In a game playing search tree, upto which depth $\alpha-\beta$ pruning can be applied?

(A) Root $(0)$ level

(B) $6$ level

(C) $8$ level

(D) Depends on utility value in a breadth first order

Choose the correct answer from the options given below:

$\alpha-\beta$ pruning is an optimization technique used with the minimax algorithm in game playing search trees.

It can be applied at any depth of the game tree.

It is not restricted to only one particular level.

Now check each statement:

(A) Root $(0)$ level

At the root level, $\alpha$ and $\beta$ values are initialized and the search starts from this level.

So, $\alpha-\beta$ pruning can be applied from root level.

Therefore, statement (A) is correct.

(B) $6$ level

If the game tree is searched up to depth $6$, then $\alpha-\beta$ pruning can be applied up to level $6$.

Therefore, statement (B) is correct.

(C) $8$ level

Similarly, if the game tree is searched up to depth $8$, then $\alpha-\beta$ pruning can also be applied up to level $8$.

Therefore, statement (C) is correct.

(D) Depends on utility value in a breadth first order

This is incorrect because $\alpha-\beta$ pruning is normally applied using depth first search, not breadth first search.

It depends on $\alpha$ and $\beta$ values during depth first minimax search.

Therefore, only (A), (B) and (C) are correct.