/**
* Finds a minimum spanning tree in the graph.
*
* The MST is found using a modifed DFS algorithm. The only difference
* to the algorithm implemented by DepthFirstSearch() method, is that
* here we record the edges that were crossed throughout the algorithm.
* These edges make up the MST at the end of the DFS search.
*
* @param start_index The index of the vertex where search starts at.
* @param mst Unweighted tree instance that will become
* an MST in this method. The MST instance must
* already contain all the original's graph
* vertices.
*
* @return The unweighted graph instance representing the MST. Note
* that NULL is returned if there is no path from the vertex at
* start_index to one or more vertices in the graph.
*
* @throws ArgumentException exception if start_index is negative
* or greater-or-equal to the number of vertices in the graph.
*/
protected IUnweightedGraph <VertexT> FindMinimumSpanningTree(
int start_index, IUnweightedGraph <VertexT> mst)
{
if (start_index < 0 || start_index >= Size)
{
throw new ArgumentException();
}
// Tracks the visited vertices so that we don't visit the same
// vertex multiple times
BitArray visited = new BitArray(Size, false);
// After they are visited, the vertices are pushed to the stack
// so that search can be continued at them at later time
StackViaLinkedList <int> stack = new StackViaLinkedList <int>();
// Push the start vertex to the queue and mark it as visited.
stack.Push(start_index);
visited[start_index] = true;
int added_edges_count = 0;
// The column of the adjacency matrix where the search for adjacent
// vertices needs to start from. This is set to stack.Pop() + 1 so
// that we don't re-scan the entire row of the adjacency matrix
// when we continue looking at the adjacent vertices of the vertex
// that was pushed to the stack before
int column = 0;
while (!stack.IsEmpty())
{
for (; column < Size; ++column)
{
if (Edges.EdgeExists(stack.Peak(), column) && !visited[column])
{
// Found an unvisited adjacent vertex. Add an edge between
// this vertex and the vertex at the top of the stack.
// Note that if this is an undirected graph, the AddEdge
// method bellow will also add an edge in the opposite
// direction.
mst.AddEdge(stack.Peak(), column);
// Mark it as visited and push it to the stack
stack.Push(column);
visited[column] = true;
++added_edges_count;
// Reset the column to 0 so that the adjacency matrix row
// corresponding to unvisited vertex is scanned from the
// beginning
column = 0;
// Break the the loop as we need to look at the adjecent
// vertices of the new vertex at the top of the stack next
break;
}
}
if (column == Size)
{
// We've found no unvisited adjecent vertices of the vertex
// at the top of the stack. Pop it off the stack so the next
// iteration will look at other adjacent vertices of the
// new top of the stack. Note that column is set to
// stack.Pop() + 1 so we start scanning that vertex's
// adjacency matrix row from where we left off
column = stack.Pop() + 1;
}
}
// The MST must consists of Size - 1 edges. If this is not the
// case, the graph is disconnected and MST doesn't exist (in
// which case NULL is returned)
return(added_edges_count == Size - 1 ? mst : null);
}
/**
* Uses DFS to find all vertices connected to the vertex at the start_index.
*
* TODO: describe the algorithm
*
* This is an iterator method that yields the control to the
* caller each time a new vertex is visited.
*
* @param start_index The vertex index where DFS is started from.
*
* @return An iterator interface type used to iterate over the vertices
* produced by the DFS algorithm.
*
* @note The method returns a vertex index and not the vertex itself.
* The caller can use GetVertex() to get access the vertex.
*
* @throws @throws ArgumentException exception if vertex_index is negative
* or greater-or-equal to the number of vertices in the graph.
*/
public IEnumerable <int> DepthFirstSearch(int start_index)
{
if (start_index < 0 || start_index >= Size)
{
throw new ArgumentException();
}
// Tracks which vertices are visited during the DFS search
BitArray visited_vertices = new BitArray(Size, false);
// Once visited, vertex indicies are pushed onto the stack
StackViaLinkedList <int> stack = new StackViaLinkedList <int>();
// Visit the starting vertex
yield return(start_index);
stack.Push(start_index);
visited_vertices[start_index] = true;
// The adjacency matrix column from which to start checking for
// adjacent vertices of the vertex at the top of the stack.
int column = 0;
// DFS algorithm is done once stack becomes empty
while (!stack.IsEmpty())
{
// Scan the adjacency matrix row corresponding to the vertex
// at the top of the stack
for (; column < Size; ++column)
{
if (Edges.EdgeExists(stack.Peak(), column) && !visited_vertices[column])
{
// Found an adjecent vertex that hasn't been visited yet.
// Visit it and push it to the stack
yield return(column);
stack.Push(column);
visited_vertices[column] = true;
break;
}
}
if (column == Size)
{
// This means that the for-loop didn't find an unvisited
// adjecent vertex of the vertex at the stack's top. Pop
// the stack and assign the (stack.Pop() + 1) to the column
// variable. This make sure that the next iteration scans
// the row corresponding to the vertex at the top of the
// stack from the index that it reached earlier, instead
// of re-scaning the entire row.
column = stack.Pop() + 1;
}
else
{
// The previous for-loop found an unvisited adjecent vertex
// of the vertex at the top of the stack. Reset column to
// 0 as the next iteration needs to scan the row that
// corresponds to the new stack's top from the start.
column = 0;
}
}
}
