/// <summary>
/// check that pre() and post() are consistent with pre(v) and post(v)
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
public bool Check(Digraph g)
{
// check that post(v) is consistent with post()
var r = 0;
foreach (int v in Post())
{
if (Post(v) != r)
{
Console.WriteLine("post(v) and post() inconsistent");
return false;
}
r++;
}
// check that pre(v) is consistent with pre()
r = 0;
foreach (int v in Pre())
{
if (Pre(v) != r)
{
Console.WriteLine("pre(v) and pre() inconsistent");
return false;
}
r++;
}
return true;
}
private Collections.Stack<Integer> _cycle; // directed cycle (or null if no such cycle)
#endregion Fields
#region Constructors
/// <summary>
/// Determines whether the digraph <tt>G</tt> has a directed cycle and, if so,
/// finds such a cycle.
/// </summary>
/// <param name="g">g the digraph</param>
public DirectedCycle(Digraph g)
{
_marked = new bool[g.V];
_onStack = new bool[g.V];
_edgeTo = new int[g.V];
for (var v = 0; v < g.V; v++)
if (!_marked[v] && _cycle == null) Dfs(g, v);
}
/// <summary>
/// Computes the vertices in digraph <tt>G</tt> that are
/// connected to any of the source vertices <tt>sources</tt>.
/// </summary>
/// <param name="g">g the graph</param>
/// <param name="sources">sources the source vertices</param>
public DirectedDFS(Digraph g, IEnumerable<Integer> sources)
{
_marked = new bool[g.V];
foreach (int v in sources)
{
if (!_marked[v]) Dfs(g, v);
}
}
private void Dfs(Digraph g, int v)
{
_count++;
_marked[v] = true;
foreach (int w in g.Adj(v))
{
if (!_marked[w]) Dfs(g, w);
}
}
/// <summary>
/// Computes the shortest path from any one of the source vertices in <tt>sources</tt>
/// to every other vertex in graph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
/// <param name="sources">sources the source vertices</param>
public BreadthFirstDirectedPaths(Digraph g, IEnumerable<Integer> sources)
{
_marked = new bool[g.V];
_distTo = new int[g.V];
_edgeTo = new int[g.V];
for (var v = 0; v < g.V; v++)
_distTo[v] = INFINITY;
Bfs(g, sources);
}
private readonly bool[] _marked; // marked[v] = is there an s->v path?
#endregion Fields
#region Constructors
/// <summary>
/// Computes the shortest path from <tt>s</tt> and every other vertex in graph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
/// <param name="s">s the source vertex</param>
public BreadthFirstDirectedPaths(Digraph g, int s)
{
_marked = new bool[g.V];
_distTo = new int[g.V];
_edgeTo = new int[g.V];
for (var v = 0; v < g.V; v++)
_distTo[v] = INFINITY;
Bfs(g, s);
}
private int _preCounter; // counter or preorder numbering
#endregion Fields
#region Constructors
/// <summary>
/// Determines a depth-first order for the digraph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
public DepthFirstOrder(Digraph g)
{
_pre = new int[g.V];
_post = new int[g.V];
_postorder = new Collections.Queue<Integer>();
_preorder = new Collections.Queue<Integer>();
_marked = new bool[g.V];
for (var v = 0; v < g.V; v++)
if (!_marked[v]) Dfs(g, v);
}
public void Run()
{
Console.WriteLine("Choose file:"); // Prompt
Console.WriteLine("1 - tinyDG.txt"); // Prompt
Console.WriteLine("or quit"); // Prompt
var fileNumber = Console.ReadLine();
string fileName;
switch (fileNumber)
{
case "1":
fileName = "tinyDG.txt";
break;
case "quit":
return;
default:
return;
}
var @in = new In($"Files\\Graphs\\{fileName}");
var lines = @in.ReadAllLines();
var lineIterator = 0;
var v = 0;
var e = 0;
var edges = new List<EdgeD>();
foreach (var line in lines)
{
if (lineIterator == 0)
{
v = Convert.ToInt32(line);
}
if (lineIterator == 1)
{
e = Convert.ToInt32(line);
}
if (lineIterator > 1)
{
var lineSplitted = line.Split(new[] {' '}, StringSplitOptions.RemoveEmptyEntries);
var ve = Convert.ToInt32(lineSplitted[0]);
var we = Convert.ToInt32(lineSplitted[1]);
var edge = new EdgeD(ve, we);
edges.Add(edge);
}
lineIterator++;
}
var digraph = new Digraph(v, e, edges);
Console.WriteLine(digraph);
Console.ReadLine();
}
/// <summary>
/// Returns a complete binary tree digraph on <tt>V</tt> vertices.
/// </summary>
/// <param name="v">V the number of vertices in the binary tree</param>
/// <returns>a digraph that is a complete binary tree on <tt>V</tt> vertices</returns>
public static Digraph BinaryTree(int v)
{
var g = new Digraph(v);
var vertices = new int[v];
for (var i = 0; i < v; i++)
vertices[i] = i;
StdRandom.Shuffle(vertices);
for (var i = 1; i < v; i++)
{
g.AddEdge(vertices[i], vertices[(i - 1) / 2]);
}
return g;
}
/// <summary>
/// does the id[] array contain the strongly connected components?
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
public bool Check(Digraph g)
{
var tc = new TransitiveClosure(g);
for (var v = 0; v < g.V; v++)
{
for (var w = 0; w < g.V; w++)
{
if (StronglyConnected(v, w) != (tc.Reachable(v, w) && tc.Reachable(w, v)))
return false;
}
}
return true;
}
private readonly int[] _rank; // rank[v] = position of vertex v in topological order
#endregion Fields
#region Constructors
/// <summary>
/// Determines whether the digraph <tt>G</tt> has a topological order and, if so,
/// finds such a topological order.
/// </summary>
/// <param name="g">g the digraph</param>
public Topological(Digraph g)
{
var finder = new DirectedCycle(g);
if (!finder.HasCycle())
{
var dfs = new DepthFirstOrder(g);
_order = dfs.ReversePost();
_rank = new int[g.V];
var i = 0;
foreach (int v in _order)
_rank[v] = i++;
}
}
public void Run()
{
const int v = 50;
const int e = 100;
// Eulerian cycle
var g1 = DigraphGenerator.EulerianCycle(v, e);
DirectedEulerianCycle.UnitTest(g1, "Eulerian cycle");
Console.WriteLine("---------------------------------------------------------------");
// Eulerian path
var g2 = DigraphGenerator.EulerianPath(v, e);
DirectedEulerianCycle.UnitTest(g2, "Eulerian path");
Console.WriteLine("---------------------------------------------------------------");
// empty digraph
var g3 = new Digraph(v);
DirectedEulerianCycle.UnitTest(g3, "empty digraph");
Console.WriteLine("---------------------------------------------------------------");
// self loop
var g4 = new Digraph(v);
var v4 = StdRandom.Uniform(v);
g4.AddEdge(v4, v4);
DirectedEulerianCycle.UnitTest(g4, "single self loop");
Console.WriteLine("---------------------------------------------------------------");
// union of two disjoint cycles
var h1 = DigraphGenerator.EulerianCycle(v / 2, e / 2);
var h2 = DigraphGenerator.EulerianCycle(v - v / 2, e - e / 2);
var perm = new int[v];
for (var i = 0; i < v; i++)
perm[i] = i;
StdRandom.Shuffle(perm);
var g5 = new Digraph(v);
for (var vi = 0; vi < h1.V; vi++)
foreach (int w in h1.Adj(vi))
g5.AddEdge(perm[vi], perm[w]);
for (var vi = 0; vi < h2.V; vi++)
foreach (int w in h2.Adj(vi))
g5.AddEdge(perm[v / 2 + vi], perm[v / 2 + w]);
DirectedEulerianCycle.UnitTest(g5, "Union of two disjoint cycles");
Console.WriteLine("---------------------------------------------------------------");
// random digraph
var g6 = DigraphGenerator.Simple(v, e);
DirectedEulerianCycle.UnitTest(g6, "simple digraph");
Console.WriteLine("---------------------------------------------------------------");
Console.ReadLine();
}
private int _pre; // preorder number counter
#endregion Fields
#region Constructors
/// <summary>
/// Computes the strong components of the digraph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
public TarjanSCC(Digraph g)
{
_marked = new bool[g.V];
_stack = new Stack<Integer>();
_id = new int[g.V];
_low = new int[g.V];
for (var v = 0; v < g.V; v++)
{
if (!_marked[v]) Dfs(g, v);
}
// check that id[] gives strong components
//assert check(G);
}
private readonly Collections.Stack<Integer> _path; // Eulerian path; null if no suh path
#endregion Fields
#region Constructors
/// <summary>
/// Computes an Eulerian path in the specified digraph, if one exists.
/// </summary>
/// <param name="g">g the digraph</param>
public DirectedEulerianPath(Digraph g)
{
// find vertex from which to start potential Eulerian path:
// a vertex v with outdegree(v) > indegree(v) if it exits;
// otherwise a vertex with outdegree(v) > 0
var deficit = 0;
var s = NonIsolatedVertex(g);
for (var v = 0; v < g.V; v++)
{
if (g.Outdegree(v) > g.Indegree(v))
{
deficit += (g.Outdegree(v) - g.Indegree(v));
s = v;
}
}
// digraph can't have an Eulerian path
// (this condition is needed)
if (deficit > 1) return;
// special case for digraph with zero edges (has a degenerate Eulerian path)
if (s == -1) s = 0;
// create local view of adjacency lists, to iterate one vertex at a time
var adj = new IEnumerator<Integer>[g.V];
for (var v = 0; v < g.V; v++)
adj[v] = g.Adj(v).GetEnumerator();
// greedily add to cycle, depth-first search style
var stack = new Collections.Stack<Integer>();
stack.Push(s);
_path = new Collections.Stack<Integer>();
while (!stack.IsEmpty())
{
int v = stack.Pop();
while (adj[v].MoveNext())
{
stack.Push(v);
v = adj[v].Current;
}
// push vertex with no more available edges to path
_path.Push(v);
}
// check if all edges have been used
if (_path.Size() != g.E + 1)
_path = null;
//assert check(G);
}
/// <summary>
/// Returns a cycle digraph on <tt>V</tt> vertices.
/// </summary>
/// <param name="v">V the number of vertices in the cycle</param>
/// <returns>a digraph that is a directed cycle on <tt>V</tt> vertices</returns>
public static Digraph Cycle(int v)
{
var g = new Digraph(v);
var vertices = new int[v];
for (var i = 0; i < v; i++)
vertices[i] = i;
StdRandom.Shuffle(vertices);
for (var 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 complete binary tree digraph on <tt>V</tt> vertices.
/// </summary>
/// <param name="v">V the number of vertices in the binary tree</param>
/// <returns>a digraph that is a complete binary tree on <tt>V</tt> vertices</returns>
public static Digraph BinaryTree(int v)
{
var g = new Digraph(v);
var vertices = new int[v];
for (var i = 0; i < v; i++)
{
vertices[i] = i;
}
StdRandom.Shuffle(vertices);
for (var i = 1; i < v; i++)
{
g.AddEdge(vertices[i], vertices[(i - 1) / 2]);
}
return(g);
}
/// <summary>
/// Returns a path digraph on <tt>V</tt> vertices.
/// </summary>
/// <param name="v">V the number of vertices in the path</param>
/// <returns>a digraph that is a directed path on <tt>V</tt> vertices</returns>
public static Digraph Path(int v)
{
var g = new Digraph(v);
var vertices = new int[v];
for (var i = 0; i < v; i++)
{
vertices[i] = i;
}
StdRandom.Shuffle(vertices);
for (var i = 0; i < v - 1; i++)
{
g.AddEdge(vertices[i], vertices[i + 1]);
}
return(g);
}
public void Run()
{
const int v = 50;
const int e = 100;
// Eulerian cycle
var g1 = DigraphGenerator.EulerianCycle(v, e);
DirectedEulerianPath.UnitTest(g1, "Eulerian cycle");
Console.WriteLine("---------------------------------------------------------------");
// Eulerian path
var g2 = DigraphGenerator.EulerianPath(v, e);
DirectedEulerianPath.UnitTest(g2, "Eulerian path");
Console.WriteLine("---------------------------------------------------------------");
// add one random edge
var g3 = new Digraph(g2);
g3.AddEdge(StdRandom.Uniform(v), StdRandom.Uniform(v));
DirectedEulerianPath.UnitTest(g3, "one random edge added to Eulerian path");
Console.WriteLine("---------------------------------------------------------------");
// self loop
var g4 = new Digraph(v);
var v4 = StdRandom.Uniform(v);
g4.AddEdge(v4, v4);
DirectedEulerianPath.UnitTest(g4, "single self loop");
Console.WriteLine("---------------------------------------------------------------");
// single edge
var g5 = new Digraph(v);
g5.AddEdge(StdRandom.Uniform(v), StdRandom.Uniform(v));
DirectedEulerianPath.UnitTest(g5, "single edge");
Console.WriteLine("---------------------------------------------------------------");
// empty digraph
var g6 = new Digraph(v);
DirectedEulerianPath.UnitTest(g6, "empty digraph");
Console.WriteLine("---------------------------------------------------------------");
// random digraph
var g7 = DigraphGenerator.Simple(v, e);
DirectedEulerianPath.UnitTest(g7, "simple digraph");
Console.WriteLine("---------------------------------------------------------------");
Console.ReadLine();
}
private int _pre; // preorder number counter
#endregion Fields
#region Constructors
/// <summary>
/// Computes the strong components of the digraph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
public GabowSCC(Digraph g)
{
_marked = new bool[g.V];
_stack1 = new Stack<Integer>();
_stack2 = new Stack<Integer>();
_id = new int[g.V];
_preorder = new int[g.V];
for (var v = 0; v < g.V; v++)
_id[v] = -1;
for (var v = 0; v < g.V; v++)
{
if (!_marked[v]) Dfs(g, v);
}
// check that id[] gives strong components
//assert check(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 tournament digraph on <tt>V</tt> 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">V the number of vertices</param>
/// <returns>a random tournament digraph on <tt>V</tt> vertices</returns>
public static Digraph Tournament(int v)
{
var g = new Digraph(v);
for (var ve = 0; ve < g.V; ve++)
{
for (var we = ve + 1; we < g.V; we++)
{
if (StdRandom.Bernoulli(0.5))
{
g.AddEdge(ve, we);
}
else
{
g.AddEdge(we, ve);
}
}
}
return(g);
}
private readonly int[] _rank; // rank[v] = order where vertex v appers in order
#endregion Fields
#region Constructors
/// <summary>
/// Determines whether the digraph <tt>G</tt> has a topological order and, if so,
/// finds such a topological order.
/// </summary>
/// <param name="g">g the digraph</param>
public TopologicalX(Digraph g)
{
// indegrees of remaining vertices
var indegree = new int[g.V];
for (var v = 0; v < g.V; v++)
{
indegree[v] = g.Indegree(v);
}
// initialize
_rank = new int[g.V];
_order = new Collections.Queue<Integer>();
var count = 0;
// initialize queue to contain all vertices with indegree = 0
var queue = new Collections.Queue<Integer>();
for (var v = 0; v < g.V; v++)
if (indegree[v] == 0) queue.Enqueue(v);
for (var j = 0; !queue.IsEmpty(); j++)
{
int v = queue.Dequeue();
_order.Enqueue(v);
_rank[v] = count++;
foreach (int w in g.Adj(v))
{
indegree[w]--;
if (indegree[w] == 0) queue.Enqueue(w);
}
}
// there is a directed cycle in subgraph of vertices with indegree >= 1.
if (count != g.V)
{
_order = null;
}
//assert check(G);
}
private readonly ST<string, Integer> _st; // string -> index
#endregion Fields
#region Constructors
/// <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="lines"></param>
/// <param name="delimiter"></param>
public SymbolDigraph(IList<string> lines, char delimiter)
{
_st = new ST<string, Integer>();
// First pass builds the index by reading strings to associate
// distinct strings with an index
foreach (var line in lines)
{
var a = line.Split(new[] { delimiter }, StringSplitOptions.RemoveEmptyEntries);
foreach (var word in a)
{
if (!_st.Contains(word))
_st.Put(word, _st.Size());
}
}
// inverted index to get string keys in an aray
_keys = new string[_st.Size()];
foreach (var name in _st.Keys())
{
_keys[_st.Get(name)] = name;
}
// second pass builds the digraph by connecting first vertex on each
// line to all others
G = new Digraph(_st.Size());
foreach (var line in lines)
{
var a = line.Split(new[] { delimiter }, StringSplitOptions.RemoveEmptyEntries);
int v = _st.Get(a[0]);
for (var i = 1; i < a.Length; i++)
{
int w = _st.Get(a[i]);
G.AddEdge(v, w);
}
}
}
/// <summary>
/// Returns an Eulerian path digraph on <tt>V</tt> vertices.
/// </summary>
/// <param name="v">V the number of vertices in the path</param>
/// <param name="e">E the number of edges in the path</param>
/// <returns>a digraph that is a directed Eulerian path on <tt>V</tt> vertices and <tt>E</tt> edges</returns>
/// <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");
}
var g = new Digraph(v);
var vertices = new int[e + 1];
for (var i = 0; i < e + 1; i++)
{
vertices[i] = StdRandom.Uniform(v);
}
for (var i = 0; i < e; i++)
{
g.AddEdge(vertices[i], vertices[i + 1]);
}
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 simple digraph on <tt>V</tt> vertices, with an
/// edge between any two vertices with probability <tt>p</tt>. This is sometimes
/// referred to as the Erdos-Renyi random digraph model.
/// This implementations takes time propotional to V^2 (even if <tt>p</tt> is small).
///
/// </summary>
/// <param name="v">V the number of vertices</param>
/// <param name="p">p the probability of choosing an edge</param>
/// <returns>a random simple digraph on <tt>V</tt> vertices, with an edge between any two vertices with probability <tt>p</tt></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");
}
var g = new Digraph(v);
for (var i = 0; i < v; i++)
{
for (var j = 0; j < v; j++)
{
if (i != j)
{
if (StdRandom.Bernoulli(p))
{
g.AddEdge(i, j);
}
}
}
}
return(g);
}
private readonly bool[] _marked; // marked[v] = is there an s->v path?
#endregion Fields
#region Constructors
/// <summary>
/// Computes the vertices reachable from the source vertex <tt>s</tt> in the digraph <tt>G</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
/// <param name="s">s the source vertex</param>
public NonrecursiveDirectedDFS(Digraph g, int s)
{
_marked = new bool[g.V];
// to be able to iterate over each adjacency list, keeping track of which
// vertex in each adjacency list needs to be explored next
var adj = new IEnumerator<Integer>[g.V];
for (var v = 0; v < g.V; v++)
adj[v] = g.Adj(v).GetEnumerator();
// depth-first search using an explicit stack
var stack = new Collections.Stack<Integer>();
_marked[s] = true;
stack.Push(s);
while (!stack.IsEmpty())
{
int v = stack.Peek();
if (adj[v].MoveNext())
{
int w = adj[v].Current;
// StdOut.printf("check %d\n", w);
if (!_marked[w])
{
// discovered vertex w for the first time
_marked[w] = true;
// edgeTo[w] = v;
stack.Push(w);
// StdOut.printf("dfs(%d)\n", w);
}
}
else
{
// StdOut.printf("%d done\n", v);
stack.Pop();
}
}
}
private readonly string _regexp; // regular expression
#endregion Fields
#region Constructors
/// <summary>
/// Initializes the NFA from the specified regular expression.
/// </summary>
/// <param name="regexp">regexp the regular expression</param>
public NFA(string regexp)
{
_regexp = regexp;
_m = regexp.Length;
var ops = new Stack<Integer>();
_g = new Digraph(_m + 1);
for (var i = 0; i < _m; i++)
{
var lp = i;
if (regexp[i] == '(' || regexp[i] == '|')
ops.Push(i);
else if (regexp[i] == ')')
{
int or = ops.Pop();
// 2-way or operator
if (regexp[or] == '|')
{
lp = ops.Pop();
_g.AddEdge(lp, or + 1);
_g.AddEdge(or, i);
}
else if (regexp[or] == '(')
lp = or;
//else assert false;
}
// closure operator (uses 1-character lookahead)
if (i < _m - 1 && regexp[i + 1] == '*')
{
_g.AddEdge(lp, i + 1);
_g.AddEdge(i + 1, lp);
}
if (regexp[i] == '(' || regexp[i] == '*' || regexp[i] == ')')
_g.AddEdge(i, i + 1);
}
}
/// <summary>
/// Returns an Eulerian cycle digraph on <tt>V</tt> vertices.
/// </summary>
/// <param name="v">V the number of vertices in the cycle</param>
/// <param name="e">E the number of edges in the cycle</param>
/// <returns>a digraph that is a directed Eulerian cycle on <tt>V</tt> vertices and <tt>E</tt> 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");
}
var g = new Digraph(v);
var vertices = new int[e];
for (var i = 0; i < e; i++)
{
vertices[i] = StdRandom.Uniform(v);
}
for (var i = 0; i < e - 1; i++)
{
g.AddEdge(vertices[i], vertices[i + 1]);
}
g.AddEdge(vertices[e - 1], vertices[0]);
return(g);
}
public void Run()
{
Console.WriteLine("Choose file:"); // Prompt
Console.WriteLine("1 - tinyDG.txt"); // Prompt
Console.WriteLine("or quit"); // Prompt
var fileNumber = Console.ReadLine();
string fileName;
switch (fileNumber)
{
case "1":
fileName = "tinyDG.txt";
break;
case "quit":
return;
default:
return;
}
var @in = new In($"Files\\Graphs\\{fileName}");
var lines = @in.ReadAllLines();
var lineIterator = 0;
var v = 0;
var e = 0;
var edges = new List<EdgeD>();
foreach (var line in lines)
{
if (lineIterator == 0)
{
v = Convert.ToInt32(line);
}
if (lineIterator == 1)
{
e = Convert.ToInt32(line);
}
if (lineIterator > 1)
{
var lineSplitted = line.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
var ve = Convert.ToInt32(lineSplitted[0]);
var we = Convert.ToInt32(lineSplitted[1]);
var edge = new EdgeD(ve, we);
edges.Add(edge);
}
lineIterator++;
}
var digraph = new Digraph(v, e, edges);
Console.WriteLine(digraph);
Console.WriteLine("------------------------------------------------------");
var bag1 = new Core.Collections.Bag<Integer> { new Integer(1) };
var bag2 = new Core.Collections.Bag<Integer> { new Integer(2) };
var bag3 = new Core.Collections.Bag<Integer> { new Integer(6) };
var listSources = new List<Core.Collections.Bag<Integer>> { bag1, bag2, bag3 };
foreach (var sources in listSources)
{
foreach (var source in sources)
{
// multiple-source reachability
var dfs = new NonrecursiveDirectedDFS(digraph, source.Value);
// print out vertices reachable from sources
for (var i = 0; i < digraph.V; i++)
{
if (dfs.Marked(i)) Console.Write($"{i} ");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("---------------------------------------------------------");
}
Console.ReadLine();
}
/// <summary>
/// run DFS in digraph G from vertex v and compute preorder/postorder
/// </summary>
/// <param name="g"></param>
/// <param name="v"></param>
private void Dfs(Digraph g, int v)
{
_marked[v] = true;
_pre[v] = _preCounter++;
_preorder.Enqueue(v);
foreach (int w in g.Adj(v))
{
if (!_marked[w])
{
Dfs(g, w);
}
}
_postorder.Enqueue(v);
_post[v] = _postCounter++;
}
public static void UnitTest(Digraph g, string description)
{
Console.WriteLine(description);
Console.WriteLine("-------------------------------------");
Console.Write(g);
var euler = new DirectedEulerianPath(g);
Console.Write("Eulerian path: ");
if (euler.HasEulerianPath())
{
foreach (int v in euler.Path())
{
Console.Write($"{v} ");
}
Console.WriteLine();
}
else
{
Console.WriteLine("none");
}
Console.WriteLine();
}
/// <summary>
/// returns any non-isolated vertex; -1 if no such vertex
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
private static int NonIsolatedVertex(Digraph g)
{
for (var v = 0; v < g.V; v++)
if (g.Outdegree(v) > 0)
return v;
return -1;
}
/// <summary>
/// Determines whether a digraph has an Eulerian path using necessary
/// and sufficient conditions (without computing the path itself):
/// - indegree(v) = outdegree(v) for every vertex,
/// except one vertex v may have outdegree(v) = indegree(v) + 1
/// (and one vertex v may have indegree(v) = outdegree(v) + 1)
/// - the graph is connected, when viewed as an undirected graph
/// (ignoring isolated vertices)
/// This method is solely for unit testing.
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
private static bool HasEulerianPath(Digraph g)
{
if (g.E == 0) return true;
// Condition 1: indegree(v) == outdegree(v) for every vertex,
// except one vertex may have outdegree(v) = indegree(v) + 1
var deficit = 0;
for (var v = 0; v < g.V; v++)
if (g.Outdegree(v) > g.Indegree(v))
deficit += (g.Outdegree(v) - g.Indegree(v));
if (deficit > 1) return false;
// Condition 2: graph is connected, ignoring isolated vertices
var h = new Graph(g.V);
for (var v = 0; v < g.V; v++)
foreach (int w in g.Adj(v))
h.AddEdge(v, w);
// check that all non-isolated vertices are connected
var s = NonIsolatedVertex(g);
var bfs = new BreadthFirstPaths(h, s);
for (var v = 0; v < g.V; v++)
if (h.Degree(v) > 0 && !bfs.HasPathTo(v))
return false;
return true;
}
public bool Check(Digraph g)
{
// internal consistency check
if (HasEulerianPath() == (Path() == null)) return false;
// hashEulerianPath() returns correct value
if (HasEulerianPath() != HasEulerianPath(g)) return false;
// nothing else to check if no Eulerian path
if (_path == null) return true;
// check that path() uses correct number of edges
if (_path.Size() != g.E + 1) return false;
// check that path() is a directed path in G
// TODO
return true;
}
/// <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);
}
private void Dfs(Digraph g, int v)
{
_marked[v] = true;
_low[v] = _pre++;
var min = _low[v];
_stack.Push(v);
foreach (int j in g.Adj(v))
{
if (!_marked[j]) Dfs(g, j);
if (_low[j] < min) min = _low[j];
}
if (min < _low[v])
{
_low[v] = min;
return;
}
int w;
do
{
w = _stack.Pop();
_id[w] = _count;
_low[w] = g.V;
} while (w != v);
_count++;
}
public void Run()
{
Console.WriteLine("Choose file:"); // Prompt
Console.WriteLine("1 - tinyDG.txt"); // Prompt
Console.WriteLine("2 - mediumDG.txt"); // Prompt
Console.WriteLine("or quit"); // Prompt
var fileNumber = Console.ReadLine();
string fileName;
switch (fileNumber)
{
case "1":
fileName = "tinyDG.txt";
break;
case "2":
fileName = "mediumDG.txt";
break;
case "quit":
return;
default:
return;
}
var @in = new In($"Files\\Graphs\\{fileName}");
var lines = @in.ReadAllLines();
var lineIterator = 0;
var v = 0;
var e = 0;
var edges = new List<EdgeD>();
foreach (var line in lines)
{
if (lineIterator == 0)
{
v = Convert.ToInt32(line);
}
if (lineIterator == 1)
{
e = Convert.ToInt32(line);
}
if (lineIterator > 1)
{
var lineSplitted = line.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
var ve = Convert.ToInt32(lineSplitted[0]);
var we = Convert.ToInt32(lineSplitted[1]);
var edge = new EdgeD(ve, we);
edges.Add(edge);
}
lineIterator++;
}
var digraph = new Digraph(v, e, edges);
Console.WriteLine(digraph);
Console.WriteLine("------------------------------------------------------");
const int s = 3;
var bfs = new BreadthFirstDirectedPaths(digraph, s);
for (var i = 0; i < digraph.V; i++)
{
if (bfs.HasPathTo(i))
{
Console.Write($"{s} to {i} ({bfs.DistTo(i)}): ");
foreach (int x in bfs.PathTo(i))
{
if (x == s) Console.Write(x);
else Console.Write("->" + x);
}
Console.WriteLine();
}
else
{
Console.Write($"{s} to {i} (-): not connected{Environment.NewLine}");
}
}
Console.ReadLine();
}
private int _count; // number of vertices reachable from s
/// <summary>
/// Computes the vertices in digraph <tt>G</tt> that are
/// reachable from the source vertex <tt>s</tt>.
/// </summary>
/// <param name="g">g the digraph</param>
/// <param name="s">s the source vertex</param>
public DirectedDFS(Digraph g, int s)
{
_marked = new bool[g.V];
Dfs(g, s);
}