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Alpha beta search time complexity

I understand the basics of minimax and alpha beta cropping. Throughout the literature, they talk about time complexity for the best case: O (b ^ (d / 2)), where b = branching coefficient and d = tree depth, and the base case - when all the preferred nodes are first expanded.

In my “best case” example, I have a binary tree of 4 levels, so out of 16 terminal nodes I need to deploy no more than 7 nodes. How does this relate to O (b ^ (d / 2))?

I do not understand how they reach O (b ^ (d / 2)).

Please, can someone explain this to me? Thats a lot!

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O (b ^ (d/2)) --. :

( ) b d , node, ( ) O (bb... * b) = O (b ^ d) - , . ( , ), node O (b * 1 * b * 1 *... * b) O (b * 1 * b * 1 *... * 1) , O (b ^ (d/2)). , , , , , .

b * 1 * b * 1 *... , , , - , , ( ) - - , .

, "" :

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O , , O (b ^ (d/2)) b d .

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