For path planning, the computing agent of a driverless car $($e$.$g$.,$ robot$)$ has access to the given directed graph that shows the road network where nodes are representing different cities, edges are the roadways, and their weights$/$costs are the distance in miles.

$1)[30$ marks$]$: Use Grassfire algorithm and determine the optimum path from the START node to the GOAL node.

$2)[40$ marks$]$: Use Dijkstra$$s algorithm and find all the shortest paths from the START node to the GOAL node.

$3)[30$ marks$]$: Explain the difference between the algorithms and their solutions for this given problem.