Does clustered index sort order have impact on performance

Question

If a PK of a table is a standard auto-increment int (Id) and the retrieved and updated records are almost always the ones closer to the max Id will it make any difference performance-wise whether the PK clustered index is sorted as ascending or descending?

When such PK is created, SSMS by default sets the sort order of the index as ascending and since the rows most accessed are always the ones closer to the current max Id, I'm wondering if changing the sorting to descending would speed up the retrieval since the records will be sorted top-down instead of bottom-up and the records close to the top are accessed most frequently.

Answer 1

I don't think there will be any performance hit. Since, it's going to perform a binary search for the index key to access and then the specific data block with that key. Either way, that binary search will hit O(log N) complexity. So in total O(log N) + 1 and since it's clustered index, it actually should be O(log N) time complexity; since the table records are physically ordered instead of having a separate index page/block.