Shortest path

[Haneetha]

I have programmed by robot to explore the maze using the left wall follower algorithm. Program is working properly but I want to add extra bits like returning to the start point from the end point by remembering the path it came.

In the bottom pic, robot is starting from the start position, and following the left wall as shown with the arrow and comes to end. What I wanted is once it gets to end I want to robot to get back to home without rounding the whole maze. I heard this can be done using some shortest path algorithm. But I don't how to use that for my program. Can someone help me with this please.