The Path and Distance Matrices of $\backslash (\backslash$mathbf$\{$D$\}\backslash )$ after the Fifth Stage $(\backslash (\backslash$mathbf$\{$k $=5\}\backslash ))$

A$.$ Compute and show $\backslash (\backslash$Delta$^\{$k$\}\backslash )$ and $\backslash (\backslash$pi$^\{$k$\}\backslash ),$ the final distance and path matrices after execution of the algorithm. $[18$ points$]$

The Final Distance Matrix of D after the Fifth Stage $(\backslash (\backslash$mathbf$\{$k $=6\}\backslash ))$

The Final Path Matrix of $\backslash (\backslash$mathbf$\{$D$\}\backslash )$ after the Fifth Stage $\backslash (($k$=6)\backslash )$

n$*$

B$.$ What is $\backslash (\backslash$pi$^\{(\}(1,3)\backslash ),$ the shortest distance from vertex $1$ to vertex $3?[2$ points$]$

C$.$ Give $\backslash (\backslash$times$(1,3)\backslash ),$ the complete shortest path from vertex $1$ to vertex $3,$ as an integer whose first digit is $1$ and whose last digit is $3[3$ points$]$

D$.$ What is the in$-$degree of vertex $2$ in the all$-$pairs shortest path graph that is minimal with respect to edges that generates the final matrices: $[2$ points$]$