optimization problems

You have started a new travel website that finds the cheapest direct or multi-leg flight between any given origin and destination. You do this by first asking your customer to enter information about his/her desired departure date, time, and the origin, as well as his/her desired arrival date, time, and the destination. You will then get information on all flights departing from the origin whose departure times are within your customer’s specifications (leg 1). For each of those flights, you will get information on all flights that will depart after at least an hour from the first flight’s arrival time from the same airport (leg 2). You will repeat this until a flight’s destination is the same as your customer’s destination or its arrival date and time is not within your customer’s acceptable arrival date and time. This will give you a table like the following: 

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