dijsktra

Author: jsabherwal

02. Algorithms/05. Graphs/04. Dijkstra/Dijkstra.cpp

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+// Program to find Dijkstra's shortest path using
+// priority_queue in STL
+#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. This is weird syntax in C++.
+	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 (or all
+	distances are not finalized) */
+	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 (it
+		// has to be done this way to keep the vertices
+		// sorted distance (distance must be first item
+		// in 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 to test methods of graph class
+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;
+}