The sliding$-$tile puzzle consists of three black tiles, three white tiles, and an empty space in some order. The goal is to arrive at the

goal configuration shown below by legal moves $[$B$-$ Black tile, W$-$White tile$].$

B B B W W W

The puzzle has two legal moves with associated costs

Move #$1$: A tile may move into an adjacent empty location. This has a cost of $1.$

Move #$2$: A tile can hopover one or two other tiles into the empty position. This has a cost equal to the number of tiles

jumped over

$(2-$a$)$ What are measures using which the complexity of a state space can be measured. List each of them and provide the

corresponding expression $/$ value for this problem.