write program in C++ for the givien instruction using the execution table the pr

Question

write program in C++ for the givien instruction using the execution table the program should display the graph.

instructions: You implement the small label first algorithm. For a particular graph and a starting vertex, your program should display this graph and show shortest distances to each vertex from the starting point.

eRender.jpg Section 8.3 Shortest Paths 405 GURE 8.10 8.10 Anexecution of labelcorrectingalgorithm(), which apo which applies a deque. active vertex deque d g d h d 0o 1 1 0 01 9 o 00000 071 1

Explanation / Answer

// A C / C++ program for Dijkstra's single source shortest path algorithm.
// The program is for adjacency matrix representation of the graph

#include <stdio.h>
#include <limits.h>
#include <bits/stdc++.h>
using namespace std;
// Number of vertices in the graph
#define V 100

// A utility function to find the vertex with minimum distance value, from
// the set of vertices not yet included in shortest path tree
int minDistance(int dist[], bool sptSet[])
{
   // Initialize min value
   int min = INT_MAX, min_index;

   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
int printSolution(int dist[], int n)
{
   printf("Vertex   Distance from Sourcen");
   for (int i = 0; i < V; i++)
      printf("%d tt %dn", i, dist[i]);
}

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

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

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

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

// driver program to test above function
int main()
{
   /* Let us create the example graph discussed above */
   int distance,v;
   char x,y;
   cout<<"Enter the no of vertex: ";
   cin>>v;
   int graph[v][v];
   for(int i=0;i<v;i++)
    for (int j= 0; j< v; j++)
    {
        cout<<"Enter distance between "<<i<<" and "<<j<<": ";
        cin>>graph[i][j];
    }
  
       dijkstra(graph, 0);
  

    return 0;
}

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