Avoiding Airports

I have been trying to solve this question on kattis(Avoiding Airports) since 7 months. I know the dp solution. Which is sort all flights by start time and then calculate total frustration of taking each flight.

{flight[i].s is start time of flight i and flight[i].e is end time of flight i}.

frustration of i'th flight f[i] = min(f[j]+(flight[i].s-flight[j].e)^2) for j < i . Many people then told me that you can make this faster by using convex hull trick. Where slope here is -2*flight[j].e and constant = dp[j]+flight[j].e^2 So for a particular flight with start time flight[i].s I have to find the best (slope,constant). But I don't know how to make the query because the slope/-2 < flight[i].s has to be satisfied. How can I still make queries. Most problems I took to learn CHT didn't have any conditions on the slope. If someone can give another example to some problem that would also help.

Avoiding Airports How to solve avoiding airports. I wrote a shortest distance approach using dijkstra but gives TLE. How to avoid going in loops to catch some flight at a particular node that leads to the destination. Can someone give a solution to this problem.