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Discard Key Ranges at Every Level

A B-tree stores sorted keys in balanced levels. The top of the tree is called the root, and the search follows branches down to a leaf that points to the actual data. For example, searching for id = 4200 follows a single path from the root to the matching leaf. Each branch directs the search to a smaller key range, and all leaves remain at the same depth. After finding the first range key, the scan can continue through neighboring leaves in order.

Why does tree height grow slowly as keys are added?