"How many people can actually write BFS on the spot, without preparing for it in advance?" A lot of people. You should too, even if you're just a front-end.
I would at least offer something back, like a loop that randomly chooses left/right, restarts loop if dead end, exit loop if solved. Then verbally walk through how you might improve on it incrementally.
Should all front-end developers be able to create a maze solving algorithm on the spot, during an interview, under time pressure?