What is the difference between lower bound and tight bound?

Question

With the reference of this answer, what is Theta (tight bound)?

Omega is lower bound, quite understood, the minimum time an algorithm may take. And we know Big-O is

Answer 1

Θ-notation (theta notation) is called tight-bound because it's more precise than O-notation and Ω-notation (omega notation).

If I were lazy, I could say that binary search on a sorted array is O(n²), O(n³), and O(2ⁿ), and I would be technically correct in every case. That's because O-notation only specifies an upper bound, and binary search is bounded on the high side by all of those functions, just not very closely. These lazy estimates would be useless.

Θ-notation solves this problem by combining O-notation and Ω-notation. If I say that binary search is Θ(log n), that gives you more precise information. It tells you that the algorithm is bounded on both sides by the given function, so it will never be significantly faster or slower than stated.