Midterm Quick Review 1: Main Topics in Algorithms and Proofs
18 Questions
1 Views

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

What type of running time does O(n log n) denote?

  • Logarithmic
  • Log-linear (correct)
  • Exponential
  • Linear

    • In the context of big-O notation, what does O(1) denote?

  • Constant running time (correct)
  • Logarithmic running time
  • Exponential running time
  • Linear running time

    • What type of input size does O(n^2) represent in terms of running time?

  • Exponential
  • Logarithmic
  • Quadratic (correct)
  • Linear

    • If a function has a complexity of O(n), what is the order of growth for this function?

    <p>Linear</p> Signup and view all the answers

    What is the best case scenario for finding an element in a list?

    <p>Minimum running time</p> Signup and view all the answers

    How are elements added to or removed from a stack?

    <p>Only at the top end</p> Signup and view all the answers

    What is the purpose of an algorithm?

    <p>To map inputs to outputs</p> Signup and view all the answers

    Which statement best describes Big-O notation?

    <p>It represents the worst-case runtime behavior of an algorithm.</p> Signup and view all the answers

    What is the exponential form of log3(27) = 3?

    <p>3^3 = 27</p> Signup and view all the answers

    In evaluating log6(36) = x, what is the value of x?

    <p>2</p> Signup and view all the answers

    Which statement accurately reflects the relationship between algorithms and programs?

    <p>A program is a specific implementation of an algorithm in a programming language.</p> Signup and view all the answers

    What does Big-Theta notation classify?

    <p>The exact growth rate of a function within constant factors</p> Signup and view all the answers

    What does it mean when f(x) is O(g(x)) in Big-O notation?

    <p>g(x) is an upper bound for f(x)</p> Signup and view all the answers

    In Big-Omega notation, what does f(x) being Ω(g(x)) imply?

    <p>g(x) is a lower bound for f(x)</p> Signup and view all the answers

    When f(x) is θ(g(x)), what relationship exists between the growth rates of f(x) and g(x)?

    <p>f(x) is a tight lower bound and a tight upper bound for g(x)</p> Signup and view all the answers

    How is a direct proof useful in mathematics?

    <p>To demonstrate the validity of a claim using logical reasoning</p> Signup and view all the answers

    What is the goal of Proof by Induction in mathematics?

    <p>To prove that something is true for all natural numbers</p> Signup and view all the answers

    How do Big-Oh, Big-Omega, and Big-Theta notations help analyze algorithms?

    <p>By providing insights into the runtime efficiency of algorithms</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser