/// <summary>
/// Label all nodes according to whether they are (1) on the shortest path, (2) are on a loop to the shortest path,
/// (3) are on a path resulting in a dead end, and (4) are not connected to the maze.
/// All labels are inclusive, i.e. the starting point of a dead end is a node labeled as on the shorted path.
/// The shortest path is found using Dijkstra's algorithm.
/// </summary>
/// <returns>List of nodes with path labels.</returns>
/// <param name="mazeFrame">List of nodes.</param>
protected void LabelNodesWRTPath(ref MazeFrame mazeFrame)
{
//
// This function labels each node according to the following booleans:
//
// onShortestPath - whether node is on the path found using psuedo Dijkstra's method
// onLoop - whether node is on path that diverges from the shortest path, but returns to it eventually
// onDeadEnd - whether the node is on a dead end, defined as a path that (1) diverges from the shortest path and doesn't return
// notConnectedToPath - whether node has a connection on path or is superfluous visual filler
// (junction nodes have more than one label)
// Find shortest path from beginning to end using Dijkstra's algorithm
// From wikipedia/other:
/*
* 1) Mark all nodes unvisited, mark selected initial node with a current distance of 0 and the rest with infinity.
* 2) Set the non-visited node with the smallest current distance as the current node C.
* 3) For each neighbour N of current node C: add the current distance of C with the weight of the edge
* connecting C-N. If it's smaller than the current distance of N, set it as the new current distance of N.
* 4) Mark the current node C as visited.
* 5) If end not touched yet, and if there are non-visited nodes, go to step 2.
*/
// Check start/end node active status
if (!mazeFrame.StartNode.IsActive || !mazeFrame.EndNode.IsActive)
{
throw new System.Exception("Start/end nodes are required to be active.");
}
// Prep storage of labels and initilaze as false
int activeNodeCount = 0;
foreach (MazeNode nd in mazeFrame.Nodes)
{
if (nd.IsActive)
{
activeNodeCount++;
}
}
Dictionary <string, bool> onShortestPath = new Dictionary <string, bool>(activeNodeCount);
Dictionary <string, bool> onDeadEnd = new Dictionary <string, bool>(activeNodeCount);
Dictionary <string, bool> onLoop = new Dictionary <string, bool>(activeNodeCount);
Dictionary <string, bool> notConnectedToPath = new Dictionary <string, bool>(activeNodeCount);
foreach (MazeNode nd in mazeFrame.Nodes)
{
if (nd.IsActive)
{
onShortestPath.Add(nd.Identifier, false);
onDeadEnd.Add(nd.Identifier, false);
onLoop.Add(nd.Identifier, false);
notConnectedToPath.Add(nd.Identifier, false);
}
}
// Find start and end node
MazeNode startNode = mazeFrame.StartNode;
MazeNode endNode = mazeFrame.EndNode;
// Create bookkeeping for visits and set all nodes to unvisitied
Dictionary <string, bool> isVisited = new Dictionary <string, bool>(mazeFrame.Nodes.Count);
foreach (MazeNode nd in mazeFrame.Nodes)
{
if (nd.IsActive)
{
isVisited.Add(nd.Identifier, false);
}
else
{
isVisited.Add(nd.Identifier, true);
}
}
// Ignore nodes without neighbors
foreach (MazeNode nd in mazeFrame.Nodes)
{
if (nd.ConnectedNeighbors.Count == 0)
{
isVisited[nd.Identifier] = true;
}
}
// Set distance to start, and initialize at infinity
Dictionary <string, float> distToStart = new Dictionary <string, float>(activeNodeCount);
foreach (MazeNode nd in mazeFrame.Nodes)
{
if (nd.IsActive)
{
distToStart.Add(nd.Identifier, float.PositiveInfinity);
}
}
// Start search
MazeNode currentNode;
distToStart[startNode.Identifier] = 0;
int count = 0;
bool endFound = false;
while (!endFound)
{
// Set current unvisited node based on distance to start
int currentNodeInd = -1;
float lastDist = float.PositiveInfinity;
for (int i = 0; i < mazeFrame.Nodes.Count; i++)
{
if (!isVisited[mazeFrame.Nodes[i].Identifier])
{
float currDist = distToStart[mazeFrame.Nodes[i].Identifier];
if (currDist <= lastDist)
{
currentNodeInd = i; lastDist = currDist;
}
}
}
currentNode = mazeFrame.Nodes[currentNodeInd];
// Find unvisited neighbors of current node
List <MazeNode> unvisitedNeighbors = new List <MazeNode>();
foreach (MazeNode nb in currentNode.ConnectedNeighbors)
{
if (isVisited[nb.Identifier] == false)
{
unvisitedNeighbors.Add(nb);
}
}
// For each neighbor, set distToStart as min of (currentNode disttostart + dist to current) and neighbor disttostart
foreach (MazeNode nb in unvisitedNeighbors)
{
// Distance in case of non-equidistant nodes
//float distToCurrentNode = Vector3.Distance(currentNode.position, nb.position);
// Distance in case of equidistant nodes
float distToCurrentNode = 1;
// Update neighbor
distToStart[nb.Identifier] = Mathf.Min((distToStart[currentNode.Identifier] + distToCurrentNode), distToStart[nb.Identifier]);
}
// Set current node to visisted
isVisited[currentNode.Identifier] = true;
// end reached?
endFound |= currentNode == endNode;
// Safety check
count++;
if (count > mazeFrame.Nodes.Count)
{
throw new System.Exception("Finding shortest path loop did not terminate correctly.");
}
}
// Store shortest path length in maze frame now that we know it
int shortestPathLength = (int)distToStart[endNode.Identifier];
// Backtrack along distToStart and label each node as being on the shortest path
currentNode = endNode;
onShortestPath[currentNode.Identifier] = true;
count = 0;
while (currentNode != startNode)
{
// Find neighbor with shortest distance to start
MazeNode nextNodeOnPath = currentNode;
foreach (MazeNode nb in currentNode.ConnectedNeighbors)
{
if (nb.IsActive && distToStart[nb.Identifier] < distToStart[nextNodeOnPath.Identifier]) // There is ALWAYS a node closer than the current one
{
nextNodeOnPath = nb;
}
}
// Update and continue
currentNode = nextNodeOnPath;
onShortestPath[currentNode.Identifier] = true;
// Safety check
count++;
if (count > mazeFrame.Nodes.Count)
{
throw new System.Exception("Finding shortest path loop did not terminate correctly.");
}
}
/* Label each node as onLoop/onDeadEnd/notConnectedToPath as follows:
*
* 1) Find all nodes that are adjacent to the path
* 2) For each of these:
* 3) Create stack to keep unlabeled nodes, and set allLabeled flag
* 4) While !allLabeled
* 5) Create list of unlabeled neighbors of current node that are not on the stack
* 6) If current node has 1+ unlabeled neighbors --> explore
* 7) Add current node to stack and set an unlabeled neighbor not on the stack as current node
* 8) If current node has 0 unlabeled neighbors not on the stack --> label and backtrack
* 9) If current node has only 1 connected neighbor --> onDeadEnd
* 10) If more than one connected neighbors, and one was onLoop --> onLoop
* 11) If more than one connected neighbors, and one of them was onShortestPath (or two if at seed node) --> onLoop (loop connection found!)
* 12) If more than one connected neighbors, and no onLoop/onShortestPath --> onDeadEnd (backtracking from only dead ends)
* 13) If stack is not empty, pop node and set as current node, go to 5)
* 14) If stack is empty, all nodes are labeled, set allLabeled to true;
*
* 15) Set all junctions by finding all nodes adjacent to onDeadEnd/onLoop, and set them likewise.
* 16) Set all unlabeled nodes to notConnectedToPath
*/
// First, find unlabeled nodes that are connected to the path (1)
List <MazeNode> unlabeledSeedNode = new List <MazeNode>();
for (int i = 0; i < mazeFrame.Nodes.Count; i++)
{
if (mazeFrame.Nodes[i].IsActive && !onShortestPath[mazeFrame.Nodes[i].Identifier])
{
foreach (MazeNode nb in mazeFrame.Nodes[i].ConnectedNeighbors)
{
if (nb.IsActive && onShortestPath[nb.Identifier])
{
unlabeledSeedNode.Add(mazeFrame.Nodes[i]); break;
}
}
}
}
// Start the search (2)
for (int inode = 0; inode < unlabeledSeedNode.Count; inode++)
{
// set seed node
MazeNode seedNode = unlabeledSeedNode[inode];
if (onDeadEnd[seedNode.Identifier] || onLoop[seedNode.Identifier]) // check whether node was touched from a previous cycle below
{
continue;
}
// Create stack for to be labeled nodes
Stack <MazeNode> nodesToLabel = new Stack <MazeNode>(); // FIXME should I initialize with conservative estimate?
// Search from the starting node until the stack is empty (all are labeled) (4)
count = 0;
currentNode = seedNode;
bool allLabeled = false;
while (!allLabeled)
{
// Parse current neighbors
List <MazeNode> unlabeledNeighborsNotOnStack = new List <MazeNode>();
bool hasOnShortestPath = false;
bool hasOnLoop = false;
int shortestPathCount = 0;
foreach (MazeNode nb in currentNode.ConnectedNeighbors)
{
if (nb.IsActive)
{
if (onShortestPath[nb.Identifier])
{
shortestPathCount++;
}
else if (onLoop[nb.Identifier])
{
hasOnLoop = true;
}
else if (onDeadEnd[nb.Identifier])
{
}
else
{
if (!nodesToLabel.Contains(nb))
{
unlabeledNeighborsNotOnStack.Add(nb);
}
}
}
}
// If we're at the seed node, the first onShortestPath node is ignored (it's the hook), otherwise any one is fine
if (currentNode == seedNode)
{
hasOnShortestPath = shortestPathCount > 1;
}
else
{
hasOnShortestPath = shortestPathCount > 0;
}
// Move forward or label and backtrack
// If current node has an unlabeled node not on the stack --> explore (6)
if (unlabeledNeighborsNotOnStack.Count > 0)
{
// Add current node to stack and set first neighbor not on stack (order doesn't matter) as current node
foreach (MazeNode nb in unlabeledNeighborsNotOnStack)
{
nodesToLabel.Push(currentNode);
currentNode = nb;
break;
}
}
else
// If there are no more unlabeled nodes that are not on the stack, we can label and backtrack
{
int activeConnectedNeighborsCount = 0;
foreach (MazeNode nb in currentNode.ConnectedNeighbors)
{
if (nb.IsActive)
{
activeConnectedNeighborsCount++;
}
}
if (activeConnectedNeighborsCount <= 1) // easiest case
{
onDeadEnd[currentNode.Identifier] = true;
}
else if (hasOnLoop || (hasOnShortestPath && currentNode != seedNode))
{
onLoop[currentNode.Identifier] = true;
}
else
{
onDeadEnd[currentNode.Identifier] = true;
}
// Backtrack if there are still unlabeled, otherwise end
if (nodesToLabel.Count != 0)
{
currentNode = nodesToLabel.Pop();
}
else
{
allLabeled = true;
}
}
// Safety check
count++;
if (count > mazeFrame.Nodes.Count * 2)
{
throw new System.Exception("Labeling nodes loop did not terminate correctly.");
}
}
}
// Set junctions
// onDeadEnd junctions
List <MazeNode> nodesNeighboringOnDeadEnd = new List <MazeNode>();
List <MazeNode> nodesNeighboringOnLoop = new List <MazeNode>();
for (int i = 0; i < mazeFrame.Nodes.Count; i++)
{
if (!mazeFrame.Nodes[i].IsActive)
{
continue;
}
// Every node neighboring an onDeadEnd is a junction for a dead ending path
foreach (MazeNode nb in mazeFrame.Nodes[i].ConnectedNeighbors)
{
if (nb.IsActive && onDeadEnd[nb.Identifier])
{
nodesNeighboringOnDeadEnd.Add(mazeFrame.Nodes[i]); break;
}
}
// Only nodes that are onShortestPath neighboring an onLoop can be an onLoop junction
if (onShortestPath[mazeFrame.Nodes[i].Identifier])
{
foreach (MazeNode nb in mazeFrame.Nodes[i].ConnectedNeighbors)
{
if (nb.IsActive && onLoop[nb.Identifier])
{
nodesNeighboringOnLoop.Add(mazeFrame.Nodes[i]); break;
}
}
}
}
foreach (MazeNode nd in nodesNeighboringOnDeadEnd)
{
onDeadEnd[nd.Identifier] = true;
}
foreach (MazeNode nd in nodesNeighboringOnLoop)
{
onLoop[nd.Identifier] = true;
}
// Find remaining nodes, and label them as notConnectedToPath
foreach (MazeNode nd in mazeFrame.Nodes)
{
if (nd.IsActive && !onShortestPath[nd.Identifier] && !onLoop[nd.Identifier] && !onDeadEnd[nd.Identifier])
{
notConnectedToPath[nd.Identifier] = true;
}
}
// Assign elements to maze frame
int shortestPathInd = 0;
bool indNotFound = true;
while (indNotFound)
{
if (mazeFrame.ShortestPathInd.Contains(shortestPathInd))
{
shortestPathInd++;
}
else
{
indNotFound = false;
}
}
mazeFrame.SetShortestPathLength(shortestPathLength, shortestPathInd);
mazeFrame.SetOnShortestPath(onShortestPath, shortestPathInd);
mazeFrame.SetOnDeadEnd(onDeadEnd);
mazeFrame.SetOnLoop(onLoop);
mazeFrame.SetNotConnectedToPath(notConnectedToPath);
}
