a$)$ Identify the optimal path from the starting point $($Lagos$)$ to the goal $($Abuja$)$ in the provided figure using:

i$)$ A$*$ Star Search

ii$)$ Best First Search $($BFS$)$

The number outside the oval is the heuristics and the numbers within the oval are the edge cost. Ensure to show every step involved in detail.

b$)$ Discuss the broad types of search algorithms and the difference between them.