Implement cheapest itinerary with date filters

Implement a function that computes the cheapest itinerary from a given origin to a destination using a list of flights, where each flight has (id, source, destination, departure_time, arrival_time, price). Only consider itineraries whose first departure falls within a provided date range. Return the minimum total price and the ordered list of flight IDs forming the itinerary; return -1 if no valid itinerary exists. Explain your algorithm, time/space complexity, and how you enforce time ordering between connections and avoid cycles.