L2 03 Understanding Big O, Omega, and Theta Notations

Big O

____ describes the Upper bound on algorithm running time, indicating the worst-case scenario as the input size grows large.

Big Omega

____ describes the Lower bound on algorithm running time, indicating the best-case scenario as the input size grows large.

Theta

____ describes the Both upper and lower bounds on running time.

Asymptotic Notation

____ describes the growth rates of functions.

Upper Bound

____ describes the Maximum growth rate as input size increases.

Lower Bound

____ describes the Minimum growth rate as input size increases.

Quadratic Growth

Growth proportional to n squared.

Constant Factor

A fixed multiplier in growth rate.

Worst Case

Maximum running time scenario for an algorithm.

Running Time

Time taken by an algorithm to complete.

Memory Usage

Amount of memory consumed by an algorithm.

Polynomial Expression

Mathematical expression involving powers of variables.

Irrelevant Terms

Lower order terms that do not affect growth.

Growth Rate

Speed at which a function increases.

Algorithm Analysis

Study of algorithm efficiency and performance.

Constant Time

O(1) complexity; independent of input size.

Cubic Growth

Growth proportional to n cubed.

Asymptotic Growth

Behavior of functions as input size approaches infinity.

Vague Description

Ambiguous characterization of algorithm performance.

Precise Description

Clear and specific characterization of performance.

Placeholder Notation

Simplifies expressions by omitting lower order terms.

Relationship Analogy

Using asymptotic terms to describe affection.

How can you informally think of Big O, Big Omega, and Theta?

Big O is "less than or equal," Big Omega is "greater than or equal," and Theta is "equal" in terms of asymptotic growth rates.

What is the difference between saying an algorithm is O(n^2) and Theta(n^2)?

O(n^2) indicates that the running time is at most proportional to n^2, while Theta(n^2) confirms that the running time is exactly proportional to n^2 in the worst case.

What does it mean if an algorithm uses Big Omega(n^2) memory?

It means that the memory usage grows at least quadratically with the input size, indicating a substantial rate of memory growth.

How is asymptotic notation used in mathematical expressions?

Asymptotic notation can simplify expressions by hiding lower-order terms, making it easier to analyze the growth of functions.

Why is it important to use Theta notation when possible?

Using Theta notation provides more precise information about the algorithm's performance, as it indicates both upper and lower bounds.