$1.$Examine the pseudo code below:

let path $[$V$][$V $]=\{0\}$

let weight $[$V$][$V $]=$ initialWeights

for all k in V

for all i in V

for all J in V

if i $==$ j or i $==$ k or j $==$ k

continue;

let wt $=$ weight $[$i$,$ k$]+$ weight $[$k$,$ j$]$

if wt $<$ weight $[$i$,$ j$]$

weight $[$i$,$ j$]=$ wt

path $[$i$,$ j$]=$ k

Q$1$: What algorithm is this?

Q$2$: After the algorithm has completed, I want to be able to print the path from i $=$ v$1$ to j $=$ v$2$

Give pseudo code to print the discovered path from v$1$ to v$2.$

$2.$Examine the pseudo code below:

$//$ a and b are nodes in a graph

$//$ path$[$a$,$b$]$ defines the next node on the shortest route from a to b$.$

$//$ If there is no in$-$between node then path$[$a$,$b$]==$ b

function PrintPath$($a$,$b$)//$start and end points in graph

k $=$ path$[$a$,$b$]//$the in$-$between point

while k $!=$ b $//$if k $==$ b then there's no in$-$between

while path$[$a$,$k$]!=$ k $//$search for second stop

k $=$ path$($a$,$ k$)$

print $($a$)//$print first point

a $=$ k $//$second point becomes first point

k $=$ path$[$a$,$ b$]//$set the in$-$between point for next iteration

print $($a$)$

print $($b$)$

end

This recovers the path from Floyd$-$Warshall APSP. Assume a suitable adjacency matrix. Give the Floyd$-$Warshall algorithm for building the path table used above.