You're an organizer of a major campus event featuring multiple sessions and guest speakers. These sessions cover a range of specific topics, and each speaker may be giving one or several talks, but each talk would be on a different topic. You want to manage the event in a way such that the cost is minimized. The cost will be minimal if you reduce operational cost by making the conference span the least number of days possible. You know that one session is an hour and that the conference can run from 9AM to 6PM every day. You are given the list of speakers along with the talks that they will be given and the topics that these talks go under. Assume every talk is 20 mins. Design a schedule that minimizes the cost of the conference while ensuring that no conflict is caused for any of the speakers.

first, apply problem reduction and graph modeling then find the matched graph problem that can be solved using one of the graph algorithms based on the matching objectives between the constructed graph of the problem and the graph algorithm. Use c++