� r r� r r� � s r� c C s: |d � | |�}t| ||�}|D ]}||v r | S q dS )z*The stem of Bu(v) is the edge uv in Bu(v).r N)Zget_edge_ids_by_node_idsr� )r5 r; r Zuv_edgesZ buv_edgesr r r r r7 � s r7 c C s |d | S )z The L1 lowpoint of the node.r r r� r r r r � s r c C s |d | S )z The L2 lowpoint of the node.r r r� r r r r � s r c C s |d � | |�}|d | S )z'The wt_u[v] function used in the paper.r r )r+ )r5 r; r r r r r r9 � s r9 c C sF t � }t| d �� �D ]&\}}|d }t||| �r|�|� qt|�S )z:L(T) contains leaves and branch points for the DFS-tree T.r r )r� r) r* rQ �add)r Znode_setr; r rV r r r �_L� s r� c C s |d | S )z$The b(u) function used in the paper.r3 r r� r r r r8 � s r8 c C s |d | S )z$The N(u) function used in the paper.r2 r r� r r r �N� s r� c C s |d | S )z%The N'(u) function used in the paper.ZN_prime_u_lookupr r� r r r �N_prime s r� c C s |d | S )z'The block of fronds in the frond graph.rD r �ry r r r r �F s r� c C s t | |�d S )z6The set of fronds on the left side of the frond graph.r �r� r� r r r rn s rn c C s t | |�d S )z7The set of fronds on the right side of the frond graph.r r� r� r r r rq s rq c C s t | |�d S )z;The minimum vertex (DFS-number) in a frond contained in Li.r5 �rn r� r r r r5 s r5 c C s t | |�d S )z;The maximum vertex (DFS-number) in a frond contained in Li.r; r� r� r r r r; s r; c C sF zt | |�d W S ty@ } z|d �� W Y d}~S d}~0 0 dS )z;The minimum vertex (DFS-number) in a frond contained in Ri.rG r N)rq � ExceptionrL �ry r �er r r r` ! s r` c C s< zt | |�d W S ty6 } zW Y d}~dS d}~0 0 dS )z;The maximum vertex (DFS-number) in a frond contained in Ri.rH Nr )rq r� r� r r r rH * s rH c C s | d d }| d | d S )z\The minimum frond endpoint that can be embedded on the left side of the current frond block.rD rJ rB r r )r rJ r r r r^ 3 s r^ c C s | d d }| d | d S )z]The minimum frond endpoint that can be embedded on the right side of the current frond block.rD rK rC r r )r rK r r r r_ 9 s r_ )F)N)B�__doc__� collectionsr Z searching.depth_first_searchr r r r r r r r4 r rN rP rR ra rb r\ r] ro rc rv rw r~ r r| r� r r r r� r r� r� r� r� r� rQ r� r� r� r� r> rU r� r� r� r� r7 r r r9 r� r8 r� r� r� rn rq r5 r; r` rH r^ r_ r r r r �<module> s� < 5 v$" $ $
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