// For example, edges like (0, 1, 99), (1, 2, -3) => there's an edge between vertices 0 and 1 and 1 and 2.
// Creating from edges also initializes depths and subtree sizes, because we have to DFS regardless.
public static WeightedRootedTree <int> CreateFromEdges(int vertexCount, int rootID, int[,] edges)
{
var tree = new WeightedRootedTree <int>(vertexCount, rootID);
for (int i = 0; i < vertexCount - 1; ++i)
{
var firstVertex = tree.Vertices[edges[i, 0]];
var secondVertex = tree.Vertices[edges[i, 1]];
int weight = edges[i, 2];
firstVertex.AddNeighbor(secondVertex, weight);
secondVertex.AddNeighbor(firstVertex, weight);
}
// Now we need to wire up the parent-child relationships. We have to DFS just like
// InitializeDepthsAndSubtreeSizes, so we might as well initialize depths & subtree sizes too.
var verticesToVisit = new Stack <WeightedRootedTree <int> .Vertex>();
verticesToVisit.Push(tree.Root);
while (verticesToVisit.Count > 0)
{
var vertex = verticesToVisit.Peek();
// If Depth is null, it's the first time we're visiting the vertex. Visit its children.
if (!vertex.Depth.HasValue)
{
vertex.Depth = 1 + (vertex.Parent?.Depth ?? -1);
foreach (var childEdge in vertex.NeighborEdges.Where(ne => ne.Key != vertex.Parent))
{
childEdge.Key.SetParent(vertex, childEdge.Value);
verticesToVisit.Push(childEdge.Key);
}
}
// At this point, we know all the children have been visited, so we're good to pop.
else
{
verticesToVisit.Pop();
vertex.SubtreeSize = 1 + vertex.Children.Sum(c => c.SubtreeSize);
}
}
tree.HasInitializedDepthsAndSubtreeSizes = true;
return(tree);
}
// E.g. if verticesChildEdges[1] = ((3, 99) (4, -3)), vertices w/ ID 3, 4 are the children of vertex w/ ID 1.
// Creating from explicit children doesn't initialize depths or subtree sizes; do that separately if needed.
public static WeightedRootedTree <int> CreateFromChildren(
int vertexCount, int rootID, List <KeyValuePair <int, int> >[] verticesChildEdges)
{
var tree = new WeightedRootedTree <int>(vertexCount, rootID);
for (int id = 0; id < vertexCount; ++id)
{
if (!verticesChildEdges[id]?.Any() ?? true)
{
continue;
}
var parent = tree.Vertices[id];
foreach (var childEdge in verticesChildEdges[id])
{
tree.Vertices[childEdge.Key].SetParent(parent, childEdge.Value);
}
}
return(tree);
}
internal Vertex(WeightedRootedTree <T> tree, int ID)
{
_tree = tree;
this.ID = ID;
}
