How do we define an admissible heuristic in A$*$ search?

Select one:

A heuristic h$($n$)$

is admissible if it equals the true cost h$($n$)$

from n

to the goal, making it perfectly accurate and eliminating the need for search.

For a heuristic h$($n$)$

to be admissible, it must underestimate the costs for some nodes n

and overestimate for others, balancing out to the true cost h$($n$)$

on average.

An admissible heuristic h$($n$)$

guarantees the fastest path to the goal by aggressively underestimating the true cost h$($n$)$

from each node n

to the goal.

An admissible heuristic h$($n$)$

overestimates, for every node n

$,$ the true cost h$($n$)$

from n

to the goal, ensuring it explores more nodes than necessary.

A heuristic h$($n$)$

is admissible if$,$ for every node n

$,$ h$($n$)<=$h$($n$)$

$,$ where h$($n$)$

is the true cost from n

to the goal.