Free tree graph class. More...

#include <free_tree.hpp>

Inheritance diagram for lal::graphs::free_tree:

Public Member Functions
	free_tree () noexcept
	Empty constructor.

	free_tree (uint32_t n) noexcept
	Constructor with number of vertices.

	free_tree (const free_tree &t) noexcept
	Copy constructor.

	free_tree (free_tree &&t) noexcept
	Move constructor.

	free_tree (const undirected_graph &t) noexcept
	Copy constructor with undirected graph.

	free_tree (undirected_graph &&t) noexcept
	Move constructor with undirected graph.

virtual	~free_tree () noexcept
	Destructor.

free_tree &	operator= (const free_tree &f) noexcept
	Copy assignment operator.

free_tree &	operator= (free_tree &&f) noexcept
	Copy assignment operator.

free_tree &	add_edge (node s, node t, bool norm=true, bool check_norm=true) noexcept
	Adds an edge to the tree.

free_tree &	add_edge_bulk (node s, node t) noexcept
	Adds an edge to the graph.

void	finish_bulk_add (bool norm=true, bool check=true) noexcept
	Finishes adding edges in bulk.

free_tree &	add_edges (const std::vector< edge > &edges, bool norm=true, bool check_norm=true) noexcept
	Adds a list of edges to the graph.

free_tree &	set_edges (const std::vector< edge > &edges, bool norm=true, bool check_norm=true) noexcept
	Sets the edges to the graph.

virtual free_tree &	remove_edges_incident_to (node u, bool norm=true, bool check_norm=true) noexcept
	Remove all edges incident to a given vertex.

void	disjoint_union (const free_tree &t) noexcept
	Disjoint union of trees.

void	calculate_tree_type () noexcept
	Calculates the type of tree.

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

head_vector	get_head_vector (node r=0) const noexcept
	Converts a free tree into a head vector.

virtual undirected_graph &	remove_edge (node s, node t, bool norm=false, bool check_norm=true) noexcept
	Remove an edge from this graph.

virtual undirected_graph &	remove_edges (const std::vector< edge > &edges, bool norm=true, bool check_norm=true) noexcept
	Remove an edge from this graph.

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

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

const neighbourhood &	get_neighbours (node u) const noexcept
	Returns the neighbourhood of node u.

uint32_t	get_degree (node u) const noexcept
	Returns the number of neighbours of u.

bool	has_edge (node u, node v) const noexcept
	Returns true if the edge \(\{u,v\}\) exists in the graph.

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

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

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

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

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

uint32_t	get_num_nodes_component (node u) const noexcept
	Amount of nodes in a connected component of the tree.

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

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

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

virtual void	init (uint32_t n) noexcept
	Allocates the necessary memory for this class.

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

virtual void	normalise () noexcept
	Normalises the graph.

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

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

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

uint32_t	get_num_nodes () const noexcept
	Returns the number of ndoes.

uint32_t	get_num_edges () const noexcept
	Returns the number of edges.

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

Protected Member Functions
virtual void	_init (uint32_t n) noexcept

virtual void	_clear () noexcept

void	call_union_find_after_add (node u, node v, uint32_t const root_of, uint32_t const root_size) noexcept
	A call to the union find method.

void	call_union_find_after_add (node u, node v, uint32_t const root_of, uint32_t const root_size) const noexcept
	A const call to the union find method.

void	call_union_find_after_remove (node u, node v, uint32_t const root_of, uint32_t const root_size) noexcept
	A call to the union find method.

void	call_union_find_after_remove (node u, node v, uint32_t const root_of, uint32_t const root_size) const noexcept
	A const call to the union find method.

void	copy_full_free_tree (const free_tree &f) noexcept
	Copies all members of this class and the parent class.

void	move_full_free_tree (free_tree &&f) noexcept
	Moves all members of this class and the parent class.

void	copy_full_undirected_graph (const undirected_graph &u) noexcept
	Copies all members of this class and the parent class.

void	move_full_undirected_graph (undirected_graph &&u) noexcept
	Moves all members of this class and the parent class.

void	tree_only_init (uint32_t n) noexcept
	Initialises only the memory of class tree.

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	extra_work_per_edge_add (node u, node v) noexcept
	Do some extra work after an edge has been added.

void	extra_work_per_edge_remove (node u, node v) noexcept
	Do some extra work after an edge has been removed.

void	tree_only_extra_work_edges_set () noexcept

void	fill_union_find () noexcept

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.

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

void	normalise_after_remove (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< uint32_t >	m_root_size
	The size of the connected component that a root belongs to.

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?

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

uint32_t	m_num_edges = 0
	Amount of edges of this graph.

bool	m_normalised = true
	Is this graph normalised?

Private Member Functions
void	disjoint_union (const undirected_graph &g) noexcept
	Disjoint union of graphs.

void	remove_single_edge (node u, node v, neighbourhood &out_u, neighbourhood &in_v) noexcept
	Removes a single edge.

Detailed Description

Free tree graph class.

This class constrains the addition of edges so that the resulting graphs does not contain cycles. Furthermore, the edges added are undirected.

For another type of tree-like graphs, see rooted_tree.

Constructor & Destructor Documentation

◆ free_tree() [1/5]

lal::graphs::free_tree::free_tree ( uint32_t n )

inlinenoexcept

Constructor with number of vertices.

Parameters

n	Number of vertices

◆ free_tree() [2/5]

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

inlinenoexcept

Copy constructor.

Parameters

t	Free tree.

◆ free_tree() [3/5]

lal::graphs::free_tree::free_tree ( free_tree && t )

inlinenoexcept

Move constructor.

Parameters

t	Free tree.

◆ free_tree() [4/5]

lal::graphs::free_tree::free_tree ( const undirected_graph & t )

noexcept

Copy constructor with undirected graph.

Parameters

t	An undirected graph.

Precondition: Graph t is a tree.

◆ free_tree() [5/5]

lal::graphs::free_tree::free_tree ( undirected_graph && t )

noexcept

Move constructor with undirected graph.

Parameters

t	An undirected graph.

Precondition: Graph t is a 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.

◆ _clear()

virtual void lal::graphs::free_tree::_clear ( )

protectedvirtualnoexcept

Clears the memory of free_tree, undirected_graph and graph classes.

Reimplemented from lal::graphs::undirected_graph.

◆ _init()

virtual void lal::graphs::free_tree::_init ( uint32_t n )

protectedvirtualnoexcept

Initialises memory of free_tree, undirected_graph and graph classes.

Reimplemented from lal::graphs::undirected_graph.

◆ add_edge()

free_tree & lal::graphs::free_tree::add_edge	(	node	s,
		node	t,
		bool	norm = true,
		bool	check_norm = true )

virtualnoexcept

Adds an edge to the tree.

This operation checks that the edge added does not produce cycles only in a debug compilation of the library. For a more controlled addition of the edges, see can_add_edge.

For developers: method graph::extra_work_per_edge_add is called after the edge has been added.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).
norm	Should the graph be normalised?
check_norm	If norm is false then, should we check whether the result is normalised or not? This might be useful in case the resulting graph is normalised. If norm is true then check_norm is ignored.

Precondition: \(s \neq t\); Edge \(\{s,t\}\) is not part of the graph.

Postcondition: If norm is true the graph is guaranteed to be normalised after the addition of the edge.

Reimplemented from lal::graphs::undirected_graph.

◆ add_edge_bulk()

free_tree & lal::graphs::free_tree::add_edge_bulk	(	node	s,
		node	t )

noexcept

Adds an edge to the graph.

This method only adds an edge, and does no other work: normalisation is not checked, and no extra work per edge is done.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).

Precondition: \(u \neq v\).; The edge \(\{s,t\}\) is not part of the graph.

Postcondition: If norm is true the graph is guaranteed to be normalised after the addition of the edge.

◆ add_edges()

free_tree & lal::graphs::free_tree::add_edges	(	const std::vector< edge > &	edges,
		bool	norm = true,
		bool	check_norm = true )

virtualnoexcept

Adds a list of edges to the graph.

This function checks that edges will not produce cycles only in a debug compilation of the library. Moreover, this operation is faster than calling add_edge since the edges are added in bulk. For a more controlled addition of the edges, see can_add_edges.

For developers: method graph::extra_work_per_edge_add is called after each edge has been added.

Parameters

edges	The edges to be added.
norm	Normalise the graph after the insertions.
check_norm	If norm is false then, should we check whether the result is normalised or not? This might be useful in case the resulting graph is normalised. If norm is true then check_norm is ignored.

Precondition: All the edges in edges must meet the precondition of method add_edge.; None of the subsets of the list of edges can produce cycles when added.

Postcondition: If norm is true the graph is guaranteed to be normalised after the addition of the edges.

Reimplemented from lal::graphs::undirected_graph.

◆ calculate_tree_type()

void lal::graphs::free_tree::calculate_tree_type ( )

virtualnoexcept

Calculates the type of tree.

See tree_type for the list of different tree types.

Implements lal::graphs::tree.

◆ call_union_find_after_add() [1/2]

void lal::graphs::free_tree::call_union_find_after_add	(	node	u,
		node	v,
		uint32_t *const	root_of,
		uint32_t *const	root_size ) const

protectedvirtualnoexcept

A const call to the union find method.

This is a helper method to be able to call a template in the lal::internal 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.

Implements lal::graphs::tree.

◆ call_union_find_after_add() [2/2]

void lal::graphs::free_tree::call_union_find_after_add	(	node	u,
		node	v,
		uint32_t *const	root_of,
		uint32_t *const	root_size )

protectedvirtualnoexcept

A call to the union find method.

This is a helper method to be able to call a template in the lal::internal 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.

Implements lal::graphs::tree.

◆ call_union_find_after_remove() [1/2]

void lal::graphs::free_tree::call_union_find_after_remove	(	node	u,
		node	v,
		uint32_t *const	root_of,
		uint32_t *const	root_size ) const

protectedvirtualnoexcept

A const call to the union find method.

This is a helper method to be able to call a template in the lal::internal 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.

Implements lal::graphs::tree.

◆ call_union_find_after_remove() [2/2]

void lal::graphs::free_tree::call_union_find_after_remove	(	node	u,
		node	v,
		uint32_t *const	root_of,
		uint32_t *const	root_size )

protectedvirtualnoexcept

A call to the union find method.

This is a helper method to be able to call a template in the lal::internal 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.

Implements lal::graphs::tree.

◆ can_add_edge()

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

noexceptinherited

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.

Parameters

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

Returns: Whether the addition of this new edge can be added to the tree without producing cycles.

◆ can_add_edges()

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

noexceptinherited

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.

Parameters

edges List of edges.

Returns: Whether the addition of these new edges can be added to the tree without producing cycles.

◆ 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.

◆ disjoint_union() [1/2]

void lal::graphs::free_tree::disjoint_union ( const free_tree & t )

noexcept

Disjoint union of trees.

Given a free tree, append it to the current tree.

All the nodes in t are relabelled starting at n, the number of nodes of the current tree.

Parameters

t	Input tree.

Postcondition: The current tree is not an actual tree, i.e., method is_tree() returns false since the resulting tree lacks an edge.

◆ disjoint_union() [2/2]

void lal::graphs::undirected_graph::disjoint_union ( const undirected_graph & g )

privatenoexcept

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.

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

◆ fill_union_find()

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

protectednoexceptinherited

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

◆ finish_bulk_add()

void lal::graphs::free_tree::finish_bulk_add	(	bool	norm = true,
		bool	check = true )

virtualnoexcept

Finishes adding edges in bulk.

Parameters

norm	Normalise the tree.
check	Check whether the tree is normalised or not.

Precondition: All edges have been added.

Implements lal::graphs::graph.

◆ get_degree()

uint32_t lal::graphs::undirected_graph::get_degree ( node u ) const

inlinenoexceptinherited

Returns the number of neighbours of u.

Parameters

u	Node to be queried.

Returns: The number of adjacent nodes.

◆ get_head_vector()

head_vector lal::graphs::free_tree::get_head_vector ( node r = 0 ) const

noexcept

Converts a free tree into a head vector.

A head vector of an n-vertex tree is a list of non-negative integer numbers. The number at position i denotes the parent node of the vertex at said position. Value '0' denotes the root. In this case, the vertex corresponding to the value '0' is not labelled as a root.

Each tree is formatted as a list of whole, positive numbers (including zero), each representing a node of the tree. The number 0 denotes the root of the tree, and a number at a certain position indicates its parent node. For example, when number 4 is at position 9 it means that node 9 has parent node 4. Therefore, if number 0 is at position 1 it means that node 1 is the root of the tree. A complete example of such a tree's representation is the following

  0 3 4 1 6 3

which should be interpreted as

(a) predecessor:       0 3 4 1 6 3
(b) node of the tree:  1 2 3 4 5 6

Note that lines like these are not valid:

(1) 0 2 2 2 2 2
(2) 2 0 0

Line (1) is not valid due to a self-reference in the second position, and (2) is not valid since it contains two '0' (i.e., two roots).

Methods lal::io::read_head_vector read a head vector from a file in disk.

Parameters

r	A fictional root to be used to calculate the head vector.

Returns: The head vector representation of this tree.

Precondition: This tree is a valid free tree (see is_tree).

◆ get_neighbours()

const neighbourhood & lal::graphs::undirected_graph::get_neighbours ( node u ) const

inlinenoexceptinherited

Returns the neighbourhood of node u.

Parameters

u Node.

Returns: The list of nodes adjacent to node u.

◆ get_num_nodes_component()

uint32_t lal::graphs::tree::get_num_nodes_component ( node u ) const

inlinenoexceptinherited

Amount of nodes in a connected component of the tree.

When tree has had an edge removed, or when it is not completely built, i.e., it lack some edges, the resulting graph is clearly a forest. This function returns the size of the forest node u belongs to.

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

Parameters

u	Input node.

Returns: The size of the connected component of u.

◆ get_Q()

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

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.

Implements lal::graphs::graph.

◆ get_tree_type_list()

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

noexceptinherited

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 ( uint32_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

inlinenoexceptinherited

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

inlinenoexceptinherited

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 [19] (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

inlinenoexceptinherited

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]

free_tree & lal::graphs::free_tree::operator= ( const free_tree & f )

inlinenoexcept

Copy assignment operator.

Parameters

f	A lal::graphs::free_tree.

◆ operator=() [2/2]

free_tree & lal::graphs::free_tree::operator= ( free_tree && f )

inlinenoexcept

Copy assignment operator.

Parameters

f	A lal::graphs::free_tree.

◆ remove_edge()

virtual undirected_graph & lal::graphs::undirected_graph::remove_edge	(	node	s,
		node	t,
		bool	norm = false,
		bool	check_norm = true )

virtualnoexceptinherited

Remove an edge from this graph.

For developers: method graph::extra_work_per_edge_remove is called after the edge has been removed.

Parameters

s	Valid node index: \(0 \le s < n\).
t	Valid node index: \(0 \le t < n\).
norm	Normalise the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalised or not? This might be useful in case the resulting graph is normalised. If norm is true then check_norm is ignored.

Precondition: The edge must exist.

Postcondition: If norm is true the graph is guaranteed to be normalised after the addition of the edge.

◆ remove_edges()

virtual undirected_graph & lal::graphs::undirected_graph::remove_edges	(	const std::vector< edge > &	edges,
		bool	norm = true,
		bool	check_norm = true )

virtualnoexceptinherited

Remove an edge from this graph.

This operation is faster than removing edges one by one with remove_edge(node,node,bool,bool) since the edges are removed in bulk.

For developers: method graph::extra_work_per_edge_remove is called after each edge has been removed.

Parameters

edges	The edges to be deleted.
norm	Normalise the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalised or not? This might be useful in case the resulting graph is normalised. If norm is true then check_norm is ignored.

Precondition: All the edges in edges must meet the precondition of method add_edge(node,node,bool,bool).

Postcondition: If norm is true the graph is guaranteed to be normalised after the addition of the edge.

◆ remove_edges_incident_to()

virtual free_tree & lal::graphs::free_tree::remove_edges_incident_to	(	node	u,
		bool	norm = true,
		bool	check_norm = true )

virtualnoexcept

Remove all edges incident to a given vertex.

This operation is faster than removing edges one by one with remove_edge(node,node,bool,bool) since the edges are removed in bulk.

For developers: method lal::graphs::graph::extra_work_per_edge_remove is called after each edge has been removed.

Parameters

u	The node whose incident vertices are to be removed.
norm	Normalise the graph after the deletion.
check_norm	If norm is false then, should we check whether the result is normalised or not? This might be useful in case the resulting graph is normalised. If norm is true then check_norm is ignored.

Postcondition: If norm is true the graph is guaranteed to be normalised after the addition of the edge.

Reimplemented from lal::graphs::undirected_graph.

◆ remove_single_edge()

void lal::graphs::undirected_graph::remove_single_edge	(	node	u,
		node	v,
		neighbourhood &	out_u,
		neighbourhood &	in_v )

privatenoexceptinherited

Removes a single edge.

Parameters

u	First node of edge.
v	Second node of edge.
out_u	Out-neighbourhood of node u.
in_v	In-neighbourhood of node v.

◆ set_edges()

free_tree & lal::graphs::free_tree::set_edges	(	const std::vector< edge > &	edges,
		bool	norm = true,
		bool	check_norm = true )

virtualnoexcept

Sets the edges to the graph.

Sets the edges of this graph assuming that the nodes indexed in the list are, at most, the number of nodes of this graph.

This list of edges is assumed to be all the edges that are going to be added to this graph. This means that the internal data structures are constructed more efficiently than when adding edges one by one (see add_edge) or in several chunks (see add_edges). For a more controlled addition of the edges, see can_add_edges.

Moreover, the current structure of the graph is cleared before setting the new edges.

Parameters

edges	The edges to be added.
norm	Normalise the graph after the insertions.
check_norm	If norm is false then, should we check whether the result is normalised or not? This might be useful in case the resulting graph is normalised. If norm is true then check_norm is ignored.

Precondition: The graph has been initialized with as many nodes as vertices in the list of edges.; There are no repeated edges in the list.

Postcondition: If norm is true the graph is guaranteed to be normalised after the addition of the edge.

Reimplemented from lal::graphs::undirected_graph.

◆ tree_only_extra_work_edges_set()

void lal::graphs::tree::tree_only_extra_work_edges_set ( )

protectednoexceptinherited

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

◆ tree_only_init()

void lal::graphs::tree::tree_only_init ( uint32_t n )

protectednoexceptinherited

Initialises only the memory of class tree.

Parameters

n	Number of vertices.

Member Data Documentation

◆ m_is_tree_type_valid

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

protectedinherited

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<uint32_t> lal::graphs::tree::m_root_size

protectedinherited

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/free_tree.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ free_tree() [1/5]

◆ free_tree() [2/5]

◆ free_tree() [3/5]

◆ free_tree() [4/5]

◆ free_tree() [5/5]

Member Function Documentation

◆ __disjoint_union()

◆ _clear()

◆ _init()

◆ add_edge()

◆ add_edge_bulk()

◆ add_edges()

◆ calculate_tree_type()

◆ call_union_find_after_add() [1/2]

◆ call_union_find_after_add() [2/2]

◆ call_union_find_after_remove() [1/2]

◆ call_union_find_after_remove() [2/2]

◆ can_add_edge()

◆ can_add_edges()

◆ check_normalised()

◆ clear()

◆ disjoint_union() [1/2]

◆ disjoint_union() [2/2]

◆ fill_union_find()

◆ finish_bulk_add()

◆ get_degree()

◆ get_head_vector()

◆ get_neighbours()

◆ 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]

◆ remove_edge()

◆ remove_edges()

◆ remove_edges_incident_to()

◆ remove_single_edge()

◆ set_edges()

◆ tree_only_extra_work_edges_set()

◆ tree_only_init()

Member Data Documentation

◆ m_is_tree_type_valid

◆ m_normalised

◆ m_root_size