Prims Minimum Spanning Tree

Greedy Algorithms/Prims Minimum Spanning Tree.cpp

@@ -1,98 +1,82 @@
-// A C / C++ program for Prim's Minimum Spanning Tree (MST) algorithm. 
+#include <iostream>
-// The program is for adjacency matrix representation of the graph
+using namespace std;
 
-#include <stdio.h>
-#include <limits.h>
-
-// Number of vertices in the graph
 #define V 4
+#define INFINITY 99999
 
-// A utility function to find the vertex with minimum key value, from
-// the set of vertices not yet included in MST
-int minKey(int key[], bool mstSet[])
-{
-// Initialize min value
-int min = INT_MAX, min_index;
-
-for (int v = 0; v < V; v++)
-	if (mstSet[v] == false && key[v] < min)
-		min = key[v], min_index = v;
-
-return min_index;
-}
-
-// A utility function to print the constructed MST stored in parent[]
-int printMST(int parent[], int n, int graph[V][V])
-{
-printf("Edge Weight\n");
-for (int i = 1; i < V; i++)
-	printf("%d - %d %d \n", parent[i], i, graph[i][parent[i]]);
-}
-
-// Function to construct and print MST for a graph represented using adjacency
-// matrix representation
-void primMST(int graph[V][V])
-{
-	int parent[V]; // Array to store constructed MST
-	int key[V]; // Key values used to pick minimum weight edge in cut
-	bool mstSet[V]; // To represent set of vertices not yet included in MST
-
-	// Initialize all keys as INFINITE
-	for (int i = 0; i < V; i++)
-		key[i] = INT_MAX, mstSet[i] = false;
-
-	// Always include first 1st vertex in MST.
-	key[0] = 0;	 // Make key 0 so that this vertex is picked as first vertex
-	parent[0] = -1; // First node is always root of MST 
-
-	// The MST will have V vertices
-	for (int count = 0; count < V-1; count++)
-	{
-		// Pick the minimum key vertex from the set of vertices
-		// not yet included in MST
-		int u = minKey(key, mstSet);
-
-		// Add the picked vertex to the MST Set
-		mstSet[u] = true;
-
-		// Update key value and parent index of the adjacent vertices of
-		// the picked vertex. Consider only those vertices which are not yet
-		// included in MST
-		for (int v = 0; v < V; v++)
-
-		// graph[u][v] is non zero only for adjacent vertices of m
-		// mstSet[v] is false for vertices not yet included in MST
-		// Update the key only if graph[u][v] is smaller than key[v]
-		if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v])
-			parent[v] = u, key[v] = graph[u][v];
-	}
-
-	// print the constructed MST
-	printMST(parent, V, graph);
-}
-
-
-// driver program to test above function
-int main()
-{
-/* Let us create the following graph
-		2 3
-	(0)--(1)--(2)
-	| / \ |
-	6| 8/ \5 |7
-	| /	 \ |
-	(3)-------(4)
-			9		 */
 int graph[V][V] = {
-	{0, 2, 1, 2},
+	{0, 5, 1, 2},
-	{2, 0, 3, 3},
+	{5, 0, 3, 3},
 	{1, 3, 0, 4},
 	{2, 3, 4, 0}
 };
 
 
-	// Print the solution
+struct mst
-	primMST(graph);
+{
+	bool visited;
+	int key;
+	int near;
+};
 
+mst MST_Array[V];
+
+void initilize()
+{
+	for (int i = 0; i < V; i++)
+	{
+		MST_Array[i].visited=false;
+		MST_Array[i].key=INFINITY;		// considering INFINITY as inifinity
+		MST_Array[i].near=i;
+	}
+
+	MST_Array[0].key=0;
+}
+
+void updateNear()
+{
+	for (int v = 0; v < V; v++)
+	{
+		int min=INFINITY;
+		int minIndex=0;
+		for (int i = 0; i < V; i++)
+		{
+			if (MST_Array[i].key<min && MST_Array[i].visited==false && MST_Array[i].key!=INFINITY)
+			{
+				min=MST_Array[i].key;
+				minIndex=i;
+			}
+		}
+	
+		MST_Array[minIndex].visited=true;
+	
+		for (int i = 0; i < V; i++)
+		{
+			if (graph[minIndex][i]!=0 && graph[minIndex][i]<INFINITY)
+			{
+				if (graph[minIndex][i]<MST_Array[i].key)
+				{
+					MST_Array[i].key=graph[minIndex][i];
+					MST_Array[i].near=minIndex;
+				}
+			}
+		}
+	}
+}
+
+void show()
+{
+	for (int i = 0; i < V; i++)
+	{
+		cout<<i<<"  -  "<<MST_Array[i].near<<"\t"<<graph[i][MST_Array[i].near]<<"\n";
+	}
+}
+
+
+int main()
+{
+	initilize();
+	updateNear();
+	show();
 	return 0;
 }