Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

Asymptotic Notations in Algorithm Analysis

18 Questions

1 Views

Asymptotic Notations in Algorithm Analysis

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which algorithm has the worst time complexity for computing 1+2+...+n?

Algorithm C (correct)

Algorithm B

Algorithm A

The time complexity is the same for all algorithms

In Algorithm B, what is the purpose of the inner loop (for j = n to i)?

To subtract 1 from sum

To perform division operations

To add 1 to sum (correct)

To multiply i by n and add it to sum

Which algorithm provides a closed-form expression for the sum of 1 to n?

Algorithm B

Algorithm A

None of the algorithms

Algorithm C (correct)

What is the purpose of the loop in Algorithm A that runs from 1 to n?

To add 1 to sum each iteration Signup and view all the answers

Which algorithm requires the least number of total operations to compute 1+2+...+n?

Algorithm A Signup and view all the answers

If n is the input size, what is the complexity of Algorithm B in terms of T(n)?

$O(n^2)$ Signup and view all the answers

What is the definition of f(n) = Ω(g(n))?

There exist positive constants c and n0 such that f(n) ≥ c.g(n) for all n ≥ n0 Signup and view all the answers

In Example 2, what is the value of c and n0 used to prove that T(n) = 3n + 2 is an element of Ω(n)?

c = 3, n0 = 1 Signup and view all the answers

What is the relationship between the Θ(g(n)) and O(g(n)) notations?

If f(n) = Θ(g(n)), then f(n) = O(g(n)) and f(n) = Ω(g(n)) Signup and view all the answers

In Example 4, what is the value of c and n0 used to prove that T(n) = 10n^2 + 4n + 2 is an element of O(n^2)?

c = 11, n0 = 5 Signup and view all the answers

What is the purpose of the Ω(g(n)) notation?

To provide a loose lower bound for f(n) in terms of g(n) Signup and view all the answers

In Example 3, what are the values of c1, c2, and n0 used to prove that T(n) = 3n + 2 is an element of Θ(n)?

c1 = 3, c2 = 4, n0 = 2 Signup and view all the answers

How do we prove that $T(n) = \Omega(n^2)$?

We need to find constants $c > 0$ and $n_0 \geq 0$ such that $T(n) \geq c \ n^2$ for all $n \geq n_0$. Signup and view all the answers

For the function $T(n) = 10n^2 + 4n + 2$, what values of $c$ and $n_0$ can be used to prove $T(n) = \Omega(n^2)$?

$c = 1, n_0 = 1$ Signup and view all the answers

What is the Big-Oh time complexity of multiplying two arrays of size $n$?

$O(n^2)$ Signup and view all the answers

What is the best case time complexity of a function $f(n)$, denoted as $\Omega(g(n))$?

The case where $f(n)$ is always greater than or equal to $g(n)$. Signup and view all the answers

For the function $f(n) = 3n^2 + 20$, what values of $c$ and $n_0$ can be used to prove $f(n) = O(n^2)$?

$c = 4, n_0 = 5$ Signup and view all the answers

What is the time complexity of the function $T(n) = 2n + 3$?

$O(n)$ Signup and view all the answers