Write pseudo-code to modify Dijkstra algorithm to find the shortest path with the least number of hops. Demonstrate your approach to find that shortest path from vertex 1 to vertex 7 in the following graph. Show your work. 1 1 2 8 1 4 3 3 5 5 4 4

Use Dijkstra's algorithm to construct a shortest path tree starting from vertex_ that includes all vertices in the original graph. Use the format shown in the given table. After filling in the table, draw the resulting shortest path tree in the empty box. 2 6 b fringe list 2 a STEP vertices in tree next edge to add 9 9 1 d с 4 12 2 2 2 f 9 1 h 3 4 5 6 7 8

Improve Luby’s MIS algorithm coded in Python by selecting a vertex at random,finding its neighbors and then finding the vertex with the minimum assignedrandom value to be included in the MIS.

Design an algorithm to find the maximum spanning tree  of any graph with a run time of O(m log m).