Given the following edge$-$weighted graph:

$6,15$

$0-1,1\mathrm{.}3$

$0-2,5\mathrm{.}2$

$0-3,2\mathrm{.}1$

$0-4,6\mathrm{.}8$

$0-5,3\mathrm{.}5$

$1-2,5\mathrm{.}6$

$1-3,2\mathrm{.}0$

$1-4,6\mathrm{.}9$

$1-5,3\mathrm{.}6$

$2-3,5\mathrm{.}7$

$2-4,6\mathrm{.}1$

$2-5,6\mathrm{.}0$

$3-4,7\mathrm{.}0$

$3-5,5\mathrm{.}1$

$4-5,7\mathrm{.}8$

a$)$ Show a trace of the execution of Kruskal's Algorithm on this graph.

Your trace should be in the style of the trace shown on page $624$ of

the text. $[5]$

b$)$ How many elements are inserted into the priority queue used by Kruskal's

algorithm when computing the MST for this graph? $[1]$

c$)$ How many elements of the priority queue do you consume before the algorithm

completes computing the MST$?[1]$

d$)$ Show a trace of the execution of the eager version of Prim's Algorithm on

this graph. Your trace should be in the style of the trace shown on page

$621$ of the text. $[5]$

e$)$ As Prim's algorithm executes, how many elements of each of the edgeTo$[]$ and

distTo$[]$ arrays must be updated each time an edge is added to the MST$?[1]$

f$)$ Which of the two algorithms is a better choice for computing the MST for

this graph? Why? $[2]$