$(16$ points$).$ Minimum Spanning Trees $($MST$)$: Finding a Minimum Spanning Tree for the following graph based on each of the following algorithm. You need to show the procedures step$-$by$-$step. You could directly draw the final MST but indicate the sequence of your search by writing a series of letters, i$.$e$.($a$),($b$),($c$)...$ under the edges of the MST$.$ This type of answer is preferred. Or else, you need to draw a graph for each step separately.

$($a$)(8$ points$)$ Kruskal's algorithm.

$($b$)(8$ points$)$ Prim's algorithm $($start with the node 'ORD$).$

Fig. $1.$ A weighted graph whose vertices represent major U$.$S$.$ airports and whose edge weights represent distances in miles.