$[10$ marks$]2.$ Write a program that codes the greedy coloring algorithm. You should input a Graph and output a list of colors, so that color$\_$graph$[$i$]=\backslash$#the color of vertex i$.$ Once you have written your code, determine it's complexity $($see CISC$121$ or Ch $3.$ of Rosen$).$

You have a line limit of $60$ lines $($If you really all need more, let me know, but $60$ should be enough$).$

You should consider a graph $\backslash ($ G$=($V$,$ E$)\backslash )$ is stored as a list of vertices V $\backslash (=[\backslash$mathrm$\{$v$\}1,\backslash$mathrm$\{$v$\}2,\backslash$ldots$,\backslash$mathrm$\{$vn$\}]\backslash )$ and n$-$length list, and a list of tuples for the edges $\backslash ($ E$=[($v i$,$ v j$),($v i$,$ v j$)]\backslash ).$ You do not need to define any classes or import any packages. Note that the edges are NOT directed so the edge from $\backslash ($ u $\backslash )$ to $\backslash ($ v $\backslash )$ may be stored as either $(\backslash (\backslash$mathrm$\{$u$\},\backslash$mathrm$\{$v$\}\backslash ))$ or $(\backslash (\backslash$mathrm$\{$v$\},\backslash$mathrm$\{$u$\}\backslash ))$

Note: it may be beneficial to create a list or dictionary of neighbors.