Aleph-w 3.0
A C++ Library for Data Structures and Algorithms
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Public Types | Public Member Functions | Static Public Attributes | Private Types | Private Member Functions | Static Private Member Functions | Private Attributes | List of all members
Aleph::lca_detail::Rooted_Tree_Data< GT, SA > Class Template Reference

#include <LCA.H>

Inheritance diagram for Aleph::lca_detail::Rooted_Tree_Data< GT, SA >:
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Collaboration diagram for Aleph::lca_detail::Rooted_Tree_Data< GT, SA >:
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Public Types

using Node = typename GT::Node
 
using Arc = typename GT::Arc
 

Public Member Functions

 Rooted_Tree_Data (const GT &g, Node *root, SA sa=SA())
 
size_t size () const noexcept
 
bool is_empty () const noexcept
 
Node * root () const noexcept
 
size_t root_id () const noexcept
 
const Array< Node * > & id_to_node () const noexcept
 
const Array< size_t > & parent () const noexcept
 
const Array< size_t > & depth () const noexcept
 
const Array< size_t > & tin () const noexcept
 
const Array< size_t > & tout () const noexcept
 
const Array< size_t > & first () const noexcept
 
const Array< size_t > & euler () const noexcept
 
size_t euler_size () const noexcept
 
size_t id_of (const Node *node) const
 
Node * node_of (const size_t id) const
 
void validate_id (const size_t id, const char *where) const
 
bool is_ancestor (const size_t u, const size_t v) const
 

Static Public Attributes

static constexpr size_t NONE = std::numeric_limits<size_t>::max()
 

Private Types

using Pair_Key = std::pair< size_t, size_t >
 

Private Member Functions

void index_nodes ()
 
void build_simple_adjacency ()
 
void build_dfs_data ()
 
void check_id (const size_t id, const char *where) const
 

Static Private Member Functions

static Pair_Key normalize_pair (size_t u, size_t v) noexcept
 

Private Attributes

const GT * graph_ = nullptr
 
SA sa_
 
Node * root_ = nullptr
 
size_t root_id_ = NONE
 
size_t n_ = 0
 
Array< Node * > id_to_node_
 
MapOLhash< Node *, size_t > node_to_id_
 
Array< Array< size_t > > adjacency_
 
Array< size_t > parent_
 
Array< size_t > depth_
 
Array< size_t > tin_
 
Array< size_t > tout_
 
Array< size_t > first_
 
Array< size_t > euler_
 
size_t euler_size_ = 0
 

Detailed Description

template<class GT, class SA>
class Aleph::lca_detail::Rooted_Tree_Data< GT, SA >

Definition at line 126 of file LCA.H.

Member Typedef Documentation

◆ Arc

template<class GT , class SA >
using Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::Arc = typename GT::Arc

Definition at line 130 of file LCA.H.

◆ Node

template<class GT , class SA >
using Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::Node = typename GT::Node

Definition at line 129 of file LCA.H.

◆ Pair_Key

template<class GT , class SA >
using Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::Pair_Key = std::pair<size_t, size_t>
private

Definition at line 135 of file LCA.H.

Constructor & Destructor Documentation

◆ Rooted_Tree_Data()

template<class GT , class SA >
Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::Rooted_Tree_Data ( const GT &  g,
Node *  root,
SA  sa = SA() 
)
inline

Definition at line 344 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes().

Member Function Documentation

◆ build_dfs_data()

template<class GT , class SA >
void Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data ( )
inlineprivate

Definition at line 255 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::adjacency_, ah_domain_error_if, ah_runtime_error_unless, Aleph::Array< T >::create(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::depth_, Aleph::divide_and_conquer_partition_dp(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_size_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::first_, Aleph::DynListStack< T >::is_empty(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::n_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::NONE, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::parent_, Aleph::DynListStack< T >::pop(), Aleph::DynListStack< T >::push(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_id_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tin_, Aleph::DynListStack< T >::top(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tout_.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::Rooted_Tree_Data().

◆ build_simple_adjacency()

template<class GT , class SA >
void Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency ( )
inlineprivate

Definition at line 201 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::adjacency_, ah_domain_error_if, ah_runtime_error_unless, Aleph::and, Aleph::divide_and_conquer_partition_dp(), GraphCommon< GT, Node, Arc >::get_src_node(), GraphCommon< GT, Node, Arc >::get_tgt_node(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::graph_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::n_, Aleph::Filter_Iterator< Container, It, Show_Item >::next_ne(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::node_to_id_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::normalize_pair(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::sa_, and Aleph::MapOpenHash< Key, Data, Cmp, HashTable >::search().

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::Rooted_Tree_Data().

◆ check_id()

template<class GT , class SA >
void Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::check_id ( const size_t  id,
const char *  where 
) const
inlineprivate

Definition at line 337 of file LCA.H.

References ah_out_of_range_error_if, Aleph::divide_and_conquer_partition_dp(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::n_.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::is_ancestor(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::node_of(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::validate_id().

◆ depth()

template<class GT , class SA >
const Array< size_t > & Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::depth ( ) const
inlinenoexcept

Definition at line 359 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::depth_.

Referenced by Aleph::Gen_Euler_RMQ_LCA< GT, SA >::build_rmq(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::depth_of_id(), Aleph::Gen_Euler_RMQ_LCA< GT, SA >::depth_of_id(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::distance_id(), Aleph::Gen_Euler_RMQ_LCA< GT, SA >::distance_id(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::kth_ancestor_id(), and Aleph::Gen_Binary_Lifting_LCA< GT, SA >::lca_id().

◆ euler()

template<class GT , class SA >
const Array< size_t > & Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler ( ) const
inlinenoexcept

Definition at line 363 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_.

Referenced by Aleph::Gen_Euler_RMQ_LCA< GT, SA >::build_rmq(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::euler_tour().

◆ euler_size()

template<class GT , class SA >
size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_size ( ) const
inlinenoexcept

Definition at line 364 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_size_.

Referenced by Aleph::Gen_Euler_RMQ_LCA< GT, SA >::build_rmq(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::euler_tour_size().

◆ first()

template<class GT , class SA >
const Array< size_t > & Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::first ( ) const
inlinenoexcept

Definition at line 362 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::first_.

Referenced by Aleph::Gen_Euler_RMQ_LCA< GT, SA >::lca_id().

◆ id_of()

template<class GT , class SA >
size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_of ( const Node *  node) const
inline

Definition at line 366 of file LCA.H.

References ah_domain_error_if, ah_invalid_argument_if, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::node_to_id_, and Aleph::MapOpenHash< Key, Data, Cmp, HashTable >::search().

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::id_of(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::id_of().

◆ id_to_node()

template<class GT , class SA >
const Array< Node * > & Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_to_node ( ) const
inlinenoexcept

Definition at line 357 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_to_node_.

◆ index_nodes()

template<class GT , class SA >
void Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes ( )
inlineprivate

Definition at line 163 of file LCA.H.

References ah_domain_error_if, ah_runtime_error_unless, Aleph::Array< T >::create(), Aleph::divide_and_conquer_partition_dp(), Aleph::MapOpenHash< Key, Data, Cmp, HashTable >::find(), GraphCommon< GT, Node, Arc >::get_num_nodes(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::graph_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_to_node_, Aleph::MapOpenHash< Key, Data, Cmp, HashTable >::insert(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::n_, Aleph::Filter_Iterator< Container, It, Show_Item >::next_ne(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::node_to_id_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_id_, and Aleph::MapOpenHash< Key, Data, Cmp, HashTable >::search().

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::Rooted_Tree_Data().

◆ is_ancestor()

template<class GT , class SA >
bool Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::is_ancestor ( const size_t  u,
const size_t  v 
) const
inline

Definition at line 389 of file LCA.H.

References Aleph::and, Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::check_id(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tin_, and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tout_.

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::is_ancestor_id(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::is_ancestor_id().

◆ is_empty()

template<class GT , class SA >
bool Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::is_empty ( ) const
inlinenoexcept

Definition at line 353 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::n_.

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::is_empty(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::is_empty().

◆ node_of()

template<class GT , class SA >
Node * Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::node_of ( const size_t  id) const
inline

Definition at line 378 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::check_id(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_to_node_.

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::node_of(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::node_of().

◆ normalize_pair()

template<class GT , class SA >
static Pair_Key Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::normalize_pair ( size_t  u,
size_t  v 
)
inlinestaticprivatenoexcept

Definition at line 156 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency().

◆ parent()

template<class GT , class SA >
const Array< size_t > & Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::parent ( ) const
inlinenoexcept

Definition at line 358 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::parent_.

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::build_jump_table(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::lca_id(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::parent_id(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::parent_id().

◆ root()

template<class GT , class SA >
Node * Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root ( ) const
inlinenoexcept

Definition at line 354 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_.

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::root(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::root().

◆ root_id()

template<class GT , class SA >
size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_id ( ) const
inlinenoexcept

Definition at line 355 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_id_.

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::root_id(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::root_id().

◆ size()

template<class GT , class SA >
size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::size ( ) const
inlinenoexcept

Definition at line 352 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::n_.

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::n(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::size(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::size().

◆ tin()

template<class GT , class SA >
const Array< size_t > & Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tin ( ) const
inlinenoexcept

Definition at line 360 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tin_.

◆ tout()

template<class GT , class SA >
const Array< size_t > & Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tout ( ) const
inlinenoexcept

Definition at line 361 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tout_.

◆ validate_id()

template<class GT , class SA >
void Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::validate_id ( const size_t  id,
const char *  where 
) const
inline

Definition at line 384 of file LCA.H.

References Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::check_id(), and Aleph::divide_and_conquer_partition_dp().

Referenced by Aleph::Gen_Binary_Lifting_LCA< GT, SA >::depth_of_id(), Aleph::Gen_Euler_RMQ_LCA< GT, SA >::depth_of_id(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::kth_ancestor_id(), Aleph::Gen_Euler_RMQ_LCA< GT, SA >::lca_id(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::lca_id(), Aleph::Gen_Binary_Lifting_LCA< GT, SA >::parent_id(), and Aleph::Gen_Euler_RMQ_LCA< GT, SA >::parent_id().

Member Data Documentation

◆ adjacency_

template<class GT , class SA >
Array<Array<size_t> > Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::adjacency_
private

Definition at line 147 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency().

◆ depth_

template<class GT , class SA >
Array<size_t> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::depth_
private

Definition at line 149 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::depth().

◆ euler_

template<class GT , class SA >
Array<size_t> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_
private

Definition at line 153 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler().

◆ euler_size_

template<class GT , class SA >
size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_size_ = 0
private

Definition at line 154 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::euler_size().

◆ first_

template<class GT , class SA >
Array<size_t> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::first_
private

Definition at line 152 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::first().

◆ graph_

template<class GT , class SA >
const GT* Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::graph_ = nullptr
private

Definition at line 137 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes().

◆ id_to_node_

template<class GT , class SA >
Array<Node *> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_to_node_
private

Definition at line 144 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_to_node(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::node_of().

◆ n_

template<class GT , class SA >
size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::n_ = 0
private

Definition at line 142 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::check_id(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::is_empty(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::size().

◆ node_to_id_

template<class GT , class SA >
MapOLhash<Node *, size_t> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::node_to_id_
private

Definition at line 145 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::id_of(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes().

◆ NONE

template<class GT , class SA >
constexpr size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::NONE = std::numeric_limits<size_t>::max()
staticconstexpr

Definition at line 132 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data().

◆ parent_

template<class GT , class SA >
Array<size_t> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::parent_
private

Definition at line 148 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::parent().

◆ root_

template<class GT , class SA >
Node* Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_ = nullptr
private

Definition at line 139 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root().

◆ root_id_

template<class GT , class SA >
size_t Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_id_ = NONE
private

Definition at line 140 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::index_nodes(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::root_id().

◆ sa_

template<class GT , class SA >
SA Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::sa_
private

Definition at line 138 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_simple_adjacency().

◆ tin_

template<class GT , class SA >
Array<size_t> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tin_
private

Definition at line 150 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::is_ancestor(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tin().

◆ tout_

template<class GT , class SA >
Array<size_t> Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tout_
private

Definition at line 151 of file LCA.H.

Referenced by Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::build_dfs_data(), Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::is_ancestor(), and Aleph::lca_detail::Rooted_Tree_Data< GT, SA >::tout().

The documentation for this class was generated from the following file: