Djikstra implementation with file reading in java

Now the closest node for which distance has been finalized is node 4. The shortest distance for node 4 has been finalized. Now, from node 4, we can reach node 1 by traveling less distance. So we will update the distance array value for node 1. The next closest unsettled node is node 5. From node 5, we cannot reach any node by traveling a lesser distance. So no distance value will be updated in this step. Node 1 is chosen as the next closest node. From node 1, the only node whose distance can be updated is node 2.

The next closest node will also be node 2. Now, all the nodes have been visited and the shortest distance has been settled for all of them. The loop will terminate. A major drawback of Dijkstra's algorithm is that it cannot handle negative edge weights. This happens because Dijkstra's algorithm uses a greedy approach.

Whenever the closest node is chosen from the distance array, we mark that node's distance as finalized. We won't ever update that node's distance. This works perfectly fine for positive weights but may give inconsistent solutions for negative edge weights.

Let's consider vertex A as the source. In the first iteration, the distance for B and C is updated. Since C is the closest node, we will mark that node's shortest finalized distance as 5. From C, we cannot reach any other node. Next node B will be chosen as the closest, and the distance for this node is also marked as final. All nodes have been visited and the shortest distance has been finalized, so the algorithm ends.

But we can reach node C via node B by traveling a shorter distance But Dijkstra's algorithm says that the shortest distance from A to C is 5. Let's first take a look at our Graph class. It has a 2-D adjacency matrix , and an integer variable used to store the number of vertices. It also has an addEdge method. We are using a directed graph for our implementation, and so two cells of the adjacency matrix will be updated when adding an edge.

Let's implement Dijkstra's algorithm in Java. We will use a helper method called getClosestVertex to find the closest unvisited node. The code for this method is shown below.

Next, we will implement the main algorithm in a dijkstrasShortestPath method. This method will take a Graph and a source vertex as parameters. It will return a shortest-distance array. For each iteration, we are calculating the distance from the closest node to all the remaining nodes. We are also maintaining two arrays distance and visited so an additional space equal to the number of vertices is required. The space complexity for the above implementation is O V. Dijkstra's algorithm is used to find the shortest distance between the nodes of a graph.

In such a case, there might be multiple routes between the two cities, and the challenge then is to find the shortest one. The algorithm is ubiquitous. For example, it is used in computer networking where it ascertains the shortest path between the source router and other routers in the network. Also, each time we are navigating via google maps, complex algorithms based on Dijkstra are being used to provide us with the best route.

We have been provided with data and some code for a GUI, which generates a map of cities in the US and the different connections between them.

Our goal is to compute for the user, the shortest path between any two cities they select on the map. We need these to create instances of the vertex object, edge object and implement relevant methods in the Dijkstra. The Display. The cityxy. These are the vertices in the graph. The citypairs. Each row represents a vertex of the Graph and the number of vertices is the length of the matrix.

Now a combination of row and column defines an edge between vertices. Now, let us start our Java implementation. We have 2 arrays of size equal to the no of vertex of the graph - one is to store the visited vertex and another one to store the distance from the source vertex to other vertices.

As discussed above, the distance between source vertex to itself is zero and hence the distance array is updated to 0 for the source vertex. Next, find a neighbouring unvisited vertex having a minimum distance from source vertex. To update the distance of neighboring vertex, traverse all the neighbors of this vertex. In the matrix representation, the neighbors of the min vertex are present in the same row.

Hence, iterate each element of the row meaning column-wise for this row and update the distance array. From the second iteration to find the minimum distance, the source vertex is already visited and hence the min distant vertex is calculated from the neighbor vertices of the source vertex.

Once the min distant vertex is calculated again, all the distance of the neighboring vertices from this min distant vertex is calculated and their weight is updated if required based on the above formula. We use Bellman-Ford algorithm to find the shortest paths between nodes that can handle negative edges too. It uses the same concept as that of Dijkstra algorithm but requires more running time than Dijkstra's algorithm. In this article, we discussed about how we can implement Dijkstra algorithm in Java to find the shortest paths between nodes in a graph.

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