/// <summary>
/// Returns a random simple digraph containing <tt>V</tt> vertices and <tt>E</tt> edges.
/// </summary>
/// <param name="v">V the number of vertices</param>
/// <param name="e">E the number of vertices</param>
/// <returns>a random simple digraph on <tt>V</tt> vertices, containing a total of <tt>E</tt> edges</returns>
/// <exception cref="ArgumentException">if no such simple digraph exists</exception>
public static Digraph Simple(int v, int e)
{
if (e > (long)v * (v - 1))
{
throw new ArgumentException("Too many edges");
}
if (e < 0)
{
throw new ArgumentException("Too few edges");
}
var g = new Digraph(v);
var set = new SET <EdgeD>();
while (g.E < e)
{
var ve = StdRandom.Uniform(v);
var we = StdRandom.Uniform(v);
var edge = new EdgeD(ve, we);
if ((ve != we) && !set.Contains(edge))
{
set.Add(edge);
g.AddEdge(ve, we);
}
}
return(g);
}
/// <summary>
/// Returns a random simple DAG containing <tt>V</tt> vertices and <tt>E</tt> edges.
/// Note: it is not uniformly selected at random among all such DAGs.
/// </summary>
/// <param name="v">V the number of vertices</param>
/// <param name="e">E the number of vertices</param>
/// <returns>a random simple DAG on <tt>V</tt> vertices, containing a total of <tt>E</tt> edges</returns>
/// <exception cref="ArgumentException">if no such simple DAG exists</exception>
public static Digraph Dag(int v, int e)
{
if (e > (long)v * (v - 1) / 2)
{
throw new ArgumentException("Too many edges");
}
if (e < 0)
{
throw new ArgumentException("Too few edges");
}
var g = new Digraph(v);
var set = new SET <EdgeD>();
var vertices = new int[v];
for (var i = 0; i < v; i++)
{
vertices[i] = i;
}
StdRandom.Shuffle(vertices);
while (g.E < e)
{
var ve = StdRandom.Uniform(v);
var we = StdRandom.Uniform(v);
var edge = new EdgeD(ve, we);
if ((ve < we) && !set.Contains(edge))
{
set.Add(edge);
g.AddEdge(vertices[ve], vertices[we]);
}
}
return(g);
}
/// <summary>
/// Returns a random rooted-out DAG on <tt>V</tt> vertices and <tt>E</tt> 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">V the number of vertices</param>
/// <param name="e">E the number of edges</param>
/// <returns>a random rooted-out DAG on <tt>V</tt> vertices and <tt>E</tt> 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");
}
var g = new Digraph(v);
var set = new SET <EdgeD>();
// fix a topological order
var vertices = new int[v];
for (var 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 (var ve = 0; ve < v - 1; ve++)
{
var we = StdRandom.Uniform(ve + 1, v);
var edge = new EdgeD(we, ve);
set.Add(edge);
g.AddEdge(vertices[we], vertices[ve]);
}
while (g.E < e)
{
var ve = StdRandom.Uniform(v);
var we = StdRandom.Uniform(v);
var edge = new EdgeD(we, ve);
if ((ve < we) && !set.Contains(edge))
{
set.Add(edge);
g.AddEdge(vertices[we], vertices[ve]);
}
}
return(g);
}
/// <summary>
/// Returns a random simple digraph on <tt>V</tt> vertices, <tt>E</tt>
/// edges and (at least) <tt>c</tt> strong components. The vertices are randomly
/// assigned integer labels between <tt>0</tt> and <tt>c-1</tt> (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">V the number of vertices</param>
/// <param name="e">E the number of edges</param>
/// <param name="c">c the (maximum) number of strong components</param>
/// <returns>a random simple digraph on <tt>V</tt> vertices and <tt>E</tt> edges, with (at most) <tt>c</tt> strong components</returns>
/// <exception cref="ArgumentException">if <tt>c</tt> is larger than <tt>V</tt></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
var g = new Digraph(v);
// edges added to G (to avoid duplicate edges)
var set = new SET <EdgeD>();
var label = new int[v];
for (var i = 0; i < v; i++)
{
label[i] = StdRandom.Uniform(c);
}
// make all vertices with label c a strong component by
// combining a rooted in-tree and a rooted out-tree
for (var i = 0; i < c; i++)
{
// how many vertices in component c
var count = 0;
for (var ii = 0; ii < g.V; ii++)
{
if (label[ii] == i)
{
count++;
}
}
// if (count == 0) System.err.println("less than desired number of strong components");
var vertices = new int[count];
var j = 0;
for (var jj = 0; jj < v; jj++)
{
if (label[jj] == i)
{
vertices[j++] = jj;
}
}
StdRandom.Shuffle(vertices);
// rooted-in tree with root = vertices[count-1]
for (var ve = 0; ve < count - 1; ve++)
{
var we = StdRandom.Uniform(ve + 1, count);
var edge = new EdgeD(we, ve);
set.Add(edge);
g.AddEdge(vertices[we], vertices[ve]);
}
// rooted-out tree with root = vertices[count-1]
for (var ve = 0; ve < count - 1; ve++)
{
var we = StdRandom.Uniform(ve + 1, count);
var edge = new EdgeD(ve, we);
set.Add(edge);
g.AddEdge(vertices[ve], vertices[we]);
}
}
while (g.E < e)
{
var ve = StdRandom.Uniform(v);
var we = StdRandom.Uniform(v);
var edge = new EdgeD(ve, we);
if (!set.Contains(edge) && ve != we && label[ve] <= label[we])
{
set.Add(edge);
g.AddEdge(ve, we);
}
}
return(g);
}
