Question $8(11\mathrm{.}5$ points$)$

In the network below, each router calculates the shortest path to every other router using the Link$-$State algorithm. Given the connection costs between each pair of routers, what is the shortest path cost from Router A to Router D$,$ and which path would that be$?$

Router Connections with Costs:

$-\backslash (\backslash$mathbf$\{$A$\}-\backslash$mathbf$\{$B$\}$: $\backslash )$ Cost $\backslash (=2\backslash )$

$-$ A $-$ C: Cost $\backslash (=5\backslash )$

$-\backslash (\backslash$mathbf$\{$A$\}-\backslash$mathbf$\{$E$\}$: $\backslash )$ Cost $\backslash (=3\backslash )$

$-\backslash (\backslash$mathbf$\{$B$\}-\backslash$mathbf$\{$C$\}$: $\backslash )$ Cost $=1$

$-$ B $-$ D: Cost $=4$

$-$ C$-$D: Cost $=2$

$-$ C $-$ E: Cost $=3$

$-$ D $-\backslash (\backslash$mathrm$\{$E$\}$: $\backslash )$ Cost $=1$

A$.$ Path: A $->$ C $->$ D

B$.$ Path: A $->$ B $->$ D

C$.$ Path: A $->$ E $->$ D

D$.$ Path: A $->$ B $->$ C $->$ D