Q$2$ Floyd$-$Warshall algorithm

Execute the Floyd$-$Warshall algorithm on the directed graph below. For every pair of vertices $u$ and

$v$ give the distances $(u,v)$ and $(v,u).$ Give the shortest paths from $3$ to $1$ and from $2$ to $6$ as

sequence of vertices.

Q$2\mathrm{.}1$Row $1$

Give the distances from vertex $1$ to all six vertices in the graph, separated by single blank symbols. That is$,$ the first entry should be the distance from $1$ to $1,$ the second from $1$ to $2,$ the third from $1$ to $3,$ the forth from $1$ to $4,$ the fifth from $1$ to $5,$ and the sixth from $1$ to $6.$

Q$2\mathrm{.}2$ Row $2$

Give the distances from vertex $2$ to all six vertices in the graph, separated by single blank symbols.

Q$2\mathrm{.}3$Row $3$

Give the distances from vertex $3$ to all six vertices in the graph, separated by single blank symbols.

Q$2\mathrm{.}4$ Row $4$

Give the distances from vertex $4$ to all six vertices in the graph, separated by single blank symbols.

Q$2\mathrm{.}5$ Row $5$

Give the distances from vertex $5$ to all six vertices in the graph, separated by single blank symbols.

Q$2\mathrm{.}6$ Row $6$

Give the distances from vertex $6$ to all six vertices in the graph, separated by single blank symbols.

Q$2\mathrm{.}7$ Path from $3$ to $4$

Give the shortest path from $3$ to $4$ as comma$-$separated sequence of vertices, enclosed in $"("$ and $")",$ but without blank symbols.

Q$2\mathrm{.}8$ Path from $4$ to $3$

Give the shortest path from $4$ to $3$ as comma$-$separated sequence of vertices, enclosed in $"("$ and $")",$ but without blank symbols.