Prims Algo

Greedy Algorithms/Prims Minimum Spanning Tree.cpp

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+// A C / C++ program for Prim's Minimum Spanning Tree (MST) algorithm. 
+// The program is for adjacency matrix representation of the graph
+
+#include <stdio.h>
+#include <limits.h>
+
+// Number of vertices in the graph
+#define V 4
+
+// 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},
+	{2, 0, 3, 3},
+	{1, 3, 0, 4},
+	{2, 3, 4, 0}
+};
+
+
+	// Print the solution
+	primMST(graph);
+
+	return 0;
+}