// The Function That Calculates The Minimum Spanning Tree For The Graph
// Its Only Parameter Is The List Of Distinct Colors
public void MinSpanningTree(List <RGBPixel> LoD)
{
// Using A Priority Queue So That The Edges Are
// Sorted According To Their Weights In Ascending Order
// The Priority Queue Contains The Number Of Vertices (LoD.Count)
FastPriorityQueue <PQNode> PQ = new FastPriorityQueue <PQNode>(LoD.Count);
// An Array That Contains Each Node (color)
// And A Pointer To That Node's Parent
PQNode[] PQNode = new PQNode[LoD.Count];
// Initialising The First Node In The Array
// Its Parent Is Null
PQNode[0] = new PQNode(LoD[0], null);
// Inserting That First Node Into The Priority Queue
// With A Value of 0
PQ.Enqueue(PQNode[0], 0);
float weight;
// For Each Vertex (Minus The Already Added One),
// Insert That Vertex Into The Array
// With Parent = null, Then Insert It Into The PQ
// With Values = Infinity
for (int i = 1; i < LoD.Count; i++)
{
PQNode[i] = new PQNode(LoD[i], null);
PQ.Enqueue(PQNode[i], int.MaxValue);
}
// Looping Until The Priority Queue Is Empty
while (PQ.Count != 0)
{
// Dequeuing The First (Minimum) Element
// From The PQ
PQNode Minimum = PQ.Dequeue();
// Checking If The Minimum Element Is The Root Node Or Not
// (Only The Root Node Has A Null Parent In The First Iteration)
if (Minimum.Parent != null)
{
Edge edge;
edge.src = Minimum.currentVertex;
edge.dest = (RGBPixel)Minimum.Parent;
edge.weight = (Minimum.currentWeight);
MST.Add(edge); // Add the minimum weight to the MST.
MSTSum += edge.weight; // Add The Edge's Weight To The MST Sum
}
// We Have To Modify The Values Of The PQ
// Each Time
foreach (var node in PQ)
{
// Calculating The Weight Difference Between The Current Node
// And The Minimum Node
weight = WeightDifference(node, Minimum);
// If That Weight Difference Is Less Than The Node's Current Weight
// Then The Minimum Node Becomes The Parent Of That Node
// And We Adjust That Node's Weight To The Weight Difference
// By Updating The PQ
if (weight < node.currentWeight)
{
node.Parent = Minimum.currentVertex;
PQ.UpdatePriority(node, weight);
}
}
}
}
} //get_distincit
public static void grph(int CLUS)// graph construction and getting edges that will be cut that take number of clusters
{
/*
* Total complexty = O (E log (k))
* --where E is the number of edges and K is the number of clusters wanted to cut
*/
float min = 10000000, newedge;
//min is minimum value that take from moving from exesting node to another node, newedge is edge between exesting node to another node
int k = 0, count = nodes.Count; //k is the index of minimum node that i would start in next time
bool[] vstd = new bool[16777216]; //to check if node has been visited before (get values between it and all another none visited nodes)
VX = new Dictionary <GRAPH, float>(); // initialize th helper of periority_queue
H = new FastPriorityQueue <GRAPH>(CLUS - 1); //initialize periority_queue
for (int i = k; ;) //first loop to move in distincit node
{
bool ch = false; // if it still false then i can't go anywhere because all nodes have been visited
if (vstd[nodes[i]])
{
continue; // if the node that i stand in is visited then continue
}
vstd[nodes[i]] = true; //this not is not visited before then make it as visited
min = 10000000; // give minimum every time very large value
for (int j = 0; j < count; j++) //second loop to move in distincit node
{
if (vstd[nodes[j]])
{
continue; //if the node that i stand in is visited then continue
}
ch = true; //then it i found another node to move in
byte[] b = BitConverter.GetBytes(nodes[i]), bb = BitConverter.GetBytes(nodes[j]);
// convert the shifted integer to red and green and blue
newedge = (((b[0] - bb[0]) * (b[0] - bb[0])) + ((b[1] - bb[1]) * (b[1] - bb[1])) + ((b[2] - bb[2]) * (b[2] - bb[2])));
//calculate the edge between to nodes
if (newedge < min) //if the edge i have less than minimum then
{
min = newedge; //make the minimum is newedge
k = j; //and save its index to start from it the next time
}
if (MST[j].edge < min) // if the edge that is already saved is less than minimum then
{
min = MST[j].edge; //make the minimum is saved edge
k = j; //and save its index to start from it the next time
}
if (newedge < (float)MST[j].edge) // if the calculated edge before is larger than the newly calculated edge then
{
MST[j].edge = newedge; //then replace the calculaed edge with the new minimum edge
MST[j].from = nodes[i]; //and change from where it comes
}
}
i = k; //K is the minimum index that i will start the loop with
if (ch == false) // then i cant go to any node again because all nodes have been visited then choose the cutted edges
{
GRAPH T = new GRAPH(); //temp to delete the deleted edge from dictionary as it is deleted from periority_queue
for (int y = 1; y < MST.Count; y++) //move in all Minimum spanning tree
{
if (H.Count < CLUS - 1) // if the periority_queue is not filled with required number of clusters then
{
H.Enqueue(MST[y], MST[y].edge); // add in periority_queue with complexty O(log K) k is the wanted number of clusters
VX.Add(MST[y], MST[y].edge); // add in the dictionary this edge
}
else//if the periority_queue is filled with required number of clusters then
{
if (H.First.edge < MST[y].edge) //check if the edge that i stand is larger than the top of queue that contain the smallest edge
{
T = H.Dequeue(); //pop the smallest from the queue
VX.Remove(T); //remove also this node from dictionary
H.Enqueue(MST[y], MST[y].edge); //enqueue the new large node with the new large edge with complexty O(log K)
VX.Add(MST[y], MST[y].edge); //add the new large node with the new large edge
}
}
}
}
if (!ch)
{
break; //if i can't go anywhere then break
}
}//main loop
/* this to get cost of minimum spanning tree*/
/* double sum = 0;
* for (int i = 1; i < MST.Count; i++)
* {
* sum += Math.Sqrt(MST[i].edge);
* }
* MessageBox.Show(sum.ToString());*/
}