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.

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 $R(n)=1/$# of dirty palaces.

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