Running Dijkstra's algorithm

Run Dijkstra's algorithm on this graph, starting on node a$.$ To do this, fill out the table below and be sure to show your work $($cleanly cross out old values for distance and predecessor when updating existing values. If your handwriting is illegible, we may not be able to grade your submission so you might consider typing up the table as well.

In the case of a tie, add the vertex that comes first alphabetically. $\backslash$begin$\{$tabular$\}\{|$c$|$l$|$l$|$l$|\}$

$\backslash$hline vertex & distance & predecessor & processed $\backslash \backslash$

$\backslash$hline a & $0$ & None & $\backslash \backslash$

$\backslash$hline b & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline c & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline d & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline e & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline f & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline g & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline h & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline i & $\backslash (\backslash$infty $\backslash )$ & & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$