Q$\mathrm{.}1$ Given the following figure, assuming that the goal is found at node N$.$

a$.$ Apply Greedy $$Best First search algorithm?

b$.$ Finds if it is optimal $/$ admissible or not? Explain why $?$

A$-7$

B$-5$ C$-4$

E$-5$ F$-5$ G$-6$ H$-3$

K$-2$ L$-2$ M$-3$ N$-2$ O$-1$ P$-2$

Q$\mathrm{.}2$ Given the current state and goalstate below for the $8-$Puzzle Problem. Find the sum of distance out of the place $?$

Current state Goal state

Q$\mathrm{.}3$ Given the graph below where Arad is the root node and Hirsova is the goal$).$ Demonstrate the search tree by applying the A$*$ algorithm? and what is the final path?

Note: The value of each node according to f needs to be shown in the search tree?