pointer (recall that the parent pointer of the root points to itself if this pass changed the value of any position' parent pointerthen she repeats this processand goes on repeating this process until she makes scan through that does not change any position' parent value show that karen' algorithm is correct and analyze its running time for path of length projects - use an adjacency matrix to implement class supporting simplified graph adt that does not include update methods your class should include constructor method that takes two collections-- collection of vertex elements and collection of pairs of vertex elements--and produces the graph that these two collections represent - implement the simplified graph adt described in project - using the edge list structure - implement the simplified graph adt described in project - using the adjacency list structure - extend the class of project - to support the update methods of the graph adt - design an experimental comparison of repeated dfs traversals versus the floyd-warshall algorithm for computing the transitive closure of directed graph - perform an experimental comparison of two of the minimum spanning tree algorithms discussed in this (kruskal and prim-jarnikdevelop an extensive set of experiments to test the running times of these algorithms using randomly generated graphs - one way to construct maze starts with an grid such that each grid cell is bounded by four unit-length walls we then remove two boundary unit-length wallsto represent the start and finish for each remaining unit-length wall not on the boundarywe assign random value and create graph gcalled the dualsuch that each grid cell is vertex in and there is an edge joining the vertices for two cells if and only if the cells share common wall the weight of each edge is the weight of the corresponding wall we construct the maze by finding minimum spanning tree for and removing all the walls corresponding to edges in write program that uses this algorithm to generate mazes and then solves them minimallyyour program should draw the maze andideallyit should visualize the solution as well