Algorithm Analysis Quiz
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Questions and Answers

What is the goal of analysis of algorithms?

  • To compare algorithms based solely on the number of statements executed
  • To compare algorithms mainly in terms of running time but also in terms of other factors (correct)
  • To compare algorithms only in terms of memory requirements
  • To compare algorithms based on the size of the input

    • What does running time analysis determine?

  • How running time increases as the size of the problem increases (correct)
  • The prediction about the running time for random inputs
  • The absolute guarantee that the algorithm would not run longer
  • The lower bound on running time

    • What does worst case analysis provide?

  • A prediction about the running time for random inputs
  • An upper bound on running time (correct)
  • An absolute guarantee that the algorithm would not run longer
  • A lower bound on running time

    • What does best case analysis provide?

    <p>A lower bound on running time</p> Signup and view all the answers

    How do we compare algorithms?

    <p>By defining a number of objective measures, including comparing execution times</p> Signup and view all the answers

    What is a recurrence in the context of algorithms?

    <p>An equation or inequality that describes a function in terms of its value on smaller inputs</p> Signup and view all the answers

    What is the running time of an algorithm with the recurrence $T(n) = T(n-1) + n$?

    <p>$\Theta(n^2)$</p> Signup and view all the answers

    What is the running time of an algorithm with the recurrence $T(n) = T(n/2) + c$?

    <p>$\Theta(\log n)$</p> Signup and view all the answers

    What is the running time of an algorithm with the recurrence $T(n) = T(n/2) + n$?

    <p>$\Theta(n)$</p> Signup and view all the answers

    What is the running time of an algorithm with the recurrence $T(n) = 2T(n/2) + 1$?

    <p>$\Theta(n)$</p> Signup and view all the answers

    Study Notes

    Analysis of Algorithms

    • The goal of analysis of algorithms is to determine their efficiency and scalability.

    Running Time Analysis

    • Running time analysis determines how long an algorithm takes to complete, usually measured in terms of the number of basic operations performed.

    Worst Case Analysis

    • Worst case analysis provides an upper bound on the running time of an algorithm, which is the maximum amount of time it takes to complete in the worst possible scenario.

    Best Case Analysis

    • Best case analysis provides a lower bound on the running time of an algorithm, which is the minimum amount of time it takes to complete in the best possible scenario.

    Comparing Algorithms

    • Algorithms are compared based on their time and space complexities, which are measured in terms of the size of the input.

    Recurrence in Algorithms

    • A recurrence in the context of algorithms is a mathematical equation that describes the running time of an algorithm, usually involving the running time of smaller instances of the same problem.

    Running Time of Algorithms

    • An algorithm with the recurrence $T(n) = T(n-1) + n$ has a running time of O(n^2).
    • An algorithm with the recurrence $T(n) = T(n/2) + c$ has a running time of O(log n).
    • An algorithm with the recurrence $T(n) = T(n/2) + n$ has a running time of O(n log n).
    • An algorithm with the recurrence $T(n) = 2T(n/2) + 1$ has a running time of O(n).

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    Description

    Test your understanding of algorithm analysis with this quiz on asymptotic analysis. Explore the goal of analyzing algorithms and comparing them based on factors like running time, memory requirements, and programmer effort.

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