Write the Dijkstra’s algorithm for single sources shortest path problem

Dijkstra’s algorithm for single sources shortest path:

      1.      Algorithm Shortest Paths (v, cost, dist, n)

      2.      // dis [j],  1<= j <= n, is set to the length of the shortest

      3.      // path from vertex v to vertex j in a digraph G with n

      4.      // vertices. dist [v] is set to zero. G is represented by its

      5.      // cost adjacency matrix cost [1:n, 1:n]

      6.      {

      7.      for (int i=1; i<=n; i++)

      8.      { // Initialize S

      9.      S [i] = false;

   10.   dist [i] = cost [v][i];

   11.   }

   12.   S [v] = true;

   13.   dist [v] = 0.0;        // Put v in S.

   14.   for (num = 2; num < n; num ++)

   15.   {

   16.   // determine n-1 paths from v.

   17.   choose u from among those vertices not

   18.   in S such that dist [u] is minimum;

   19.   S[u] = true; // Put u in S.

   20.   for (w = 1; w <= n; w++)

   21.    // Update distances.

   22.   if ((S[w] = false) && (dist[w] > dist[u] + cost[u][w])) then dist[w] = dist[u] + cost[u][w];

   23.   }

   24.   }