Question

Which notation represents the tightest upper bound of an algorithm’s running time?

• A. O(n)
• B. \(\Omega(n)\)
• C. \(\Theta(n)\)
• D. \(\omega(n)\)

Hint:

When analyzing algorithm performance, \(\Theta(n)\) gives the most precise estimate of both upper and lower bounds.

Answer 1

The Correct Option is C

The \(\Theta(n)\) notation represents the tightest upper bound of an algorithm's running time. It provides both an upper and lower bound, making it the most accurate representation of an algorithm’s performance. Other notations like \(O(n)\) and \(\Omega(n)\) give only an upper or lower bound, not both. \(\omega(n)\) is used for the lower bound in the asymptotic analysis context, but it is not the tightest bound.