/**
* Uses BFS 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 BFS is started from.
*
* @return An iterator interface type used to iterate over the vertices
* produced by the BFS algorithm.
*
* @note The method returns a vertex index and not the vertex itself.
* The caller can use GetVertex() to get access the vertex.
*
* @throws ArgumentException exception if vertex_index is negative
* or greater-or-equal to the number of vertices in the graph.
*/
public IEnumerable <int> BreadthFirstSearch(int start_index)
{
if (start_index < 0 || start_index >= Size)
{
throw new ArgumentException();
}
// Tracks which vertices are visited during the BFS search
BitArray visited_vertices = new BitArray(Size, false);
// Once visited, vertex indices are added to the queue
QueueViaLinkedList <int> queue = new QueueViaLinkedList <int>();
// Visit the initial node and add it to the queue
yield return(start_index);
queue.Enqueue(start_index);
visited_vertices[start_index] = true;
// BFS algorithm is done once the queue becomes empty
while (!queue.IsEmpty())
{
for (int column = 0; column < Size; ++column)
{
if (Edges.EdgeExists(queue.Peak(), column) && !visited_vertices[column])
{
// Found an adjacent unvisited vertex. Visit it and push it
// to the queue so that its adjecent vertices will be visited
// later
yield return(column);
queue.Enqueue(column);
visited_vertices[column] = true;
}
}
// At this point we have visited all the adjecent vertices of
// the vertex currently at the head of the queue. Thus, remove
// this vertex from the queue so that next iteration will visit
// the adjacent vertices of the next vertex in the queue
queue.Dequeue();
}
}
/**
* Finds the shortest path between the vertices at the start_index
* and end_index.
*
* @note Uses the modified BFS algorithm to find the shortest path.
* TODO: describe the algorithm.
*
* @param start_index The index of the start vertex.
* @param end_index The index of the end vertex.
*
* @return A collection of vertex indices tracing the path from the
* start_index to end_index, or NULL if these two vertices are
* not connected. If start_index == end_index, a collection with a
* single element (start_index) is returned.
*
* @throws ArgumentException exception if start_index or end_index
* is negative or greater-or-equal to the number of vertices in the
* graph.
*/
public override ICollection <int> FindShortestPath(int start_index, int end_index)
{
if (start_index < 0 || start_index >= Size || end_index < 0 || end_index >= Size)
{
throw new ArgumentException();
}
if (start_index == end_index)
{
// Return a list with the given vertex index
return(new LinkedList <int>(new int[] { start_index }));
}
// Tracks which vertices are visited during the BFS search
BitArray visited_vertices = new BitArray(Size, false);
// Once visited, vertex indices are added to the queue
QueueViaLinkedList <int> queue = new QueueViaLinkedList <int>();
// Each entry prev[i] contain the index of the vertex visited
// immediatelly prior to vertex i (or -1 if vertex i is the
// very first visited vertex or has not been visited yet)
int[] prev = Enumerable.Repeat(-1, Size).ToArray();
// Add the index of the start vertex to the queue
queue.Enqueue(start_index);
visited_vertices[start_index] = true;
// BFS algorithm is done once the queue becomes empty
while (!queue.IsEmpty())
{
// Remove the vertex whose direct siblings are to be visited
// in this iteration
int curr_vertex_index = queue.Dequeue();
for (int column = 0; column < Size; ++column)
{
if (Edges.EdgeExists(curr_vertex_index, column) && !visited_vertices[column])
{
// Found an adjacent unvisited vertex. Visit it and push it
// to the queue so that its adjecent vertices will be visited
// later
queue.Enqueue(column);
visited_vertices[column] = true;
// Mark the vertex that was visisted immediatelly prior
// to the current one.
prev[column] = curr_vertex_index;
if (column == end_index)
{
// Traced the path to the end vertex. Clear the queue
// so that the outer while loop will terminate
queue.Clear();
break;
}
}
}
}
LinkedList <int> shortest_path = null;
if (prev[end_index] != -1)
{
// Trace the path from the vertex at end_index back to the
// start_index. This is the shortest path from start_index
// to end_index
shortest_path = new LinkedList <int>();
int index = end_index;
while (index != -1)
{
shortest_path.AddFirst(index);
index = prev[index];
}
}
return(shortest_path);
}