Draw a search graph $to$ answer these questions below $"[10$ pts$]$ Perform Depth$-$first Search $($DFS$)$ from S to G: $($a$\mathrm{.}1)[2\mathrm{.}5$ pts$]$ Return search table of DFS$.$

$($a$\mathrm{.}2)[2\mathrm{.}5$ pts$]$ What is the path returned?

$($a$\mathrm{.}3)[2\mathrm{.}5$ pts$]$ What is the node expansion order?

$($a$\mathrm{.}4)[2\mathrm{.}5$ pts$]$ What is the path cost of the returned path?

$($b$)[10$ pts$]$ Perform Breadth$-$first Search $($BFS$)$ from S to G:

$($b$\mathrm{.}1)[2\mathrm{.}5$ pts$]$ Return search table of DFS$.$

$($b$\mathrm{.}2)[2\mathrm{.}5$ pts$]$ What is the path returned?

$($b$\mathrm{.}3)[2\mathrm{.}5$ pts$]$ What is the node expansion order?

$($b$\mathrm{.}4)[2\mathrm{.}5$ pts$]$ What is the path cost of the returned path?

$($c$)[20$ pts$]$ Perform Uniform$-$cost Search $($UCS$)$ from S to G:

$($a$\mathrm{.}1)[5$ pts$]$ Return search table of UCS.

$($a$\mathrm{.}2)[5$ pts$]$ What is the path returned?

$($a$\mathrm{.}3)[5$ pts$]$ What is the node expansion order?

$($a$\mathrm{.}4)[5$ pts$]$ What is the path cost of the returned path?