Consider a state space where the start state is a tuple $(0,0)$ representing the position of a robot on a two$-$dimensional grid, and the successor function for state $($x$,$y$)$ returns a set of possible successor states obtained by moving the robot one step in one of four directions: up$,$ down, left, or right. The robot can only move to a neighboring cell if that cell is not occupied by an obstacle. The obstacles are represented as a set of coordinates in the grid.

$($a$)$ Develop the representation of the state space and design an algorithm to generate the state space. $($i$.$e return the possible successor states for a given state$).$

$($b$)$ Compute the shortest path from the initial state to a goal state $($e$.$g$.,$ a target position on the grid$)$ using Beam Search with beam$-$width two and Best First search. Compare both the approaches in terms their optimality, completeness, space and time complexities. Also, explain the suitability of A$-$algorithm in the above case.