Counting paths¶

This page contains information about the functionality of the ActionDigraph class for counting paths.

inline uint64_t libsemigroups::ActionDigraph::number_of_paths(node_type source) const¶

Returns the number of paths from a source node.

Complexity: At worst \(O(nm)\) where \(n\) is the number of nodes and \(m\) is the out-degree of the digraph.

Warning

If the number of paths exceeds 2 ^ 64, then return value of this function will not be correct.

Parameters: source – the source node.
Throws: LibsemigroupsException – if source is not a node in the digraph.
Returns: A value of type uint64_t.

inline uint64_t libsemigroups::ActionDigraph::number_of_paths(node_type source, node_type target, size_t min, size_t max, algorithm lgrthm = algorithm::automatic) const¶

Returns the number of paths between a pair of nodes with length in a given range.

Complexity

The complexity depends on the value of lgrthm as follows:

algorithm::dfs: \(O(r)\) where \(r\) is the number of paths in the digraph starting at source
algorithm::matrix: at worst \(O(n ^ 3 k)\) where \(n\) is the number of nodes and \(k\) equals max.
algorithm::acyclic: at worst \(O(nm)\) where \(n\) is the number of nodes and \(m\) is the out-degree of the digraph (only valid if the subdigraph induced by the nodes reachable from source is acyclic)
algorithm::trivial: constant (only valid in some circumstances)
algorithm::automatic: attempts to select the fastest algorithm of the preceding algorithms and then applies that.

Warning

If lgrthm is algorithm::automatic, then it is not always the case that the fastest algorithm is used.

Warning

If the number of paths exceeds 2 ^ 64, then return value of this function will not be correct.

Parameters

source – the first node
target – the last node
min – the minimum length of a path
max – the maximum length of a path
lgrthm – the algorithm to use (defaults to: algorithm::automatic).

Throws

LibsemigroupsException – if:

source is not a node in the digraph.
target is not a node in the digraph.
the algorithm specified by lgrthm is not applicable.

Returns

A value of type uint64_t.

inline uint64_t libsemigroups::ActionDigraph::number_of_paths(node_type source, size_t min, size_t max, algorithm lgrthm = algorithm::automatic) const¶

Returns the number of paths starting at a given node with length in a given range.

Complexity

The complexity depends on the value of lgrthm as follows:

algorithm::dfs: \(O(r)\) where \(r\) is the number of paths in the digraph starting at source
algorithm::matrix: at worst \(O(n ^ 3 k)\) where \(n\) is the number of nodes and \(k\) equals max.
algorithm::acyclic: at worst \(O(nm)\) where \(n\) is the number of nodes and \(m\) is the out-degree of the digraph (only valid if the subdigraph induced by the nodes reachable from source is acyclic)
algorithm::trivial: at worst \(O(nm)\) where \(n\) is the number of nodes and \(m\) is the out-degree of the digraph (only valid in some circumstances)
algorithm::automatic: attempts to select the fastest algorithm of the preceding algorithms and then applies that.

Warning

If lgrthm is algorithm::automatic, then it is not always the case that the fastest algorithm is used.

Warning

If the number of paths exceeds 2 ^ 64, then return value of this function will not be correct.

Parameters

source – the first node
min – the minimum length of a path
max – the maximum length of a path
lgrthm – the algorithm to use (defaults to: algorithm::automatic).

Throws

LibsemigroupsException – if:

source is not a node in the digraph.
the algorithm specified by lgrthm is not applicable.

Returns

A value of type uint64_t.

inline algorithm libsemigroups::ActionDigraph::number_of_paths_algorithm(node_type source) const noexcept¶

Returns the algorithm used by number_of_paths().

Complexity: Constant

Parameters: source – the source node.
Throws: (None) – This function is noexcept and is guaranteed never to throw.
Returns: A value of type algorithm.

inline algorithm libsemigroups::ActionDigraph::number_of_paths_algorithm(node_type source, node_type target, size_t min, size_t max) const¶

Returns the algorithm used by number_of_paths().

Returns the algorithm used by number_of_paths() to compute the number of paths originating at the given source node and ending at the given target node with length in the range \([min, max)\).

Complexity: At worst \(O(nm)\) where \(n\) is the number of nodes and \(m\) is the out-degree of the digraph.

Parameters

source – the source node
target – the target node
min – the minimum length of paths to count
max – the maximum length of paths to count

Throws

(None) – This function guarantees not to throw a LibsemigroupsException.

Returns

A value of type algorithm.

inline algorithm libsemigroups::ActionDigraph::number_of_paths_algorithm(node_type source, size_t min, size_t max) const¶

Returns the algorithm used by number_of_paths().

Returns the algorithm used by number_of_paths() to compute the number of paths originating at the given source node with length in the range \([min, max)\).

Complexity: At worst \(O(nm)\) where \(n\) is the number of nodes and \(m\) is the out-degree of the digraph.

Parameters

source – the source node
min – the minimum length of paths to count
max – the maximum length of paths to count

Throws

(None) – This function guarantees not to throw a LibsemigroupsException.

Returns

A value of type algorithm.