$\%$Problem $1\backslash$begin$\{$tcolorbox$\}[$title$=\{$Problem $1($Alice$\text{'}$s party, $30$ pts$)\}]\backslash$setlength$\backslash$parindent$\{1$em$\}$ Alice organizes a party and is deciding which of her $n$ friends to invite. She wants to have that for each person at the party there are at least $$5$$ other people they know and at least $$5$$ other people they do not know. Give a greedy strategy for finding the maximal number of friends she can invite $($and a corresponding guest list$),$ given a list of all pairs of people that know each other. Prove that your strategy finds the guest list of maximal size and analyze its runtime. For full credit, your algorithm should run in polynomial time. $\{\backslash$it Hint: In greedy examples we have seen so far, we greedily built up a solution from scratch. Here, you should instruct Alice to $`$greedily$\text{'}\text{'}$ cross people off her list.$\}\backslash$end$\{$tcolorbox$\}$