For each of the following search strategies, find the order in which the states are expanded, the path returned and the cost of the path. $\text{'}$S$\text{'}$ represents the Start and $\text{'}G\text{'}$ represents the Goal state. Resolve ties in alphabetic order.

a$)$ Depth$-$first search

b$)$ Breadth$-$first search

c$)$ Uniform$-$cost Search

d$)$ Greedy best$-$first search with the heuristics shown in the figure $1$

e$)$ A$*$ tree search with the heuristics shown in the figure $1$

f$)$ Weighted $A^{**}$ search with weight $W=2$

g$)$ Is the heuristics given in problem $1$ consistent?

h$)$ Is the heuristics given in problem $1$ admissible?