Question

Dijkstra’s Algorithm: You have to implement the Dijkstra’s algorithm and apply it on the graph provided below.

You have to take the input from the user as an adjacency matrix representing the graph, the source, the destination. Then you have to apply the Dijkstra’s algorithm to find the shortest path from the source and the destination, and  find the shortest route between the source and the destination.

For the input you have to read it from a file. It will have the number of nodes and the adjacency matrix as given below. The source and the destination can be given as an input as a command line

For the distance not known or for distance from a node to itself can represented as ∞ as shown above.

you can do it in any programming language but please type the code do not write on paper and code must be working

N=5 A B C DE

Answer 1

The following code has been run in "Eclipse". Just save the java file with "ShortestPath.java" and compile and run.

1// A Java program for Dijkstra's single source shortest path algorithm 2 // The program is for adjacency matrix representation of the graph 3import java.util.*; 4 import java.lang.*; 5 import java.io.*; 7 8 public class ShortestPath 9 10 // A utility function to find the vertex with minimum distance value, // from the set of vertices not yet included in shortest path tree static final int V-5; 12 13 int minDistance(int dist[], Boolean sptSet[]) 14 // Initialize min value int min = Integer.MAX VALUE, min-index--1; 17 for (int v-0; v< V; v++) if (sptSet [y] == false && dist[v] <= min) 19 20 21 min -dist[v]; min-index v; 25 26 return min_index; // A utility function to print the constructed distance array 29 void printSolution(int dist[], int n) 30 31 32 System.out.println( "Vertex Distance from Source") for (int 1-0; i < v; i++) System.out.println(i+" tt "+dist[i]); 34 35 36 37 38 // Funtion that implements Dijkstra's single source shortest path // algorithm for a graph represented using adjacency matrix // representation

39 void dijkstra(int graph[][], int src) 40 41 42 int dist[] = new int [V]; // The output array" dist[i] will hold // the shortest distance from scs to i // sptset[i] will true if vertex i is included in shortest // path tree or shortest distance from scs to i is finalized Boolean sptSet[]new Boolean[V]; 45 46 // Initialize all distances as INFINITE and stpSet[] as false for (int i-0; i< V; i++) 48 49 50 dist[i] = Integer . MAX VALUE; sptset[i]-false; 52 54 // Distance of source vertex from itself is always dist[src]-0; 56 // Find shortest path for all vertices for (int count - count < V-1; count++) 58 59 60 // Pick the minimum distance vertex from the set of vertices // not yet processed. u is always equal to scc in first // iteration int u - minDistance(dist, sptSet); 62 63 64 65 // Mark the picked vertex as processed sptSet [u] = true; 68 69 70 71 72 73 74 75 76 /1 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 scc to II v through u is smaller than current value of dist[v] if (!sptset[v] && graph[u][v]0 &&

dist[u] Integer.MAX VALUE && dist[u]+graph[u][v] < dist[v]) 78 79 80 81 82 83 84 85 86 87 public static void main (String[] args) dist[v] - dist[u] graph [u][v]; // print the constructed distance array printSolution(dist, V); // Driver method /* Let us create the example graph discussed above*/ 89 90 91 92 93 94 95 96 97 98 int graph[]new int[][1tfo, 2, 3, 0, ej (2, 0, 4, 0, 3), 13, 0, 0, 2, 0}, [o, 3, 0, 1, »}, ShortestPath tnew ShortestPath); t.dijkstra(graph, e),; 100

OUTPUT:

E-Problems @ Javadoc G Declaration Console terminateds ShortestPath lava Application] CAProgram Files Javaljire1.3.0 181\binljavaw.exe (05-May-2019, 2:29.48 PM Vertex Distance from Source 0 tt 0 1 tt 2 2 tt 3 3 tt 5 4 tt 5