🗄️ Database Index Page-I/O Lab: B+ Tree Height, Hash Probes and the Index-vs-Scan Crossover

Build a live B+ tree key by key and watch node splits, then scale the same cost model to millions of rows: tree height from fanout, cache effects on page reads, hash-index probe counts and the selectivity at which a sequential scan beats an index. Includes independent checks against a measured tree and hash table.