In the discussion of Dijkstra’s algorithm in Section 19.4, it is asserted that at each iteration, a new node is added to T and that the least-cost path for that new node passes only through nodes already in T. Demonstrate that this is true. Hint: Begin at the beginning. Show that the first node added to T must have a direct link to the source node. Then show that the second node to T must either have a direct link to the source node or a direct link to the first node added to T, and so on. Remember that all link costs are assumed nonnegative.