I want to know if i'm understand the idea behind A* tree search correctly. My understanding is that the path is given by:
$f(n) = g(n) + h(n)$
and that
$h(n) \leqslant h^*(n)$
Where $g(n)$ is the cost from start node to node n, $h(n)$ is the estimate of the cost of the cheapest path from n to the goal, and $h^*(n)$ is the exact cost to get from x to the goal.
So given all of that, can we say that at the start node $g(start) = 0 $ and that at the goal node $h(goal) = h^*(goal) = 0$ ?
Can we also say that $f(start) = f(goal)$ ?
g(start)=0 is true.
h(goal)=h∗(goal)=0 is also true.
You can't say that f(start)=f(goal) is true.
f(start) = g(start) + h(start) = h(start).
f(goal) = g(goal) + h(goal) = g(goal).
You can't say that h(start) = g(goal) because h is just an estimate, while g is a real path cost from start to goal node. These values can be different.