Write expressions for Dnew$($vnew$,$ u$)$ and Dnew$($u$,$ vnew$)$ that hold for all u in V $,$ where the

expressions are in terms of the already$-$known quantities D$($y$,$ z$)$ for y$,$ z in V $,$ and w$($y$,$ z$)$

for $($y$,$ z$)$ in E $\backslash$cup Enew. Evaluating your expressions should take O$($n$)$ time for each vertex u$,$

for a total of O$($n

$2$

$)$ time.