table showing the intermediate distance values $($dist$($v$))$ and prev values of all the nodes at each iteration of the algorithm. $($b$)$ Show the final shortest$-$path tree. $(15\text{'})$

$8$

procedure dijkstra $($G$.$l$.$s$)$

Input: Graph $G=(V,E),$ directed or undirected; positive edge lengths $\{l_e$:einE$\}$; vertex $sinV$

Output: For all vertices $u$ reachable from $s,$ dist $(u)$ is set to the distance from $s$ to $u.$

for all uinV

dist$(u)=$

prev$(u)=$nil

dist$(s)=0$

$H=$ makequeue $(V),($using dist$-$values as keys$)$

while $H$ is not empty:

$u=$ deletemin $(H)$

for all edges $(u,v)inE$:

$if$ dist $(v)>$dist$(u)+l(u,v)$:

dist $(v)=$dist$(u)+l(u,v)$

pirev $(v)=u$

decreasekey $(H,v)$