$3.$ Consider the following weighted graph $\backslash ($ G $\backslash ).$

a$)[10$pts$]$ Trace the action of procedure Kruskal for $\backslash ($ G $\backslash )$ illustrating the action of growing the forest as well as action of union and find for the collection of disjoints sets.

b$)[10$pts$]$ Trace the action of procedure Prim for $\backslash ($ G $\backslash ),$ with $\backslash ($ r$=1\backslash ).$ Illustrate the action using Figure $6\mathrm{.}11$ on page $271$ as a model.