/// <summary>
/// Returns a cycle digraph on <c>V</c> vertices.</summary>
/// <param name="V">the number of vertices in the cycle</param>
/// <returns>a digraph that is a directed cycle on <c>V</c> vertices</returns>
///
public static Digraph Cycle(int V)
{
Digraph G = new Digraph(V);
int[] vertices = new int[V];
for (int i = 0; i < V; i++)
{
vertices[i] = i;
}
StdRandom.Shuffle(vertices);
for (int i = 0; i < V - 1; i++)
{
G.AddEdge(vertices[i], vertices[i + 1]);
}
G.AddEdge(vertices[V - 1], vertices[0]);
return(G);
}
/// <summary>
/// Returns a random rooted-out DAG on <c>V</c> vertices and <c>E</c> 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.</summary>
/// <param name="V">the number of vertices</param>
/// <param name="E">the number of edges</param>
/// <returns>a random rooted-out DAG on <c>V</c> vertices and <c>E</c> edges</returns>
///
public static Digraph RootedOutDAG(int V, int E)
{
if (E > (long)V * (V - 1) / 2)
{
throw new ArgumentException("Too many edges");
}
if (E < V - 1)
{
throw new ArgumentException("Too few edges");
}
Digraph G = new Digraph(V);
SET <Edge> set = new SET <Edge>();
// fix a topological order
int[] vertices = new int[V];
for (int i = 0; i < V; i++)
{
vertices[i] = i;
}
StdRandom.Shuffle(vertices);
// one edge pointing from each vertex, other than the root = vertices[V-1]
for (int v = 0; v < V - 1; v++)
{
int w = StdRandom.Uniform(v + 1, V);
Edge e = new Edge(w, v);
set.Add(e);
G.AddEdge(vertices[w], vertices[v]);
}
while (G.E < E)
{
int v = StdRandom.Uniform(V);
int w = StdRandom.Uniform(V);
Edge e = new Edge(w, v);
if ((v < w) && !set.Contains(e))
{
set.Add(e);
G.AddEdge(vertices[w], vertices[v]);
}
}
return(G);
}
// tournament
/// <summary>
/// Returns a random tournament digraph on <c>V</c> 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.</summary>
/// <param name="V">the number of vertices</param>
/// <returns>a random tournament digraph on <c>V</c> vertices</returns>
///
public static Digraph Tournament(int V)
{
Digraph G = new Digraph(V);
for (int v = 0; v < G.V; v++)
{
for (int w = v + 1; w < G.V; w++)
{
if (StdRandom.Bernoulli(0.5))
{
G.AddEdge(v, w);
}
else
{
G.AddEdge(w, v);
}
}
}
return(G);
}
/// <summary>
/// Returns the reverse of the digraph.</summary>
/// <returns>the reverse of the digraph</returns>
///
public Digraph Reverse()
{
Digraph R = new Digraph(V);
for (int v = 0; v < V; v++)
{
foreach (int w in Adj(v))
{
R.AddEdge(w, v);
}
}
return(R);
}
/// <summary>
/// Initializes a digraph from a file using the specified delimiter.
/// Each line in the file contains
/// the name of a vertex, followed by a list of the names
/// of the vertices adjacent to that vertex, separated by the delimiter.</summary>
/// <param name="filename">the name of the file</param>
/// <param name="delimiter">the delimiter between fields</param>
///
public SymbolDigraph(string filename, string delimiter)
{
st = new ST <string, int>();
// First pass builds the index by reading strings to associate
// distinct strings with an index
FileStream fsIn = File.OpenRead(filename);
using (TextReader reader = new StreamReader(fsIn))
{
string nextLine = reader.ReadLine();
while (nextLine != null)
{
string[] a = nextLine.Split(delimiter.ToCharArray(), StringSplitOptions.RemoveEmptyEntries);
for (int i = 0; i < a.Length; i++)
{
if (!st.Contains(a[i]))
{
st.Put(a[i], st.Count);
}
}
nextLine = reader.ReadLine();
}
}
// inverted index to get string keys in an aray
keys = new string[st.Count];
foreach (string name in st.Keys())
{
keys[st[name]] = name;
}
// second pass builds the digraph by connecting first vertex on each
// line to all others
g = new Digraph(st.Count);
fsIn = File.OpenRead(filename);
using (TextReader reader = new StreamReader(fsIn))
{
string nextLine = reader.ReadLine();
while (nextLine != null)
{
string[] a = nextLine.Split(delimiter.ToCharArray(), StringSplitOptions.RemoveEmptyEntries);
int v = st[a[0]];
for (int i = 1; i < a.Length; i++)
{
int w = st[a[i]];
g.AddEdge(v, w);
}
nextLine = reader.ReadLine();
}
}
}
/// <summary>
/// Returns an Eulerian cycle digraph on <c>V</c> vertices.</summary>
/// <param name="V">the number of vertices in the cycle</param>
/// <param name="E">the number of edges in the cycle</param>
/// <returns>a digraph that is a directed Eulerian cycle on <c>V</c> vertices
/// and <c>E</c> edges</returns>
/// <exception cref="ArgumentException">if either V <= 0 or E <= 0</exception>
///
public static Digraph EulerianCycle(int V, int E)
{
if (E <= 0)
{
throw new ArgumentException("An Eulerian cycle must have at least one edge");
}
if (V <= 0)
{
throw new ArgumentException("An Eulerian cycle must have at least one vertex");
}
Digraph G = new Digraph(V);
int[] vertices = new int[E];
for (int i = 0; i < E; i++)
{
vertices[i] = StdRandom.Uniform(V);
}
for (int i = 0; i < E - 1; i++)
{
G.AddEdge(vertices[i], vertices[i + 1]);
}
G.AddEdge(vertices[E - 1], vertices[0]);
return(G);
}
public static void MainTest(string[] args)
{
int V = int.Parse(args[0]);
int E = int.Parse(args[1]);
// Eulerian cycle
Digraph G1 = DigraphGenerator.EulerianCycle(V, E);
DirectedEulerianPath.UnitTest(G1, "Eulerian cycle");
// Eulerian path
Digraph G2 = DigraphGenerator.EulerianPath(V, E);
DirectedEulerianPath.UnitTest(G2, "Eulerian path");
// add one random edge
Digraph G3 = new Digraph(G2);
G3.AddEdge(StdRandom.Uniform(V), StdRandom.Uniform(V));
DirectedEulerianPath.UnitTest(G3, "one random edge added to Eulerian path");
// self loop
Digraph G4 = new Digraph(V);
int v4 = StdRandom.Uniform(V);
G4.AddEdge(v4, v4);
DirectedEulerianPath.UnitTest(G4, "single self loop");
// single edge
Digraph G5 = new Digraph(V);
G5.AddEdge(StdRandom.Uniform(V), StdRandom.Uniform(V));
DirectedEulerianPath.UnitTest(G5, "single edge");
// empty digraph
Digraph G6 = new Digraph(V);
DirectedEulerianPath.UnitTest(G6, "empty digraph");
// random digraph
Digraph G7 = DigraphGenerator.Simple(V, E);
DirectedEulerianPath.UnitTest(G7, "simple digraph");
// 4-vertex digraph
//Digraph G8 = new Digraph(new TextInput("eulerianD.txt"));
//DirectedEulerianPath.UnitTest(G8, "4-vertex Eulerian digraph");
}
/// <summary>
/// Returns a complete binary tree digraph on <c>V</c> vertices.</summary>
/// <param name="V">the number of vertices in the binary tree</param>
/// <returns>a digraph that is a complete binary tree on <c>V</c> vertices</returns>
///
public static Digraph BinaryTree(int V)
{
Digraph G = new Digraph(V);
int[] vertices = new int[V];
for (int i = 0; i < V; i++)
{
vertices[i] = i;
}
StdRandom.Shuffle(vertices);
for (int i = 1; i < V; i++)
{
G.AddEdge(vertices[i], vertices[(i - 1) / 2]);
}
return(G);
}
/// <summary>
/// Returns an Eulerian path digraph on <c>V</c> vertices.</summary>
/// <param name="V">the number of vertices in the path</param>
/// <param name="E">the number of edges in the path</param>
/// <returns>a digraph that is a directed Eulerian path on <c>V</c> vertices</returns>
/// and <c>E</c> edges
/// <exception cref="ArgumentException">if either V <= 0 or E < 0</exception>
///
public static Digraph EulerianPath(int V, int E)
{
if (E < 0)
{
throw new ArgumentException("negative number of edges");
}
if (V <= 0)
{
throw new ArgumentException("An Eulerian path must have at least one vertex");
}
Digraph G = new Digraph(V);
int[] vertices = new int[E + 1];
for (int i = 0; i < E + 1; i++)
{
vertices[i] = StdRandom.Uniform(V);
}
for (int i = 0; i < E; i++)
{
G.AddEdge(vertices[i], vertices[i + 1]);
}
return(G);
}
/// <summary>
/// Returns a random simple digraph on <c>V</c> vertices, with an
/// edge between any two vertices with probability <c>p</c>. This is sometimes
/// referred to as the Erdos-Renyi random digraph model.
/// This implementations takes time propotional to V^2 (even if <c>p</c> is small).</summary>
/// <param name="V">the number of vertices</param>
/// <param name="p">the probability of choosing an edge</param>
/// <returns>a random simple digraph on <c>V</c> vertices, with an edge between
/// any two vertices with probability <c>p</c></returns>
/// <exception cref="ArgumentException">if probability is not between 0 and 1</exception>
///
public static Digraph Simple(int V, double p)
{
if (p < 0.0 || p > 1.0)
{
throw new ArgumentException("Probability must be between 0 and 1");
}
Digraph G = new Digraph(V);
for (int v = 0; v < V; v++)
{
for (int w = 0; w < V; w++)
{
if (v != w)
{
if (StdRandom.Bernoulli(p))
{
G.AddEdge(v, w);
}
}
}
}
return(G);
}
public static void MainTest(string[] args)
{
int V = int.Parse(args[0]);
int E = int.Parse(args[1]);
// Eulerian cycle
Digraph G1 = DigraphGenerator.EulerianCycle(V, E);
DirectedEulerianCycle.UnitTest(G1, "Eulerian cycle");
// Eulerian path
Digraph G2 = DigraphGenerator.EulerianPath(V, E);
DirectedEulerianCycle.UnitTest(G2, "Eulerian path");
// empty digraph
Digraph G3 = new Digraph(V);
DirectedEulerianCycle.UnitTest(G3, "empty digraph");
// self loop
Digraph G4 = new Digraph(V);
int v4 = StdRandom.Uniform(V);
G4.AddEdge(v4, v4);
DirectedEulerianCycle.UnitTest(G4, "single self loop");
// union of two disjoint cycles
Digraph H1 = DigraphGenerator.EulerianCycle(V / 2, E / 2);
Digraph H2 = DigraphGenerator.EulerianCycle(V - V / 2, E - E / 2);
int[] perm = new int[V];
for (int i = 0; i < V; i++)
{
perm[i] = i;
}
StdRandom.Shuffle(perm);
Digraph G5 = new Digraph(V);
for (int v = 0; v < H1.V; v++)
{
foreach (int w in H1.Adj(v))
{
G5.AddEdge(perm[v], perm[w]);
}
}
for (int v = 0; v < H2.V; v++)
{
foreach (int w in H2.Adj(v))
{
G5.AddEdge(perm[V / 2 + v], perm[V / 2 + w]);
}
}
DirectedEulerianCycle.UnitTest(G5, "Union of two disjoint cycles");
// random digraph
Digraph G6 = DigraphGenerator.Simple(V, E);
DirectedEulerianCycle.UnitTest(G6, "simple digraph");
// 4-vertex digraph - no data file
//Digraph G7 = new Digraph(new TextInput("eulerianD.txt"));
//DirectedEulerianCycle.UnitTest(G7, "4-vertex Eulerian digraph");
}
/// <summary>
/// Returns a random simple digraph on <c>V</c> vertices, <c>E</c>
/// edges and (at least) <c>c</c> strong components. The vertices are randomly
/// assigned integer labels between <c>0</c> and <c>c-1</c> (corresponding to
/// strong components). Then, a strong component is creates among the vertices
/// with the same label. Next, random edges (either between two vertices with
/// the same labels or from a vetex 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.</summary>
/// <param name="V">the number of vertices</param>
/// <param name="E">the number of edges</param>
/// <param name="c">the (maximum) number of strong components</param>
/// <returns>a random simple digraph on <c>V</c> vertices and
/// <c>E</c> edges, with (at most) <c>c</c> strong components</returns>
/// <exception cref="ArgumentException">if <c>c</c> is larger than <c>V</c></exception>
///
public static Digraph Strong(int V, int E, int c)
{
if (c >= V || c <= 0)
{
throw new ArgumentException("Number of components must be between 1 and V");
}
if (E <= 2 * (V - c))
{
throw new ArgumentException("Number of edges must be at least 2(V-c)");
}
if (E > (long)V * (V - 1) / 2)
{
throw new ArgumentException("Too many edges");
}
// the digraph
Digraph G = new Digraph(V);
// edges added to G (to avoid duplicate edges)
SET <Edge> set = new SET <Edge>();
int[] label = new int[V];
for (int v = 0; v < V; v++)
{
label[v] = StdRandom.Uniform(c);
}
// make all vertices with label c a strong component by
// combining a rooted in-tree and a rooted out-tree
for (int i = 0; i < c; i++)
{
// how many vertices in component c
int count = 0;
for (int v = 0; v < G.V; v++)
{
if (label[v] == i)
{
count++;
}
}
// if (count == 0) System.err.println("less than desired number of strong components");
int[] vertices = new int[count];
int j = 0;
for (int v = 0; v < V; v++)
{
if (label[v] == i)
{
vertices[j++] = v;
}
}
StdRandom.Shuffle(vertices);
// rooted-in tree with root = vertices[count-1]
for (int v = 0; v < count - 1; v++)
{
int w = StdRandom.Uniform(v + 1, count);
Edge e = new Edge(w, v);
set.Add(e);
G.AddEdge(vertices[w], vertices[v]);
}
// rooted-out tree with root = vertices[count-1]
for (int v = 0; v < count - 1; v++)
{
int w = StdRandom.Uniform(v + 1, count);
Edge e = new Edge(v, w);
set.Add(e);
G.AddEdge(vertices[v], vertices[w]);
}
}
while (G.E < E)
{
int v = StdRandom.Uniform(V);
int w = StdRandom.Uniform(V);
Edge e = new Edge(v, w);
if (!set.Contains(e) && v != w && label[v] <= label[w])
{
set.Add(e);
G.AddEdge(v, w);
}
}
return(G);
}
