Problem Description Implement the shortest path problem usin

Problem Description Implement the shortest path problem using Dijsktra and Bellman-Ford algorithms for the graph below. Program Requirements Following are the requirements for this program: Part is (Dijsktra\'s) Choose V_1 as the source. Find the shortest path from V_1 to every other vertex in the above graph. Print out your shortest path results to all vertices starting at V_1. Part 2: (Bellman-Ford) Change the edge weights of V_2 rightarrow V_3 to \"-2\", V_6 rightarrow V_7 as \"-1\" and V_2 rightarrow V_5 to \"-2\". Find the shor (measured by the number of edges) from V_1 to every other vertex in the graph. Print out your shortest path results to all vertices starting at V_1.

Solution

Implementation of shortest pathn problem using dijkstras algorithm in java

import java.util.*;
import java.lang.*;
import java.io.*;

class ShortestPath
{
    // 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=7;
    int minDistance(int dist[], Boolean sptSet[])
    {
        // Initialize min value
        int min = Integer.MAX_VALUE, min_index=-1;

        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[], int n)
    {
        System.out.println(\"Vertex   Distance from Source\");
        for (int i = 0; i < V; i++)
            System.out.println(i+\" \\t\\t \"+dist[i]);
    }

    // Funtion that implements Dijkstra\'s single source shortest path
    // algorithm for a graph represented using adjacency matrix
    // representation
    void dijkstra(int graph[][], int src)
    {
        int dist[] = new int[V]; // The output array. dist[i] will hold
                                 // the shortest distance from src to i

        // sptSet[i] will true if vertex i is included in shortest
        // path tree or shortest distance from src to i is finalized
        Boolean sptSet[] = new Boolean[V];

        // Initialize all distances as INFINITE and stpSet[] as false
        for (int i = 0; i < V; i++)
        {
            dist[i] = Integer.MAX_VALUE;
            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 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]!=0 &&
                        dist[u] != Integer.MAX_VALUE &&
                        dist[u]+graph[u][v] < dist[v])
                    dist[v] = dist[u] + graph[u][v];
        }

        // print the constructed distance array
        printSolution(dist, V);
    }

    // Driver method
    public static void main (String[] args)
    {
        /*create graph in the form of distance from each vertex to every other vertex(i.e. matrix ))*/
       int graph[][] = new int[][]{{0, 5, 8, 0, 7, 10, 0},
                                  {0, 0, 1, 0, 3, 0, 0},
                                  {0, 0, 0, 6, 0, 0, 0},
                                  {0, 0, 0, 0, 0, 0, 0},
                                  {0, 0, 0, 4, 0, 2, 7},
                                  {0, 0, 0, 0, 0, 0, 3},
                                  {0, 0, 4, 5, 0, 0, 0}
                                 
                                 };
        ShortestPath t = new ShortestPath();
        t.dijkstra(graph, 0);
    }
}
Time Complexity of the implementation is O(V^2).