//Searches through the parents of the passed UnionItems to determine which set it belongs to
public UnionItem FindSet(UnionItem x)
{
if (x != x.parent)
{
x.parent = FindSet(x.parent);
}
return(x.parent);
}
//Sets the parent to link to UnionItems together
public void Link(UnionItem x, UnionItem y)
{
if (x.rank > y.rank)
{
y.parent = x;
}
else
{
x.parent = y;
if (x.rank == y.rank)
{
y.rank++;
}
}
}
//Kruskals algorithm, determines MST by stepping through edges by weight,
//and adding them to the MST if doing so doesn't create a cycle,
//which is determined by which set a vertex belongs to
public void KruskalMST()
{
Edge[] MST = new Edge[numVertices - 1]; //Creates an array to hold our MST, by def contains 1 less than total number of vertices
Edge nextEdge = new Edge(); //Container for our next edge variable
int currentEdgeCount = 0; //Current edge count
int currentEdgeIndex = 0; //The index of the current edge
//Initialize MST array
for (int i = 0; i < numVertices - 1; ++i)
{
MST[i] = new Edge();
}
//Sorts our edges using the native CompareTo method of Edge class
Array.Sort(edges);
//Steps through until MST is complete
while (currentEdgeCount < numVertices - 1)
{
//Sets nextEdge to evaluate
nextEdge = edges[currentEdgeIndex++];
//Determines the set status of each end of the edge
UnionItem x = FindSet(unionItems[nextEdge.source - 1]);
UnionItem y = FindSet(unionItems[nextEdge.destination - 1]);
//Check for cycle, by comparing parents of each node
if (x != y)
{
//If no cycle will be created, add the edge to the MST array, and union the two sets
MST[currentEdgeCount++] = nextEdge;
Union(x, y);
}
}
//Sets our edges array to the newly created MST
edges = MST;
}
//Unions two sets together
public void Union(UnionItem x, UnionItem y)
{
Link(FindSet(x), FindSet(y));
}
//Makes a set containing only the passed UnionItem, setting the parent as itself
public void MakeSet(UnionItem x)
{
x.parent = x;
x.rank = 0;
}