// This Region Contains All The Necessary Functions
// To Implement Prim's Algorithm For
// The Minimum Spanning Tree
#region Spanning Tree Methods
// Used To Calculate The Weight Difference Between Two Nodes
private static float WeightDifference(PQNode N1, PQNode N2)
{
byte red1, green1, blue1;
byte red2, green2, blue2;
// Assigning The RGB Values Of Each Color
red1 = N1.currentVertex.red;
red2 = N2.currentVertex.red;
green1 = N1.currentVertex.green;
green2 = N2.currentVertex.green;
blue1 = N1.currentVertex.blue;
blue2 = N2.currentVertex.blue;
// Calculating The Difference Between Them
return((float)Math.Sqrt((red2 - red1) * (red2 - red1) + (green2 - green1) * (green2 - green1) + (blue2 - blue1) * (blue2 - blue1)));
}
// 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);
}
}
}
}
