Q: What is different about the two vertices representing
J in
the search tree?
A: One is deeper in the tree than the other.
Recall that h(s) is the heuristic value for any state s in the
search tree.
Let d(s) be the depth of s in the search tree.
Then if we order the priority queue by the key value h(s) + d(s),
state J-as-a-descendant-of-C will be removed from the priority
queue before state J-as-a-descendant-of-B, and the shorter path
will be found first.