Problem $4.(10$ points$)$ Find a minimum spanning tree $($MST$)$ for the graph in Figure $1$ obtained by using Prim's algorithm, using node $f$ as a starting node. Then find an MST obtained by using

$1$

Kruskal's algorithm. Then find an MST using Boruvka's algorithm. For Prim's and Kruskal's, show your answer by filling in Table $1,$ writing your answer as an ordered list of edges, showing each edge $($and its weight$)$ added at each step. For Boruvka's algorithm, write out the collection of edges added at each iteration.

L:

$q,$

$$

$q,$

Table $1$:

$\backslash$table$[[,$Prim's,,Kruskal's,$],[$Step$,$Edge Added,Weight,Edge Added,Weight$],[1,,,,],[2,,,,],[3,,,,],[4,,,,],[5,,,,],[6,,,,]]$