A) dijkstra’s shortest paths algorithm is executed on the graph above, starting at a. assume that vertices a, b,c, d,e are given numbers 0,1,2,3,4 respectively in the implementation. also assume that neighbors of a vertex are stored in alphabetical order of their names. trace the execution of the algorithm as follows: at the end of every step, show the distance array and the fringe in the table below. the fringe is stored in a min-heap, in which distance updates can be made, apart from delete min, and insert. to show the fringe, draw the binary tree heap structure, with (vertex name, distance) information at each node. every time there is a change to the heap, show the number of item-to-item comparisons needed to make that change, and also what operation (insert/delete/update) resulted in that change. (ignore the time needed to locate an item in the heap for a distance update.