In class we saw the Edmonds$-$Karp algorithm to solve Max$-$Flow. In this problem the input is a

pseudocode below:

Edmonds$-$Karp $(G=(V,E),s,l)$

for each edge $(u,v)inE$

$(u,v).f=0$

Compute the residual $G_f$

Use

$($BFS$/$DFS$)$ to find a path $p$ from

while a path $p$ exists

Compute the residual capacity $c_f($use $c_{-}f$ if necessary$)$ of $p$

for each edge $(u,v)inp$

$if(u,v)inE$

$,(u,v).f=(u,v).f$

else

$(v,u)*f=(v,u)*f$

Update $G_f$ and $p$

The while loop executes $O($