/**
* Finds the shortest possible path, measured in number of edges traversed, between two vertices,
* a and b, in a graph, and returns this distance. The distance between a vertex and itself is
* zero. Throws NoPathFoundException if there does not exist a path between a and b.
*
* @param graph the graph which contains vertices a and b
* @param a the starting vertex contained in the graph
* @param b the vertex to be traveled to (end vertex), contained in the same graph as a
* @return the number of edges traversed to get from a to b along the shortest path
* @throws NoPathFoundException if there does not exist a path from a to b
*/
public static int shortestDistance(Graph graph, Vertex a, Vertex b) throws NoPathFoundException {
Queue<Vertex> nextVertexQueue = new LinkedList<Vertex>();
HashSet<Vertex> scheduledSet = new HashSet<Vertex>();
nextVertexQueue.addAll(graph.getDownstreamNeighbors(a));
scheduledSet.addAll(graph.getDownstreamNeighbors(a));
int depth = 1;
while (!nextVertexQueue.isEmpty()) {
Queue<Vertex> currentVertexQueue = new LinkedList<Vertex>(nextVertexQueue);
nextVertexQueue = new LinkedList<>();
while (!currentVertexQueue.isEmpty()) {
Vertex currentRoot = currentVertexQueue.poll();
if (currentRoot.equals(b)) return depth;
else {
for (Vertex each_child : graph.getDownstreamNeighbors(currentRoot)) {
if (!scheduledSet.contains(each_child)) {
nextVertexQueue.add(each_child);
scheduledSet.add(each_child);
}
}
}
}
depth++;
}
throw new NoPathFoundException();
}
/**
* returns a set of lists that represent all possible breadth-first traversals of the graph. Each
* traversal is always the shortest possible way to traverse the graph from a starting index. The
* number of lists in the set represents the possible number of starting vertices.
*
* @param graph the graph to be traversed
* @return Set<List<Vertex>> the set of lists of all possible ways to traverse the graph
*/
public static Set<List<Vertex>> breadthFirstSearch(Graph graph) {
// TODO: Representation safety required
Set<List<Vertex>> result = new HashSet<List<Vertex>>();
for (Vertex a : graph.getVertices()) {
Queue<Vertex> nextVertexQueue = new LinkedList<Vertex>();
HashSet<Vertex> scheduledSet = new HashSet<Vertex>();
// initialize the first root queue
nextVertexQueue.addAll(graph.getDownstreamNeighbors(a));
scheduledSet.addAll(graph.getDownstreamNeighbors(a));
// one traversal of the graph starting at a vertex a
List<Vertex> traversal = new LinkedList<Vertex>();
traversal.add(a);
// loop until run out of new vertexes to visit
while (!nextVertexQueue.isEmpty()) {
// add the current vertex to the traversal
Vertex currentRoot = nextVertexQueue.poll();
traversal.add(currentRoot);
// add children if they aren't already scheduled
for (Vertex each_child : graph.getDownstreamNeighbors(currentRoot)) {
if (!scheduledSet.contains(each_child)) {
nextVertexQueue.add(each_child);
scheduledSet.add(each_child);
}
}
}
result.add(traversal);
}
return result;
}
/**
* traverses the graph using a depth first search algorithm. Returns a set of lists that represent
* all possible ways to traverse the graph. Each list contains the traversal of the vertices in
* the graph in the order that they were visited starting from a start index. The number of lists
* in the set represents all possible starting vertices in the graph.
*
* @param graph the graph to be traversed
* @return Set<List<Vertex>> a set of the lists of all possible ways to traverse the graph.
*/
public static Set<List<Vertex>> depthFirstSearch(Graph graph) {
Set<List<Vertex>> result = new HashSet<List<Vertex>>();
for (Vertex primaryRoot : graph.getVertices()) {
Stack<Vertex> vertexStack = new Stack<Vertex>();
HashSet<Vertex> scheduledSet = new HashSet<Vertex>();
List<Vertex> traversal = new LinkedList<Vertex>();
vertexStack.add(primaryRoot);
scheduledSet.add(primaryRoot);
traversal.add(primaryRoot);
while (!vertexStack.isEmpty()) {
boolean noChildLeft = true;
for (Vertex each_childRoot : graph.getDownstreamNeighbors(vertexStack.peek())) {
if (!scheduledSet.contains(each_childRoot)) {
scheduledSet.add(each_childRoot);
vertexStack.add(each_childRoot);
traversal.add(each_childRoot);
noChildLeft = false;
break;
}
}
if (noChildLeft) {
vertexStack.pop();
}
}
result.add(traversal);
}
return result;
}
/**
* Finds the common downstream vertices such that for each downstream vertex v, a and b are both
* one edge down from a. Returns an empty list if none exist.
*
* @param graph non-empty graph representation
* @param a Vertex contained within the graph
* @param b Vertex contained within the graph
* @return A list of vertices that are the common downstream vertices of a and b
*/
public static List<Vertex> commonDownstreamVertices(Graph graph, Vertex a, Vertex b) {
List<Vertex> aList = graph.getDownstreamNeighbors(a);
List<Vertex> bList = graph.getDownstreamNeighbors(b);
List<Vertex> commonDownStreamList = new LinkedList<Vertex>();
for (Vertex aVertex : aList) {
for (Vertex bVertex : bList) {
if (aVertex.equals(bVertex)) {
commonDownStreamList.add(aVertex);
}
}
}
return commonDownStreamList;
}