Problem II: A$*$ Search

The following table defines the successor functions Succ, heuristic $H$ and goal $B.$ The successor function Succ$(s)$ returns a set of pairs $\{(s_1,c_1),$dots,$(s_n,c_n)\}$ such that $s$ is a given state, $s_i$ is a successor state, and $c_i$ is the cost to go from state $s$ to $s_i.$ The function $H(s)$ returns an estimate of the distance between a state $s$ and a state satisfying the goal. The $B(s)$ function returns "True" if the state s matches the goal, and "False" otherwise.

Table $1$

$\backslash$table$[[$State s$,$Succ$($s$),$H$($s$),$B$($s$)],[$s$\_(0),\{($s$\_(1),2),($s$\_(2),4)\},6,$False$],[$s$\_(1),\{($s$\_(3),6),($s$\_(4),7)\},5,$False$],[$s$\_(2),\{($s$\_(4),3)\},3,$False$],[$s$\_(3),\{($s$\_(5),1)\},8,$False$],[$s$\_(4),\{($s$\_(5),5),($s$\_(6),8)\},2,$False$],[$s$\_(5),\{($s$\_(7),9)\},7,$False$],[$s$\_(6),\{($s$\_(7),2)\},4,$False$],[$s$\_(7),\{\}($no successors$),1,$True$]]$

Give a trace of the execution of the $A^{*}$ algorithm using the space of states and the goal function and the heuristic function $h$ defined in Table $1.$ For each state in the open and closed lists, give its values $f$ and $g.$

$\backslash$table$[[$Iteration$,$Open List $($state$,$ f$,$g $),$ dots,Closed List $($state$,$ f$,$g $),$ dots$],[0,,],[1,,],[,,],[,,]]$

Is the heuristic function $h$ admissible? Justify your answer.