Algorithm 1: A* shortest path Algorithm with Greedy heuristic

Require:  maze, start and goal Ensure:  $start\ne goal$ 1:procedureA_Star($maze,start,goal$)                                                                                                   ▷ returns path 2:    Add $start$ to $priorityQueue$ 3:    $searchedNodes\leftarrow \varphi$ 4:  5:    while $priorityQueue\ne \varphi$ do 6:        if $currentNode\leftarrow goal$ then 7:           return $path$ 8:        end if 9:        Remove $currentNode$ from $priorityQueue$ 10:      Add $currentNode$ to $searchedNodes$ 11:  12:      $child\leftarrow neighbor.currentNode$ 13:  14:      for each $child$ in $neighbor$ do 15:           if $child$ is in $searchedNodes$ then 16:               continue 17:           end if 18:           $child.g\leftarrow currentNode.g+d$    ▷d is distance between $currentNode$ and $child$, which is 1 in this case 19:  20:           $child.h\leftarrow$ distance from $child$ to $goal$ 21:  22:           $child.f\leftarrow child.g+child.h$       ▷h is calculated using heuristic function, Euclidean distance in this case 23:  24:           if $child.position$ is in $priorityQueue$ then 25:               if $child.g>priorityqueue.child.position.g$ then 26:                   continue 27:               end if 28:           end if 29:  30:           Add $child$ to $priorityQueue$ 31:        end for 32:    end while 33:  34:    return $failure$                              ▷ If $priorityQueue$ is $\varphi$ 35:end procedure