Package algs42
Class DigraphGenerator
java.lang.Object
algs42.DigraphGenerator
The
DigraphGenerator
class provides static methods for creating
various digraphs, including Erdos-Renyi random digraphs, random DAGs,
random rooted trees, random rooted DAGs, random tournaments, path digraphs,
cycle digraphs, and the complete digraph.
For additional documentation, see Section 4.2 of Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
- Author:
- Robert Sedgewick, Kevin Wayne
-
Nested Class Summary
-
Constructor Summary
-
Method Summary
Modifier and TypeMethodDescriptionstatic Digraph
binaryTree
(int V) Returns a complete binary tree digraph onV
vertices.static Digraph
complete
(int V) Returns the complete digraph onV
vertices.static Digraph
static Digraph
cycle
(int V) Returns a cycle digraph onV
vertices.static Digraph
dag
(int V, int E) Returns a random simple DAG containingV
vertices andE
edges.static Digraph
eulerianCycle
(int V, int E) Returns an Eulerian cycle digraph onV
vertices.static Digraph
eulerianPath
(int V, int E) Returns an Eulerian path digraph onV
vertices.static Digraph
static void
static Digraph
path
(int V) Returns a path digraph onV
vertices.private static void
Unit tests theDigraphGenerator
library.static Digraph
random
(int V, int E) Create a random digraph with V vertices and E edges.static Digraph
rootedInDAG
(int V, int E) Returns a random rooted-in DAG onV
vertices andE
edges.static Digraph
rootedInTree
(int V) Returns a random rooted-in tree onV
vertices.static Digraph
rootedOutDAG
(int V, int E) Returns a random rooted-out DAG onV
vertices andE
edges.static Digraph
rootedOutTree
(int V) Returns a random rooted-out tree onV
vertices.static Digraph
simple
(int V, double p) Returns a random simple digraph onV
vertices, with an edge between any two vertices with probabilityp
.static Digraph
simple
(int V, int E) Returns a random simple digraph containingV
vertices andE
edges.static Digraph
strong
(int V, int E, int c) Returns a random simple digraph onV
vertices,E
edges and (at most)c
strong components.static Digraph
tournament
(int V) Returns a random tournament digraph onV
vertices.
-
Constructor Details
-
DigraphGenerator
public DigraphGenerator()
-
-
Method Details
-
fromIn
-
copy
-
random
Create a random digraph with V vertices and E edges. Expected running time is proportional to V + E. -
simple
Returns a random simple digraph containingV
vertices andE
edges.- Parameters:
V
- the number of verticesE
- the number of vertices- Returns:
- a random simple digraph on
V
vertices, containing a total ofE
edges - Throws:
IllegalArgumentException
- if no such simple digraph exists
-
simple
Returns a random simple digraph onV
vertices, with an edge between any two vertices with probabilityp
. This is sometimes referred to as the Erdos-Renyi random digraph model. This implementations takes time propotional to V^2 (even ifp
is small).- Parameters:
V
- the number of verticesp
- the probability of choosing an edge- Returns:
- a random simple digraph on
V
vertices, with an edge between any two vertices with probabilityp
- Throws:
IllegalArgumentException
- if probability is not between 0 and 1
-
complete
Returns the complete digraph onV
vertices.- Parameters:
V
- the number of vertices- Returns:
- the complete digraph on
V
vertices
-
dag
Returns a random simple DAG containingV
vertices andE
edges. Note: it is not uniformly selected at random among all such DAGs.- Parameters:
V
- the number of verticesE
- the number of vertices- Returns:
- a random simple DAG on
V
vertices, containing a total ofE
edges - Throws:
IllegalArgumentException
- if no such simple DAG exists
-
tournament
Returns a random tournament digraph onV
vertices. A tournament digraph is a DAG in which for every two vertices, there is one directed edge. A tournament is an oriented complete graph.- Parameters:
V
- the number of vertices- Returns:
- a random tournament digraph on
V
vertices
-
rootedInDAG
Returns a random rooted-in DAG onV
vertices andE
edges. A rooted in-tree is a DAG in which there is a single vertex reachable from every other vertex. The DAG returned is not chosen uniformly at random among all such DAGs.- Parameters:
V
- the number of verticesE
- the number of edges- Returns:
- a random rooted-in DAG on
V
vertices andE
edges
-
rootedOutDAG
Returns a random rooted-out DAG onV
vertices andE
edges. A rooted out-tree is a DAG in which every vertex is reachable from a single vertex. The DAG returned is not chosen uniformly at random among all such DAGs.- Parameters:
V
- the number of verticesE
- the number of edges- Returns:
- a random rooted-out DAG on
V
vertices andE
edges
-
rootedInTree
Returns a random rooted-in tree onV
vertices. A rooted in-tree is an oriented tree in which there is a single vertex reachable from every other vertex. The tree returned is not chosen uniformly at random among all such trees.- Parameters:
V
- the number of vertices- Returns:
- a random rooted-in tree on
V
vertices
-
rootedOutTree
Returns a random rooted-out tree onV
vertices. A rooted out-tree is an oriented tree in which each vertex is reachable from a single vertex. It is also known as a arborescence or branching. The tree returned is not chosen uniformly at random among all such trees.- Parameters:
V
- the number of vertices- Returns:
- a random rooted-out tree on
V
vertices
-
path
Returns a path digraph onV
vertices.- Parameters:
V
- the number of vertices in the path- Returns:
- a digraph that is a directed path on
V
vertices
-
binaryTree
Returns a complete binary tree digraph onV
vertices.- Parameters:
V
- the number of vertices in the binary tree- Returns:
- a digraph that is a complete binary tree on
V
vertices
-
cycle
Returns a cycle digraph onV
vertices.- Parameters:
V
- the number of vertices in the cycle- Returns:
- a digraph that is a directed cycle on
V
vertices
-
eulerianCycle
Returns an Eulerian cycle digraph onV
vertices.- Parameters:
V
- the number of vertices in the cycleE
- the number of edges in the cycle- Returns:
- a digraph that is a directed Eulerian cycle on
V
vertices andE
edges - Throws:
IllegalArgumentException
- if eitherV <= 0
orE <= 0
-
eulerianPath
Returns an Eulerian path digraph onV
vertices.- Parameters:
V
- the number of vertices in the pathE
- the number of edges in the path- Returns:
- a digraph that is a directed Eulerian path on
V
vertices andE
edges - Throws:
IllegalArgumentException
- if eitherV <= 0
orE < 0
-
strong
Returns a random simple digraph onV
vertices,E
edges and (at most)c
strong components. The vertices are randomly assigned integer labels between0
andc-1
(corresponding to strong components). Then, a strong component is created among the vertices with the same label. Next, random edges (either between two vertices with the same labels or from a vertex with a smaller label to a vertex with a larger label). The number of components will be equal to the number of distinct labels that are assigned to vertices.- Parameters:
V
- the number of verticesE
- the number of edgesc
- the (maximum) number of strong components- Returns:
- a random simple digraph on
V
vertices andE
edges, with (at most)c
strong components - Throws:
IllegalArgumentException
- ifc
is larger thanV
-
print
Unit tests theDigraphGenerator
library. -
main
-