$(12$ points$)$ You are having a party and your guests are arriving and leaving at different times, $($you will be at the party the entire time.$)$ You want to find two other people to play a $3$ person game with. You would like to know how long you can play the game for so you are looking for two people who will be together at the party for the longest time.

Given the start and end times of each of $n$ guests: $(s_1,f_1),$dots,$(s_n,f_n)$ design an $O(nlogn)$ algorithm that returns the maximum time that a pair of people will be together at the party.

$($implementation level or high level description and time analysis. No correctness proof necessary.$)$

$(12$ points$)$ You are having a party and your guests are arriving and leaving at different times, $($you will be at the party the entire time.$)$ You want to find two other people to play a $3$ person game with. You would like to know how long you can play the game for so you are looking for two people who will be together at the party for the longest time.

Given the start and end times of each of $n$ guests: $(s_1,f_1),$dots,$(s_n,f_n)$ design an $O(nlogn)$ algorithm that returns the maximum time that a pair of people will be together at the party.

$($implementation level or high level description and time analysis. No correctness proof necessary.$)$