Merge pull request #27 from SAchu47/beta

Dijkstra's Algorithm with Priority Queue

Algorithms/Graph Algorithms/Dijkstra_priority_queue.cpp

@@ -0,0 +1,85 @@
+// Program to find Dijkstra's shortest path using priority_queue with vectors 
+#include<bits/stdc++.h> 
+using namespace std; 
+# define INF 0x3f3f3f3f 
+
+// iPair ==> Integer Pair 
+typedef pair<int, int> iPair; 
+
+// To add an edge 
+void addEdge(vector <pair<int, int> > adj[], int u, int v, int wt) 
+{ 
+	adj[u].push_back(make_pair(v, wt)); 
+	adj[v].push_back(make_pair(u, wt)); 
+} 
+
+
+// Prints shortest paths from src to all other vertices 
+void shortestPath(vector<pair<int,int> > adj[], int V, int src) 
+{ 
+	// Create a priority queue to store vertices that are being preprocessed.  
+	priority_queue< iPair, vector <iPair> , greater<iPair> > pq; 
+
+	// Create a vector for distances and initialize all distances as infinite (INF) 
+	vector<int> dist(V, INF); 
+
+	// Insert source itself in priority queue and initialize its distance as 0. 
+	pq.push(make_pair(0, src)); 
+	dist[src] = 0; 
+
+	// Looping till priority queue becomes empty 
+	while (!pq.empty()) 
+	{ 
+		// The first vertex in pair is the minimum distance vertex, extract it from priority queue. Vertex label is stored in second of pair. 
+		int u = pq.top().second; 
+		pq.pop(); 
+
+		// Get all adjacent of u. 
+		for (auto x : adj[u]) 
+		{ 
+			// Get vertex label and weight of current adjacent of u. 
+			int v = x.first; 
+			int weight = x.second; 
+
+			// If there is shorted path to v through u. 
+			if (dist[v] > dist[u] + weight) 
+			{ 
+				// Updating distance of v 
+				dist[v] = dist[u] + weight; 
+				pq.push(make_pair(dist[v], v)); 
+			} 
+		} 
+	} 
+
+	// Print shortest distances stored in dist[] 
+	printf("Vertex          Distance from Source\n"); 
+	for (int i = 0; i < V; ++i) 
+		printf("%d \t\t %d\n", i, dist[i]); 
+} 
+
+// Driver program
+int main() 
+{ 
+	int V = 9; 
+	vector<iPair > adj[V]; 
+
+	// making above shown graph 
+	addEdge(adj, 0, 1, 4); 
+	addEdge(adj, 0, 7, 8); 
+	addEdge(adj, 1, 2, 8); 
+	addEdge(adj, 1, 7, 11); 
+	addEdge(adj, 2, 3, 7); 
+	addEdge(adj, 2, 8, 2); 
+	addEdge(adj, 2, 5, 4); 
+	addEdge(adj, 3, 4, 9); 
+	addEdge(adj, 3, 5, 14); 
+	addEdge(adj, 4, 5, 10); 
+	addEdge(adj, 5, 6, 2); 
+	addEdge(adj, 6, 7, 1); 
+	addEdge(adj, 6, 8, 6); 
+	addEdge(adj, 7, 8, 7); 
+
+	shortestPath(adj, V, 0); 
+
+	return 0; 
+}