Consider the grid in Figure $2$ with several obstacles $($dark boxes$)$ and we are given a starting cell $($with a red circle$)$ and a target cell $($with a green circle$).$ We aim to reach the target cell $($if possible$)$ from the starting cell with the minimum possible number of moves using the $A^{**}$ algorithm. Note that only horizontal and vertical moves are allowed from each cell and diagonal moves are NOT allowed.

Figure $2$: 'Section B$,$ Q$2$

$($a$)$ Determine a suitable heuristic function such that $A^{**}$ terminates with the correct optimal solution. Justify your choice.

$($b$)$ Name the cells and show a possible state$-$space tree traced by the $A^{**}$ algorithm to find the uptimal path.