Dijkstra's single source shortest path

Like Prim’s MST, generate a SPT (shortest path tree) with a given source as a root.
 Maintain two sets, one set contains vertices included in the shortest-path tree, other set includes vertices not yet included in the shortest-path tree.
 At every step of the algorithm, find a vertex that is in the other set (set not yet included) and has a minimum distance from the source.

Author: prasantraj0808

Graph_Algorithms/Dijkstra's single source shortest path

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+// C++ program for Dijkstra's single source shortest path
+// algorithm. The program is for adjacency matrix
+// representation of the graph
+/*
+  Description
+
+  //Like Prim’s MST, generate a SPT (shortest path tree) with a given source as a root.
+  //Maintain two sets, one set contains vertices included in the shortest-path tree, other set includes vertices not yet included in the shortest-path tree.
+  //At every step of the algorithm, find a vertex that is in the other set (set not yet included) and has a minimum distance from the source.
+*/
+#include <iostream>
+using namespace std;
+#include <limits.h>
+
+// Number of vertices in the graph
+#define V 9
+
+// A utility function to find the vertex with minimum
+// distance value, from the set of vertices not yet included
+// in shortest path tree
+int minDistance(int dist[], bool sptSet[])
+{
+
+	// Initialize min value
+	int min = INT_MAX, min_index;
+
+	for (int v = 0; v < V; v++)
+		if (sptSet[v] == false && dist[v] <= min)
+			min = dist[v], min_index = v;
+
+	return min_index;
+}
+
+// A utility function to print the constructed distance
+// array
+void printSolution(int dist[])
+{
+	cout << "Vertex \t Distance from Source" << endl;
+	for (int i = 0; i < V; i++)
+		cout << i << " \t\t\t\t" << dist[i] << endl;
+}
+
+// Function that implements Dijkstra's single source
+// shortest path algorithm for a graph represented using
+// adjacency matrix representation
+void dijkstra(int graph[V][V], int src)
+{
+	int dist[V]; // The output array. dist[i] will hold the
+				// shortest
+	// distance from src to i
+
+	bool sptSet[V]; // sptSet[i] will be true if vertex i is
+					// included in shortest
+	// path tree or shortest distance from src to i is
+	// finalized
+
+	// Initialize all distances as INFINITE and stpSet[] as
+	// false
+	for (int i = 0; i < V; i++)
+		dist[i] = INT_MAX, sptSet[i] = false;
+
+	// Distance of source vertex from itself is always 0
+	dist[src] = 0;
+
+	// Find shortest path for all vertices
+	for (int count = 0; count < V - 1; count++) {
+		// Pick the minimum distance vertex from the set of
+		// vertices not yet processed. u is always equal to
+		// src in the first iteration.
+		int u = minDistance(dist, sptSet);
+
+		// Mark the picked vertex as processed
+		sptSet[u] = true;
+
+		// Update dist value of the adjacent vertices of the
+		// picked vertex.
+		for (int v = 0; v < V; v++)
+
+			// Update dist[v] only if is not in sptSet,
+			// there is an edge from u to v, and total
+			// weight of path from src to v through u is
+			// smaller than current value of dist[v]
+			if (!sptSet[v] && graph[u][v]
+				&& dist[u] != INT_MAX
+				&& dist[u] + graph[u][v] < dist[v])
+				dist[v] = dist[u] + graph[u][v];
+	}
+
+	// print the constructed distance array
+	printSolution(dist);
+}
+
+// driver's code
+int main()
+{
+
+	/* Let us create the example graph discussed above */
+	int graph[V][V] = { { 0, 4, 0, 0, 0, 0, 0, 8, 0 },
+						{ 4, 0, 8, 0, 0, 0, 0, 11, 0 },
+						{ 0, 8, 0, 7, 0, 4, 0, 0, 2 },
+						{ 0, 0, 7, 0, 9, 14, 0, 0, 0 },
+						{ 0, 0, 0, 9, 0, 10, 0, 0, 0 },
+						{ 0, 0, 4, 14, 10, 0, 2, 0, 0 },
+						{ 0, 0, 0, 0, 0, 2, 0, 1, 6 },
+						{ 8, 11, 0, 0, 0, 0, 1, 0, 7 },
+						{ 0, 0, 2, 0, 0, 0, 6, 7, 0 } };
+
+	// Function call
+	dijkstra(graph, 0);
+
+	return 0;
+}
+
+//Time Complexity: O(V2)
+//Auxiliary Space: O(V)