Algorithm Complexity: Sorting Algorithm Performance
30 Questions
0 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 is the primary factor that determines the efficiency of a computer system?

  • The amount of memory available
  • The speed of the processor
  • The type of programming language used
  • The quality of the algorithm used (correct)

    • What is the time complexity of the sorting algorithm used on computer A?

  • n
  • n lg n
  • 2n
  • n2 (correct)

    • How much faster is computer A than computer B in terms of raw computing power?

  • 500 times
  • 1000 times (correct)
  • 100 times
  • 2000 times

    • What is the approximate time taken to sort an array of 10 million numbers on computer A?

    <p>More than 5.5 hours</p> Signup and view all the answers

    What is the time complexity of the sorting algorithm used on computer B?

    <p>n lg n</p> Signup and view all the answers

    What is the approximate time taken to sort an array of 10 million numbers on computer B?

    <p>Under 20 minutes</p> Signup and view all the answers

    What is the form of the linear function of n?

    <p>an+b</p> Signup and view all the answers

    Why do we focus on the worst-case running time?

    <p>Because it gives a guaranteed upper bound on the running time</p> Signup and view all the answers

    What happens to the lower-order terms when analyzing the order of growth?

    <p>They are dropped</p> Signup and view all the answers

    What is the order of growth of the worst-case running time of insertion sort?

    <p>n2</p> Signup and view all the answers

    What does the notation Θ(n2) represent?

    <p>The running time grows like n2</p> Signup and view all the answers

    When does the worst-case running time of an algorithm often occur?

    <p>When the item being searched for is not present</p> Signup and view all the answers

    What is the name of the method that involves guessing the form of the solution and then verifying it through induction?

    <p>Substitution method</p> Signup and view all the answers

    What is the purpose of the inductive hypothesis in the substitution method?

    <p>To apply the solution to smaller values</p> Signup and view all the answers

    What is the recurrence equation given in the text?

    <p>T(n) = 4T(n/2) + n</p> Signup and view all the answers

    What is the height of the recursion tree for the recurrence T(n) = 3T(n/4) + cn^2?

    <p>log4n</p> Signup and view all the answers

    What is the purpose of constructing a recursion tree?

    <p>To determine the total cost of all levels of recursion</p> Signup and view all the answers

    What is the sub problem size at depth i in the recursion tree for the recurrence T(n) = 3T(n/4) + cn^2?

    <p>n/4i</p> Signup and view all the answers

    Why do inefficient sorting algorithms like selection sort make redundant comparisons?

    <p>Because their outcome has already been determined by earlier comparisons</p> Signup and view all the answers

    What is the purpose of converting a sorting algorithm into a decision tree?

    <p>To determine the maximum number of comparisons made by the algorithm</p> Signup and view all the answers

    What is the relationship between T(n) and the height of the decision tree?

    <p>The height of the decision tree is equal to T(n)</p> Signup and view all the answers

    What is the maximum number of different final actions that a sorting algorithm can take?

    <p>2T(n)</p> Signup and view all the answers

    What is the purpose of A(n) in the context of sorting algorithms?

    <p>To represent the number of different final actions the algorithm can take</p> Signup and view all the answers

    How many possible actions must any sorting algorithm distinguish between?

    <p>n!</p> Signup and view all the answers

    What is the minimum number of different actions required by an algorithm to sort ndistinct numbers?

    <p>n!</p> Signup and view all the answers

    What is the relationship between A(n) and n! in the context of sorting algorithms?

    <p>A(n) &gt;= n!</p> Signup and view all the answers

    What is the lower bound on the worst-case running time of a comparison-based sorting algorithm?

    <p>n log n</p> Signup and view all the answers

    What is the purpose of Stirling's approximation in the context of sorting algorithms?

    <p>To provide a lower bound on the time complexity</p> Signup and view all the answers

    What is the correct sorted order of the array a = {5, 3, 2, 9}?

    <p>{2, 3, 5, 9}</p> Signup and view all the answers

    What is the generalization of the lower bound on sorting algorithms?

    <p>It can be applied to a number of other problems</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser