--- title: Order of Growth TARGET DECK: Obsidian::STEM FILE TAGS: algorithm::complexity tags: - algorithm - complexity --- ## Overview The **running time** of an algorithm is usually considered as a function of its **input size**. How input size is measured depends on the problem at hand. For instance, [[algorithms/sorting/index|sorting]] algorithms have an input size corresponding to the number of elements to sort. %%ANKI Basic How is the running time of a program measured as a function? Back: As a function of its input size. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic How do you determine the input size used to measure an algorithm's running time? Back: This depends entirely on the specific problem/algorithm. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic What *concrete* measure is typically used to measure running time? Back: The number of primitive operations executed. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic What *abstract* measure is typically used to measure running time? Back: It's order of growth. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic Why does Cormen et al. state the scope of average-case analysis is limited? Back: What constitutes an "average" input isn't always clear. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic What about running time are algorithm designers mostly interested in? Back: It's order of growth. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic How does order of growth relate to running time? Back: Order of growth measures how quickly running time grows with respect to input size. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic Why are lower-ordered terms ignored when determining order of growth? Back: They become less significant as input size grows. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic Why are leading coefficients ignored when determining order of growth? Back: They become less significant as input size grows. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% %%ANKI Basic Polynomials describing order of growth usually have what two parts ignored? Back: Coefficients and lower-ordered terms. Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). END%% ## References * Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).