Tree graph class. More...

#include <tree.hpp>

Inheritance diagram for lal::graphs::tree:

Public Member Functions
	tree () noexcept
	Empty constructor.

	tree (const tree &t) noexcept
	Copy constructor. More...

	tree (tree &&t) noexcept
	Move constructor. More...

virtual	~tree () noexcept
	Destructor.

tree &	operator= (const tree &t) noexcept
	Copy assignment operator. More...

tree &	operator= (tree &&t) noexcept
	Move assignment operator. More...

virtual void	calculate_tree_type () noexcept=0
	Calculates the type of tree. More...

bool	is_tree () const noexcept
	Is this graph is an actual tree? More...

virtual bool	is_rooted () const noexcept=0
	Returns whether this tree is a rooted tree.

virtual bool	can_add_edge (node s, node t) const noexcept
	Can this edge be added? More...

virtual bool	can_add_edges (const std::vector< edge > &edges) const noexcept
	Can these edges be added? More...

uint64_t	get_component_representative (node u) const noexcept
	Representative node of the connected component in which u belongs. More...

bool	are_nodes_in_same_component (node u, node v) const noexcept
	Checks if two nodes are in the same connected component. More...

uint64_t	get_num_nodes_component (node u) const noexcept
	Amount of nodes in a connected component of the tree. More...

bool	is_of_tree_type (const tree_type &tt) const noexcept
	Returns whether this tree is of type tt. More...

bool	is_tree_type_valid () const noexcept
	Is the type of this tree valid? More...

std::vector< std::string >	get_tree_type_list () const noexcept
	Returns the list of types as a list of strings. More...

virtual void	init (uint64_t n) noexcept
	Allocates the necessary memory for this class. More...

virtual void	clear () noexcept
	Frees the memory occupied by this graph. More...

virtual void	normalise () noexcept
	Normalises the graph. More...

virtual bool	check_normalised () noexcept
	Checks if the graph is normalised. More...

virtual void	finish_bulk_add (bool norm=true, bool check=true) noexcept=0
	Completes the inner structure of the graph after adding a bulk of edges. More...

void	set_normalised (bool v=true) noexcept
	Sets whether this graph is normalised or not.

virtual std::vector< edge_pair >	get_Q () const noexcept=0
	Returns all independent pairs of edges of this graph. More...

bool	has_node (node u) const noexcept
	Returns true if node u is in this graph.

virtual bool	has_edge (node u, node v) const =0
	Returns true if the undirected edge (u, v) exists in the graph.

uint64_t	get_num_nodes () const noexcept
	Returns the number of ndoes.

uint64_t	get_num_edges () const noexcept
	Returns the number of edges.

virtual std::vector< edge >	get_edges () const noexcept=0
	Returns all edges of this graph.

bool	is_normalised () const noexcept
	Returns whether this graph is normalised or not. More...

virtual bool	is_directed () const noexcept=0
	Returns whether this graph is directed or not.

virtual bool	is_undirected () const noexcept=0
	Returns whether this graph is undirected or not.

Protected Member Functions
void	tree_only_init (uint64_t n) noexcept
	Initialises only the memory of class tree. More...

void	tree_only_clear () noexcept
	Clears the memory used by only class tree.

void	tree_only_copy (const tree &t) noexcept
	Copies only members of class tree.

void	tree_only_move (tree &&t) noexcept
	Moves only members of class tree.

void	actions_after_remove_node (node u) noexcept
	Do some work before an node is removed. More...

void	actions_after_add_edge (node u, node v) noexcept
	Do some work after the addition of an edge. More...

void	actions_after_remove_edge (node u, node v) noexcept
	Do some work after the removal of an edge. More...

void	actions_before_remove_edges_incident_to (node u) noexcept
	Do some work before all edges incident to a node is removed. More...

void	tree_only_set_edges () noexcept
	Updates the data structures of a tree after the graph structure has had its set of edges set. More...

void	tree_only_remove_node (node u) noexcept
	Removes a vertex from the union-find data structure. More...

void	fill_union_find () noexcept

virtual void	update_union_find_after_edge_add (node u, node v, uint64_t const root_of, uint64_t const root_size) noexcept=0
	Update the union find data structure after an edge addition. More...

virtual void	update_union_find_after_edge_add (node u, node v, uint64_t const root_of, uint64_t const root_size) const noexcept=0
	Update the union find data structure after an edge addition. More...

virtual void	update_union_find_after_edge_remove (node u, node v, uint64_t const root_of, uint64_t const root_size) noexcept=0
	Update the union find data structure after an edge removal. More...

virtual void	update_union_find_after_edge_remove (node u, node v, uint64_t const root_of, uint64_t const root_size) const noexcept=0
	Update the union find data structure after an edge removal. More...

virtual void	update_union_find_before_incident_edges_removed (node u, uint64_t const root_of, uint64_t const root_size) noexcept=0
	Update the union find data structure before the removal of all edges incident to a node. More...

virtual void	update_union_find_before_incident_edges_removed (node u, uint64_t const root_of, uint64_t const root_size) const noexcept=0
	Update the union find data structure before the removal of all edges incident to a node. More...

virtual void	_init (uint64_t n) noexcept
	Initialises memory of graph class.

virtual void	_clear () noexcept
	Clears memory for the graph class.

void	copy_full_graph (const graph &g) noexcept
	Copies all members of this class.

void	move_full_graph (graph &&g) noexcept
	Moves all members of this class.

void	__disjoint_union (const graph &g) noexcept
	Disjoint union of graphs. More...

void	normalise_after_edge_addition (bool norm, bool check) noexcept
	Normalise the graph after one (or more) edges have been added.

void	normalise_after_edge_removal (bool norm, bool check) noexcept
	Normalise the graph after one (or more) edges have been removed.

Protected Attributes
std::vector< node >	m_root_of
	The root of every vertex in the union-find data structure.

std::vector< uint64_t >	m_root_size
	The size of the connected component that a root belongs to. More...

std::array< bool, __tree_type_size >	m_tree_type
	The type of this tree.

bool	m_is_tree_type_valid = false
	Is the type of this tree valid? More...

std::vector< neighbourhood >	m_adjacency_list
	Data structure that implements the graph.

uint64_t	m_num_edges = 0
	Amount of edges of this graph.

bool	m_normalised = true
	Is this graph normalised? More...

Detailed Description

Tree graph class.

This is an abstract class for those tree-like graphs. Classes that implement different abstractions of trees and that inherit from this class are: free_tree, rooted_tree.

In these classes the addition of edges is constrained so as to ensure that the edges added actually yield trees, i.e., that cycles are never produced. For the sake of efficiency, only debug compilations of the library (compilations where the DEBUG symbol is defined) check that such additions do not produce cycles. In case of doubt, one can query the class using methods can_add_edge or can_add_edges prior to adding one or several edges.

Constructor & Destructor Documentation

◆ tree() [1/2]

lal::graphs::tree::tree ( const tree & t )

inlinenoexcept

Copy constructor.

Parameters

t Tree.

◆ tree() [2/2]

lal::graphs::tree::tree ( tree && t )

inlinenoexcept

Move constructor.

Parameters

t Tree.

Member Function Documentation

◆ __disjoint_union()

void lal::graphs::graph::__disjoint_union ( const graph & g )

protectednoexceptinherited

Disjoint union of graphs.

Given a graph, append it to the current graph.

All the nodes in g are relabelled starting at n, the number of nodes of the current graph.

Parameters

g	Input graph.

Precondition: This graph and g must be of the same type (both must be either undirected, or both directed).

Postcondition: The graph is normalised only if it was normalised before the call and g is also normalised.

◆ actions_after_add_edge()

void lal::graphs::tree::actions_after_add_edge	(	node	u,
		node	v
	)

protectedvirtualnoexcept

Do some work after the addition of an edge.

Parameters

u	First node of the edge.
v	Second node of the edge.

Postcondition: The tree type is invalidated.; Updated union-find.

Reimplemented from lal::graphs::graph.

◆ actions_after_remove_edge()

void lal::graphs::tree::actions_after_remove_edge	(	node	u,
		node	v
	)

protectedvirtualnoexcept

Do some work after the removal of an edge.

Parameters

u	First node of the edge.
v	Second node of the edge.

Postcondition: The tree type is invalidated.; Updated union-find.

Reimplemented from lal::graphs::graph.

◆ actions_after_remove_node()

void lal::graphs::tree::actions_after_remove_node ( node u )

protectedvirtualnoexcept

Do some work before an node is removed.

Parameters

u	Node to be removed.

Postcondition: The tree type is invalidated.; Updated union-find.

Reimplemented from lal::graphs::graph.

◆ actions_before_remove_edges_incident_to()

void lal::graphs::tree::actions_before_remove_edges_incident_to ( node u )

protectedvirtualnoexcept

Do some work before all edges incident to a node is removed.

Parameters

u	Node whose incident edges are to be removed.

Postcondition: The tree type is invalidated.; Updated union-find.

Reimplemented from lal::graphs::graph.

◆ are_nodes_in_same_component()

bool lal::graphs::tree::are_nodes_in_same_component	(	node	u,
		node	v
	)		const

inlinenoexcept

Checks if two nodes are in the same connected component.

Parameters

u	First node.
v	Second node.

Returns: True or false.

◆ calculate_tree_type()

virtual void lal::graphs::tree::calculate_tree_type ( )

pure virtualnoexcept

Calculates the type of tree.

See tree_type for the list of different tree types.

Implemented in lal::graphs::free_tree, and lal::graphs::rooted_tree.

◆ can_add_edge()

virtual bool lal::graphs::tree::can_add_edge	(	node	s,
		node	t
	)		const

virtualnoexcept

Can this edge be added?

In a tree, an edge can only be added if it does not produce cycles, and it has not been added before.

In a rooted tree, an edge can only be added if the in-degree of vertex t (see lal::graphs::directed_graph::get_in_degree) is exactly 1 after adding the edge.

Parameters

s	First node of the edge.
t	Second node of the edge.

Returns: Whether or not this edge can be added to the tree without producing cycles.

Reimplemented in lal::graphs::rooted_tree.

◆ can_add_edges()

virtual bool lal::graphs::tree::can_add_edges ( const std::vector< edge > & edges ) const

virtualnoexcept

Can these edges be added?

In a tree, a set of edges can only be added if their addition to the tree do not produce cycles and none of them have been added before.

In a rooted tree, edges \((s,t)\) can only be added if the in-degree of vertex t (see lal::graphs::directed_graph::get_in_degree) is exactly 1 after adding the edge.

Parameters

edges List of edges.

Returns: Whether or not these edges can be added to the tree without producing cycles.

Reimplemented in lal::graphs::rooted_tree.

◆ check_normalised()

virtual bool lal::graphs::graph::check_normalised ( )

virtualnoexceptinherited

Checks if the graph is normalised.

Checks, whether the graph's adjacency structure is normalised or not. In case it is, attribute m_normalised is set to true, so method is_normalised evaluates to true.

Reimplemented in lal::graphs::directed_graph.

◆ clear()

virtual void lal::graphs::graph::clear ( )

virtualnoexceptinherited

Frees the memory occupied by this graph.

See _clear for details.

Postcondition: The graph is normalised. The number of edges is 0.

◆ fill_union_find()

void lal::graphs::tree::fill_union_find ( )

inlineprotectednoexcept

Fills the Union-Find data structure assuming that the graph structure has all of its edges.

◆ finish_bulk_add()

virtual void lal::graphs::graph::finish_bulk_add	(	bool	norm = `true`,
		bool	check = `true`
	)

pure virtualnoexceptinherited

Completes the inner structure of the graph after adding a bulk of edges.

This is meant to be used after several calls to undirected_graph::add_edge_bulk, directed_graph::add_edge_bulk.

Also, the graph must have been completely constructed after all the bulk additions of edges to the graph.

Parameters

norm	Normalise the graph.
check	Check wether the graph is normalised or not.

Implemented in lal::graphs::directed_graph, lal::graphs::free_tree, lal::graphs::rooted_tree, and lal::graphs::undirected_graph.

◆ get_component_representative()

uint64_t lal::graphs::tree::get_component_representative ( node u ) const

inlinenoexcept

Representative node of the connected component in which u belongs.

If the current graph lacks some edges then it is clearly a forest, i.e., a series of disconnected components. This function returns a representative node of the connected component to which node u belongs.

Further, let \(cc(u)\) be the connected component of vertex u, and \(rep(cc(u))\) be the representative node of \(cc(u)\). For every other node \(v\in cc(u)\), this function will return the same representative node \(rep(cc(u))\). Therefore, \(rep(cc(u))=rep(cc(v))\) for every \(v\in cc(u)\).

Parameters

u	Input node.

Returns: The representative node of node u's component.

◆ get_num_nodes_component()

uint64_t lal::graphs::tree::get_num_nodes_component ( node u ) const

inlinenoexcept

Amount of nodes in a connected component of the tree.

If the current graph lacks some edges then it is clearly a forest, i.e., a series of disconnected components. This function returns the size of the component node u belongs to.

In rooted trees one has to see this amount as the number of nodes of the component in the underlying undirected forest.

Parameters

u	Input node.

Returns: The size of the connected component of u.

◆ get_Q()

virtual std::vector< edge_pair > lal::graphs::graph::get_Q ( ) const

pure virtualnoexceptinherited

Returns all independent pairs of edges of this graph.

The set \(Q(G)\) is defined as the pairs of edges of \(G\), \(E(G) \times E(G)\), that are independent, that is, that share no nodes.

Implemented in lal::graphs::directed_graph, and lal::graphs::undirected_graph.

◆ get_tree_type_list()

std::vector< std::string > lal::graphs::tree::get_tree_type_list ( ) const

noexcept

Returns the list of types as a list of strings.

Returns: The list of types as a list of strings.

◆ init()

virtual void lal::graphs::graph::init ( uint64_t n )

virtualnoexceptinherited

Allocates the necessary memory for this class.

See _init for details.

Parameters

n	Number of nodes.

◆ is_normalised()

bool lal::graphs::graph::is_normalised ( ) const

inlinenoexceptinherited

Returns whether this graph is normalised or not.

A graph is normalised if every node's adjacency list is sorted increasingly. For this, use method normalise().

Returns: The value of m_normalised.

◆ is_of_tree_type()

bool lal::graphs::tree::is_of_tree_type ( const tree_type & tt ) const

inlinenoexcept

Returns whether this tree is of type tt.

See method calculate_tree_type to know how to calculate a tree's type.

Parameters

tt	Type of tree (see lal::graphs::tree_type).

Returns: True if this tree is of type tt.

◆ is_tree()

bool lal::graphs::tree::is_tree ( ) const

inlinenoexcept

Is this graph is an actual tree?

Returns true if the number of edges is one less than the number of nodes. Note that this would not really be true if the addition of edges was not constrained. Since it is constrained in a way that no cycles can be produced (for example, see free_tree::add_edge, or free_tree::add_edges), then we only need to check for the number of edges.

For further characterisations of a tree see [23] (chapter 4, pages 32-33).

Returns: True or false depending on whether this graph fits the defintion of tree.

◆ is_tree_type_valid()

bool lal::graphs::tree::is_tree_type_valid ( ) const

inlinenoexcept

Is the type of this tree valid?

This function enables users determine when this tree's type should be calculated.

In case this function returns false, users should call function calculate_tree_type in order to obtain a valid tree type. Note, however, that prior to calling the function the type of this tree might be lal::graphs::tree_type::unknown and that the tree type may remain lal::graphs::tree_type::unknown even after the type has been calculated. Nevertheless, users should be suspicious of a tree being of lal::graphs::tree_type::unknown (in fact, of any) type if this method returns false, yet they should be sure of it if the type was calculated via method calculate_tree_type.

Returns: True or false depending on whether the tree type was calculated or not.

◆ normalise()

virtual void lal::graphs::graph::normalise ( )

virtualnoexceptinherited

Normalises the graph.

Sorts this graph's adjacency list structure in increasing order.

Besides expensive, this method may be unnecessary. Method check_normalised() checks whether the graph is normalised or not; in case it is, using this method is completely unnecessary.

Postcondition: Method is_normalised evaluates to true.

Reimplemented in lal::graphs::directed_graph.

◆ operator=() [1/2]

tree & lal::graphs::tree::operator= ( const tree & t )

inlinenoexcept

Copy assignment operator.

Parameters

t Tree.

◆ operator=() [2/2]

tree & lal::graphs::tree::operator= ( tree && t )

inlinenoexcept

Move assignment operator.

Parameters

t Tree.

◆ tree_only_init()

void lal::graphs::tree::tree_only_init ( uint64_t n )

inlineprotectednoexcept

Initialises only the memory of class tree.

Parameters

n	Number of vertices.

◆ tree_only_remove_node()

void lal::graphs::tree::tree_only_remove_node ( node u )

protectednoexcept

Removes a vertex from the union-find data structure.

Parameters

u	Node that was removed.

Postcondition: The tree type is invalidated.; Updated union-find.

◆ tree_only_set_edges()

void lal::graphs::tree::tree_only_set_edges ( )

protectednoexcept

Updates the data structures of a tree after the graph structure has had its set of edges set.

Postcondition: The tree type is invalidated.; Updated union-find.

◆ update_union_find_after_edge_add() [1/2]

virtual void lal::graphs::tree::update_union_find_after_edge_add	(	node	u,
		node	v,
		uint64_t *const	root_of,
		uint64_t *const	root_size
	)		const

protectedpure virtualnoexcept

Update the union find data structure after an edge addition.

This is a helper method to be able to call a template in the lal::detail namespace which updates the union find data structure under addition of an edge.

Parameters

u	Node that is connected to v.
v	Node that is connected to u.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implemented in lal::graphs::free_tree, and lal::graphs::rooted_tree.

◆ update_union_find_after_edge_add() [2/2]

virtual void lal::graphs::tree::update_union_find_after_edge_add	(	node	u,
		node	v,
		uint64_t *const	root_of,
		uint64_t *const	root_size
	)

protectedpure virtualnoexcept

Update the union find data structure after an edge addition.

This is a helper method to be able to call a template in the lal::detail namespace which updates the union find data structure under addition of an edge.

Parameters

u	Node that is connected to v.
v	Node that is connected to u.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implemented in lal::graphs::free_tree, and lal::graphs::rooted_tree.

◆ update_union_find_after_edge_remove() [1/2]

virtual void lal::graphs::tree::update_union_find_after_edge_remove	(	node	u,
		node	v,
		uint64_t *const	root_of,
		uint64_t *const	root_size
	)		const

protectedpure virtualnoexcept

Update the union find data structure after an edge removal.

This is a helper method to be able to call a template in the lal::detail namespace which updates the union find data structure under removal of an edge.

Parameters

u	Node that is connected to v.
v	Node that is connected to u.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implemented in lal::graphs::free_tree, and lal::graphs::rooted_tree.

◆ update_union_find_after_edge_remove() [2/2]

virtual void lal::graphs::tree::update_union_find_after_edge_remove	(	node	u,
		node	v,
		uint64_t *const	root_of,
		uint64_t *const	root_size
	)

protectedpure virtualnoexcept

Update the union find data structure after an edge removal.

This is a helper method to be able to call a template in the lal::detail namespace which updates the union find data structure under removal of an edge.

Parameters

u	Node that is connected to v.
v	Node that is connected to u.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implemented in lal::graphs::free_tree, and lal::graphs::rooted_tree.

◆ update_union_find_before_incident_edges_removed() [1/2]

virtual void lal::graphs::tree::update_union_find_before_incident_edges_removed	(	node	u,
		uint64_t *const	root_of,
		uint64_t *const	root_size
	)		const

protectedpure virtualnoexcept

Update the union find data structure before the removal of all edges incident to a node.

This is a helper method to be able to call a template in the lal::detail namespace which updates the union find data structure under removal of all incident edges to a node.

Parameters

u	Node whose incident edges are to be removed.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implemented in lal::graphs::free_tree, and lal::graphs::rooted_tree.

◆ update_union_find_before_incident_edges_removed() [2/2]

virtual void lal::graphs::tree::update_union_find_before_incident_edges_removed	(	node	u,
		uint64_t *const	root_of,
		uint64_t *const	root_size
	)

protectedpure virtualnoexcept

Update the union find data structure before the removal of all edges incident to a node.

This is a helper method to be able to call a template in the lal::detail namespace which updates the union find data structure under removal of all incident edges to a node.

Parameters

u	Node whose incident edges are to be removed.
root_of	Array of n elements relating each vertex to its root in the union find data structure.
root_size	Array of n elements relating each vertex to the size of the connected component it belongs to.

Implemented in lal::graphs::free_tree, and lal::graphs::rooted_tree.

Member Data Documentation

◆ m_is_tree_type_valid

bool lal::graphs::tree::m_is_tree_type_valid = false

protected

Is the type of this tree valid?

This attribute keeps track of whether or not the function calculate_tree_type should be called before querying the type of this tree via function is_of_tree_type.

◆ m_normalised

bool lal::graphs::graph::m_normalised = true

protectedinherited

Is this graph normalised?

An undirected graph is normalised iff every node's adjacency list is sorted in increasing order.

In directed graphs, however, it is necessary that the adjacency lists of the out-neighbours and in-neighbours of nodes be sorted.

This attribute is set to 'true' in all graph's initialisation and destruction (when clear() method is called).

◆ m_root_size

std::vector<uint64_t> lal::graphs::tree::m_root_size

protected

The size of the connected component that a root belongs to.

Formally, m_size_of[v] is the size of the connected component of a root vertex v. A vertex u is a root vertex if there exists a vertex w such that m_root_of[w] = u.

In this context, root is within the union-find data structure.

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

lal/graphs/tree.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ tree() [1/2]

◆ tree() [2/2]

Member Function Documentation

◆ __disjoint_union()

◆ actions_after_add_edge()

◆ actions_after_remove_edge()

◆ actions_after_remove_node()

◆ actions_before_remove_edges_incident_to()

◆ are_nodes_in_same_component()

◆ calculate_tree_type()

◆ can_add_edge()

◆ can_add_edges()

◆ check_normalised()

◆ clear()

◆ fill_union_find()

◆ finish_bulk_add()

◆ get_component_representative()

◆ get_num_nodes_component()

◆ get_Q()

◆ get_tree_type_list()

◆ init()

◆ is_normalised()

◆ is_of_tree_type()

◆ is_tree()

◆ is_tree_type_valid()

◆ normalise()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ tree_only_init()

◆ tree_only_remove_node()

◆ tree_only_set_edges()

◆ update_union_find_after_edge_add() [1/2]

◆ update_union_find_after_edge_add() [2/2]

◆ update_union_find_after_edge_remove() [1/2]

◆ update_union_find_after_edge_remove() [2/2]

◆ update_union_find_before_incident_edges_removed() [1/2]

◆ update_union_find_before_incident_edges_removed() [2/2]

Member Data Documentation

◆ m_is_tree_type_valid

◆ m_normalised

◆ m_root_size