(definition)

**Definition:**
A theoretical measure of the execution of an *algorithm*, usually the time or memory needed, given the problem size n, which is usually the number of items. Informally, saying some equation f(n) = Θ (g(n)) means it is within a constant multiple of g(n). The equation is read, "f of n is theta g of n".

**Formal Definition:** f(n) = Θ (g(n)) means there are positive constants c_{1}, c_{2}, and k, such that 0 ≤ c_{1}g(n) ≤ f(n) ≤ c_{2}g(n) for all n ≥ k. The values of c_{1}, c_{2}, and k must be fixed for the function f and must not depend on n.

**Also known as** asymptotically tight bound, theta.

**Generalization** (I am a kind of ...)

*big-O notation*.

**See also**
*∼*.

*Note:
This is the upper-case Greek letter Theta.*

Author: PEB

**Donald E. Knuth**, *Big Omicron and Big Omega and Big Theta*, SIGACT News, 8(2):18-24, April-June 1976.

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Entry modified 24 February 2016.

HTML page formatted Tue Feb 12 10:57:42 2019.

Cite this as:

Paul E. Black, "Θ", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 24 February 2016. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/theta.html