I am a little confused about the Hill Climbing algorithm. I want to "run" the algorithm until I found the first solution in that tree ( "a" is initial and h and k are final states ) and it says that the numbers near the states are the heuristic values. Here's the tree:

My question: I am trying to run hill climbing on the tree, so ok we start a-> f-> g and then what ?? finish(without result), but I read that hill climbing can't go back and make a new choice(example j or e)? Is that right? If I can go back then how? I mean where we change our initial choice example we choose e instead of g or j instead of f

Sorry if my question is too simple.