AI algorithms and decisions

Hi there!
I would like to know what are the commons approaches for designing AI which would allow the following cases

AI may use the direct path to the player - beside rectangle, to the stairs.

AI may decide to use rectangle and jump to the player

AI may decide to run beside rectangle and then jump directly to the player

It is not neccessary means it should choose the shortest route.
As far as I understand it should be based on some pathfinding algorithms?

P.S. I have one idea in my mind but as usual it is overly complex and not very useful for games