Recall Prim's algorithm:

Preconditions: $N$ is a connected network.

Postconditions: $T$ is a minimal spanning tree of $N.$

$Tlarr{e}_1\{\begin{array}{c}?\end{array}$ the two vertices joined by $\{$:$e_1\},$ where $e_1$ is the shortest edge of $N.$

while $T$ does not contain all of $N\text{'}$s vertices

$elarr$ the shortest edge between a vertex in $T$ and a vertex not in $T.$

llcorner Add edge e and the new vertex to $T.$

If $N$ has $n$ vertices, what is the worst$-$case number of times an edge gets added to $T?($Include the initial step when $e_1$ is added to T$.)$

$n-1$

$$

$n^2-1$

$n^2$

$lo{g}_2(n)-1$

$lo{g}_2(n)$