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Big O Notation and Algorithm Efficiency

What Big O notation measures

  • 3 things to know
  • Component 1

Overview

Time complexity, space complexity and worst case of an algorithm.

What you need to know

Answer each one before you reveal it.

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Key term

What does Big O notation describe?

Key term

What does the letter n stand for in an expression such as O(n)?

Key term

Why does Big O ignore constant factors?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What does Big O notation describe?

    Model answer

    Big O notation describes how the resource an algorithm needs grows as the size of its input grows. The measure is the shape of that growth, not an exact count of operations.

  2. 2

    What does the letter n stand for in an expression such as O(n)?

    Model answer

    The letter n stands for the size of the input, such as the number of items in a list. Complexity is always stated in terms of that size.

  3. 3

    Why does Big O ignore constant factors?

    Model answer

    A constant factor does not change the shape of the growth. An algorithm taking 3n steps and one taking 100n steps are both written O(n).

  4. 4

    Why are lower-order terms dropped from a Big O expression?

    Model answer

    The highest-order term dominates the total once n is large. An algorithm taking n² + 5n + 20 steps is written O(n²).

  5. 5

    Define time complexity.

    Model answer

    Time complexity is the way the number of operations an algorithm performs grows with the size of its input.

  6. 6

    Define space complexity.

    Model answer

    Space complexity is the way the extra memory an algorithm needs grows with the size of its input.

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