$($Extra credit: $15$ points$)$ Prim's algorithm for finding minimum spanning tree. Run Prim's algorithm on the graph below. For simplicity we use a distance array rather than a priority queue. Label each tree edge by the order in which it was selected. Use the table below to show the contents in the two arrays $D($for distance$)$ and $P($for parent vertex$)$ after each update. Please start at vertex $h.$

$\backslash$table$[[,*,$a$,$b$,$c$,$d$,$e$,$f$,$g$,$h$,$i$],[,$step $1,(\frac{?}{?}),\backslash$table$[[12],[($h$)]],(\frac{?}{?}),(\frac{?}{?}),(\frac{?}{?}),\backslash$table$[[11],[($h$)]],(\frac{?}{?}),0(n),\backslash$table$[[15],[($h$)]]],[,$step $2,,,,,,,,,],[,$step $3,,,,,,,,,],[,$step $4,,,,,,,,,],[D(P),$step $5,,,,,,,,,],[,$step $6,,,,,,,,,],[,$step $7,,,,,,,,,],[,$step $8,,,,,,,,,],[,$step $9,,,,,,,,,]]$