A* (and Dijkstra) are designed in a way that the very first solution found is the best.
Correct; but this doesn't apply to the bidirectional variants of either algorithm. The last scanned node of the first complete path needn't be on a global optimal path at all. Instead, once those path trees ...

kovarex wrote:
In the next example, the first solution found is not optimal, as the curves can be straightened, so extra steps of the algorithm is needed to find a better solution.

I take it the heuristic function is not quite admissible (i.e., the cost-to-goal estimate can sometimes be slightly ...