Question $2\mathrm{.}1$: We showed in the class that if all edges in a network topology haveQuestion $2\mathrm{.}1$: We showed in the class that if all edges in a network topology have

non$-$negative values, using the Dijkstra's algorithm can calculate the shortest

paths from a source to all the destinations. Please give an example in Figure $1.$a

that if we change the value of an edge to a negative value, the Dijkstra's algorithm

will not work and explain why. $(15$ points$)$

Question $2\mathrm{.}2$: Please give the detailed steps to show how each node $x,Y,Z$ in

Figure $1.$b determines its cost of path to all its destinations according to distance

vector routing algorithm. $(20$ points$)$

Figure $1.$a Network graph in Question $2\mathrm{.}1$

Figure $1.$b Network graph in Question $2\mathrm{.}2$

non$-$negative values, using the Dijkstra's algorithm can calculate the shortest

paths from a source to all the destinations. Please give an example in Figure $1.$a

that if we change the value of an edge to a negative value, the Dijkstra's algorithm

will not work and explain why. $(15$ points$)$

Figure $1.$a Network graph in Question $2\mathrm{.}1$