title: Time complexity of A* and Dijsktra's search
body: <p>In a grid based environment, the number of edges E = O(V).</p>
  <p>A* would, in the worst case, explore all the nodes of the grid.
  So, number of nodes in open list would be E in the worst case.
  Therefore, A's time complexity in worst case is O(E).</p>
  <p>Now, as we know that Dijsktra's time complexity is O(E + VlogV).
  And A* in worst case would explore same number of nodes as Dijkstra would explore.</p>
  <p>Thus, the time complexity of A* should have been equal to Dijkstra = O(E).
  But we have VlogV term extra in Dijkstra.</p>
  <p>What am I missing here? I request for a detailed explanation.</p>
  <p>Thanks in advance.</p>