The college course is Artificial Intelligence please give me a full detailed answer

Consider that we have a Vacuum$-$cleaner machine robot that can move left, right,

up$,$ down only, and it does the suck if the square is dirty, the Vacuum$-$cleaner robot never back to visited square.

Goals :

$$ Build a complete Search tree $($with drawing$)$

$$ Solve the search problem by using Greedy search algorithm if the heuristic function is Manhattan distance

$$ Solve the search problem by using A$*$ if the real cost is R$($n$)=1/$# of dirty palaces.Start