How RDBMS B+ Tree Indexing works for Select Query

Question

I learnt that B+ Trees are used for implementing RDBMS , and Now i want to implement an RDBMS in C/C++ , i've read about B+ Trees and also saw the SQLite.

I have a conceptual doubt of how the Search Query works on Database, we store (key,values) on the B+ Tree ,Now say i had a table

with columns {id,name,phone,address}

and i have to search for the record with phone = 'xyz' , how will database use B+ Trees to efficiently get that record.

Is it complete O(N) search on the records or optimized?

Answer 1

It is a complete O ( N ) search if you do not have an index.
It is optimized if you have an index.

Answer 2

Average case O(logb(n))

Worst Cast O(n)

A B+ tree is a blanced tree , it works more like binary search tree specially in MYSQL . its implementation can be varied.