Merge pull request #787 from lucifer2307/sd3

A C++ program for Prim's Minimum Spanning Tree (MST) algorithm. The program is for adjacency matrix representation of the graph

Advanced data structures/Prim’s Minimum.cpp

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+// A C++ program for Prim's Minimum
+// Spanning Tree (MST) algorithm. The program is
+// for adjacency matrix representation of the graph
+#include <bits/stdc++.h>
+using namespace std;
+
+// Number of vertices in the graph
+#define V 5
+
+// 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[]
+void printMST(int parent[], int graph[V][V])
+{
+	cout << "Edge \tWeight\n";
+	for (int i = 1; i < V; i++)
+		cout << parent[i] << " - " << i << " \t"
+			<< graph[i][parent[i]] << " \n";
+}
+
+// Function to construct and print MST for
+// a graph represented using adjacency
+// matrix representation
+void primMST(int graph[V][V])
+{
+	// Array to store constructed MST
+	int parent[V];
+
+	// Key values used to pick minimum weight edge in cut
+	int key[V];
+
+	// To represent set of vertices included in MST
+	bool mstSet[V];
+
+	// 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.
+	// Make key 0 so that this vertex is picked as first
+	// vertex.
+	key[0] = 0;
+	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, graph);
+}
+
+// Driver's code
+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, 0, 6, 0 },
+						{ 2, 0, 3, 8, 5 },
+						{ 0, 3, 0, 0, 7 },
+						{ 6, 8, 0, 0, 9 },
+						{ 0, 5, 7, 9, 0 } };
+
+	// Print the solution
+	primMST(graph);
+
+	return 0;
+}
+
+// This code is contributed by rathbhupendra