$1\mathrm{.}3$ Problem $3[15$ pts$]$

Problem $3.$ Consider the weighted directed graph $\backslash ($ G$($V$,$ E$,$ w$)\backslash )$ pictured below. Work through the Bellman$-$Ford algorithm with the destination vertex $\backslash ($ C $\backslash ).$ Note that you must use the version of the algorithm presented in lecture; see also slide $14$ of the in$-$class slides for Oct $\backslash (29\backslash$& $31\backslash ).$

$-$ Clearly specify the cost $\backslash ($ d$($v$)\backslash )$ of the current best path from each node $\backslash ($ v $\backslash$in V $\backslash )$ to $\backslash ($ C $\backslash )$ as well as the corresponding successor node at each iteration$/$pass$.$ You may want to make a table to store the costs and successors.

$-$ Give the shortest path tree, i$.$e$.,$ the union of all the shortest paths to $\backslash ($ C $\backslash )$ from all other vertices. For your convenience, you may want to modify the "latex code" for the given graph to draw the shortest path tree.