Figure $1$: Graph for problem $1$

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.

Depth$-$first search, Breadth$-$first search and Uniform$-$cost Search

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

$A^{**}$ tree search with the heuristics shown in the figure $1$

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

Is the heuristics given in problem $1$ consistent? and

Is the heuristics given in problem $1$ admissible?