> Without formal education you’re almost certainly not even dealing with concepts like breadth-first search, trees, or nodes, so no, a ton of people will not be inventing it on the spot.
If you're not dealing with nodes, you won't be inventing A* on the spot because you don't have a problem to which it can be applied.
But otherwise, it's literally a breadth-first search with the queue replaced by a priority queue.
> Even using a queue, that’s a data structure that a person with a task to do isn’t likely to spend the time to invent on the spot.
A to-do list is as simple as data structures get.
A heap is complex, but if you want to insist on developing everything used by the algorithm from scratch, the person faced with this problem is likely to just use a sorted list.
Try it out. Ask some people how they'd find the shortest path between two points through a weighted graph (use whatever terminology you want); see what they say.