Q$5$: 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.

Start

Goal

Build a complete Search tree

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 $R(n)=\frac{1}{\text{\#}}$ of dirty palaces.