Suppose P, Q, R, S, T are sorted sequences having lengths 20, 24, 30, 35, 50 respectively. They are to be merged into a single sequence by merging together two sequences at a time. The number of comparisons that will be needed in the worst case by the optimal algorithm for doing this is ____.

The number of distinct minimum spanning trees for the weighted graph below is ________

Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which one will be reported by Dijkstra’s shortest path algorithm? Assume that, in any iteration, the shortest path to a vertex v is updated only when a strictly shorter path to v is discovered.

An undirected graph G(V, E) contains n ( n > 2 ) nodes named v₁ , v₂ ,….v_n. Two nodes v_i , v_j are connected if and only if 0 < |i – j| <= 2. Each edge (v_i, v_j ) is assigned a weight i + j. A sample graph with n = 4 is shown below. The length of the path from v5 to v6 in the MST of previous question with n = 10 is