I have this navigation table, were d$2$ is start and d$4$ is goal, the $($a$5)($b$2)($c$2)($c$3)($d$3)$ are obstacles, the priority to pass between siblings are on alphabet order and after that priority is the number increasing.

Use Depth First Search to find path from d$2$ to d$4.$

Report nodes in the fringe in the orders they are included in the fringe.

Report the order of the nodes being expanded.

Report the final path from d$2$ to

Use Breadth First Search to find path from d$2$ to d$4.$

Report nodes in the fringe in the orders they are included in the fringe.

Report the order of the nodes being expanded.

Report the final path from d$2$ to d$4.\backslash$table$[[$a$1,$a$2,$a$3,$a$5],[$b$1,$b$2,$b$3,$b$4],[$c$1,$c$2,$c$3,$c$4],[$d$1,$d$2,$d$3,$d$4],[$e$1,$e$2,$e$3,$e$4]]$

Figure $5$