Suppose you are given a timetable T = (A,F,c,a₁,a₂,t₁,t₂)consisting of: A set A of n airports and for each airport a A, a minimum connecting time c(a) A set F of m flights For each flight f F 1. Origin airport a₁(f) A 2. Destination airport a₂(f) A 3.Departure time t₁(f) 4. Arrival time t₂(f)

Consider the following flight scheduling problem. In this problem, we are given a timetable T, airports a and b, and a time t. We wish to compute a sequence of flights F = 1,f₂,.f_k> that allows one to arrive at the earliest possible time in b when departing from a at or after time t. In the solution, the minimum connecting times at intermediate airports must be satisfied i.e flight f_i F into city a A, must arrive at least c(a) minutes before flight f_i+1 F leaves city a.Formally,this means that in a sequence of flights 1,f₂,.f_k>,for all i1(f_i+1)-t₂(f_i)2(f_i))

Describe an efficient algorithm for the flight scheduling problem, argue your algorithms correctness and analyse its running time as a function of n and m.