/// <summary>
/// Uses Prim's algorithm to build an MST spanning the mstNodes.
/// O(|mstNodes|^2) runtime.
/// </summary>
/// <param name="startFrom">A GraphNode to start from.</param>
public void Span(GraphNode startFrom)
{
var adjacentEdgeQueue = new LinkedListPriorityQueue <LinkedGraphEdge>(100);
var startIndex = startFrom.DistancesIndex;
// All nodes that are not yet included.
var toAdd = new List <int>(_mstNodes.Count);
// If the index node is already included.
var inMst = new bool[_distances.CacheSize];
// The spanning edges.
var mstEdges = new List <GraphEdge>(_mstNodes.Count);
for (var i = 0; i < _mstNodes.Count; i++)
{
var index = _mstNodes[i].DistancesIndex;
if (index != startIndex)
{
toAdd.Add(index);
var adjacentEdge = new LinkedGraphEdge(startIndex, index);
adjacentEdgeQueue.Enqueue(adjacentEdge, _distances[startIndex, index]);
}
}
inMst[startIndex] = true;
while (toAdd.Count > 0 && adjacentEdgeQueue.Count > 0)
{
int newIn;
LinkedGraphEdge shortestEdge;
// Dequeue and ignore edges that are already inside the MST.
// Add the first one that is not.
do
{
shortestEdge = adjacentEdgeQueue.Dequeue();
newIn = shortestEdge.Outside;
} while (inMst[newIn]);
mstEdges.Add(new GraphEdge(
_distances.IndexToNode(shortestEdge.Inside),
_distances.IndexToNode(shortestEdge.Outside)));
inMst[newIn] = true;
// Find all newly adjacent edges and enqueue them.
for (var i = 0; i < toAdd.Count; i++)
{
var otherNode = toAdd[i];
if (otherNode == newIn)
{
toAdd.RemoveAt(i--);
}
else
{
var edge = new LinkedGraphEdge(newIn, otherNode);
adjacentEdgeQueue.Enqueue(edge, _distances[newIn, otherNode]);
}
}
}
SpanningEdges = mstEdges;
IsSpanned = true;
}
public void TestMST()
{
// 0 -- 1 -- 2 -- 3
// \ | /
// \ | /
// 4 -- 5 -- 6 -- 7
bool[,] graph1 = {
{ false, true, false, false, true, false, false, false },
{ true, false, true, false, false, false, false, false },
{ false, true, false, true, false, true, false, false },
{ false, false, true, false, false, true, false, false },
{ true, false, false, false, false, true, false, false },
{ false, false, true, true, true, false, true, false },
{ false, false, false, false, false, true, false, true },
{ false, false, false, false, false, false, true, false },
};
SearchGraph searchGraph1 = SearchGraphFromData(graph1);
Dictionary<int, GraphNode> graphNodes1 = GetGraphNodesIdIndex(searchGraph1);
var mstNodes1 = new List<GraphNode>
{ graphNodes1[3], graphNodes1[5], graphNodes1[7], graphNodes1[0] };
var distances = new DistanceLookup(mstNodes1);
var mst1 = new MinimalSpanningTree(mstNodes1.Select(n => n.DistancesIndex).ToList(), distances);
mst1.Span(graphNodes1[0].DistancesIndex);
Assert.AreEqual(3, mst1.SpanningEdges.Count, "Wrong amount of spanning edges");
var goalEdges = new[]
{
new []{0, 5}, new []{5, 3}, new []{5, 7}
};
foreach (var edge in goalEdges)
{
Assert.AreEqual(1,
mst1.SpanningEdges.Select(e => new Tuple<ushort, ushort>(distances.IndexToNode(e.Inside).Id, distances.IndexToNode(e.Outside).Id)).Count(
t =>
(t.Item1 == edge[0] && t.Item2 == edge[1]) ||
(t.Item1 == edge[1] && t.Item2 == edge[0])),
"Edge " + edge + " not contained exactly once.");
}
}
