Consider the following problem setup: You are the Head of the Computer Science department, and you are figuring out the tutorial schedule for the Tutors in the department. The department has X Tutors and Y tutorial sessions. Each tutorial session has a known time slot, and fortunately, at most 2 tutorials are in the same time slot. In the Y tutorial sessions, you need exactly Z of them to be exam prep sessions, and the rest to be normal tutorial sessions. The following conditions MUST hold:

-Exactly one Tutor is available for each tutorial
-A tutor cannot conduct 2 tutorials at the same time slot
-Some Tutors do not conduct normal tutorial sessions, some do not conduct exam prep sessions, and others can conduct either.
-If two tutorials are in the same time slot, you also don’t want them to be the same type of session for the sake of best allocation of resources.

Q1. Formulate this as a search problem. Specifically, define the state representation, the successor
function, the start state and the goal test.
Q2.
-Propose a search algorithm to tackle the problem.
If your choice is DFS/BFS, give an explanation for your choice
-If your choice is UCS/Greedy/A* search, explain in a paragraph what cost function and/or heuristic is
being used (A qualitative description of what
the cost function/heuristic does is sufficient).
-Calculate the state space size and the branching factor of the search tree​