Big O Notation Revision
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Questions and Answers

What is the time complexity of the given code snippet: int vectorMax(Vector &v) { ... }

  • O(1)
  • O(n) (correct)
  • O(log n)
  • O(n^2)

    • What is the time complexity of the function int nestedLoop1(int n) { ... }

  • O(n)
  • O(n^2) (correct)
  • O(log n)
  • O(n^3)

    • What is the time complexity of the function int nestedLoop2(int n) { ... }

  • O(n)
  • O(n^2)
  • O(n^3) (correct)
  • O(log n)

    • What is the time complexity of the function int binarySearch(int* list, int size, int target) { ... }

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

    What is the Big O notation for the expression 34𝑛³ + 17𝑛 log 𝑛 + 19

    <p>O(n^3)</p> Signup and view all the answers

    Which of the following is an example of exponential time complexity?

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

    What is the main approach to simplifying Big O notation expressions?

    <p>Strip the constants and take the largest term</p> Signup and view all the answers

    Why do we ignore primitive operations when analyzing time complexity?

    <p>Because they have a negligible impact on the overall time complexity</p> Signup and view all the answers

    Study Notes

    Big O Notation Revision

    Complexity Notations

    • O(1) represents constant complexity
    • O(log n) represents logarithmic complexity
    • O(n) represents linear complexity
    • O(n2) represents quadratic complexity
    • O(2n) represents exponential complexity
    • O(nk) (k>=1) represents polynomial complexity, except O(n2)

    Evaluating Big O Notation

    • To evaluate the Big O notation of an expression, strip the constants and find the biggest factor
    • Example: 34𝑛3 + 17𝑛 log 𝑛 + 19 => O (𝑛3)
    • Another example: 𝑛3 + 𝑛 log 𝑛 => O (𝑛3)

    Code Analysis

    VectorMax Function

    • The function has a linear complexity of O(n) because it iterates through the vector once, ignoring primitive operations and taking the worst-case behavior

    Nested Loop Functions

    • The first nested loop function has a quadratic complexity of O(n2) due to the two nested loops
    • The second nested loop function has a polynomial complexity of O(n3) due to the three nested loops
    • The binary search function has a logarithmic complexity of O(log n) because it uses a divide-and-conquer approach

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    Description

    Review and practice Big O notation concepts, including complexity notations and evaluating expressions.

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