/// <summary>
/// Computes all shortest distance between any vertices in a given graph.
/// </summary>
/// <param name="adjacence_matrix">Square adjacence matrix. The main diagonal
/// is expected to consist of zeros, any non-existing edges should be marked
/// positive infinity.</param>
/// <returns>Two matrices D and P, where D[u,v] holds the distance of the shortest
/// path between u and v, and P[u,v] holds the shortcut vertex on the way from
/// u to v.</returns>
public static ArrayMatrix[] Floyd(ArrayMatrix adjacence_matrix)
{
if (!adjacence_matrix.IsSquare()) throw new ArgumentException("Expected square matrix.");
else if (!adjacence_matrix.IsReal()) throw new ArgumentException("Adjacence matrices are expected to be real.");
var n = adjacence_matrix.RowCount;
var D = adjacence_matrix.Clone(); // distance matrix
var P = new ArrayMatrix(n);
double buf;
for (var k = 1; k <= n; k++)
for (var i = 1; i <= n; i++)
for (var j = 1; j <= n; j++)
{
buf = D[i, k].Real + D[k, j].Real;
if (buf < D[i, j].Real)
{
D[i, j].Real = buf;
P[i, j].Real = k;
}
}
return new ArrayMatrix[] {D, P};
}
/// <summary>
/// Returns the shortest path between two given vertices i and j as
/// int array.
/// </summary>
/// <param name="P">Path matrix as returned from Floyd().</param>
/// <param name="i">One-based index of start vertex.</param>
/// <param name="j">One-based index of end vertex.</param>
/// <returns></returns>
public static ArrayList FloydPath(ArrayMatrix P, int i, int j)
{
if (!P.IsSquare()) throw new ArgumentException("Path matrix must be square.");
else if (!P.IsReal()) throw new ArgumentException("Adjacence matrices are expected to be real.");
var path = new ArrayList();
path.Add(i);
//int borderliner = 0;
//int n = P.Size()[0] + 1; // shortest path cannot have more than n vertices!
while (P[i, j] != 0)
{
i = Convert.ToInt32(P[i, j]);
path.Add(i);
//borderliner++;
//if (borderliner == n)
// throw new FormatException("P was not a Floyd path matrix.");
}
path.Add(j);
return path;
}
/// <summary>
/// Performs depth-first search for a graph given by its adjacence matrix.
/// </summary>
/// <param name="adjacence_matrix">A[i,j] = 0 or +infty, if there is no edge from i to j; any non-zero value otherwise.</param>
/// <param name="root">The vertex to begin the search.</param>
/// <returns>Adjacence matrix of the computed spanning tree.</returns>
public static ArrayMatrix DFS(ArrayMatrix adjacence_matrix, int root)
{
if (!adjacence_matrix.IsSquare()) throw new ArgumentException("Adjacence matrices are expected to be square.");
else if (!adjacence_matrix.IsReal()) throw new ArgumentException("Adjacence matrices are expected to be real.");
var n = adjacence_matrix.RowCount;
if (root < 1 || root > n) throw new ArgumentException("Root must be a vertex of the graph, e.i. in {1, ..., n}.");
var spanTree = new ArrayMatrix(n);
var marked = new bool[n + 1];
var todo = new Stack();
todo.Push(root);
marked[root] = true;
// adajacence lists for each vertex
var A = new ArrayList[n + 1];
for (var i = 1; i <= n; i++)
{
A[i] = new ArrayList();
for (var j = 1; j <= n; j++) if (adjacence_matrix[i, j].Real != 0 && adjacence_matrix[i, j].Imag != double.PositiveInfinity) A[i].Add(j);
}
int v, w;
while (todo.Count > 0)
{
v = (int) todo.Peek();
if (A[v].Count > 0)
{
w = (int) A[v][0];
if (!marked[w])
{
marked[w] = true; // mark w
spanTree[v, w].Real = 1; // mark vw
todo.Push(w); // one more to search
}
A[v].RemoveAt(0);
}
else todo.Pop();
}
return spanTree;
}