96 lines
3.2 KiB
Markdown
96 lines
3.2 KiB
Markdown
---
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title: Order of Growth
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TARGET DECK: Obsidian::STEM
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FILE TAGS: algorithm::complexity
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tags:
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- algorithm
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- complexity
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---
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## Overview
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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.
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%%ANKI
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Basic
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How is the running time of a program measured as a function?
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Back: As a function of its input size.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707334419352-->
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END%%
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%%ANKI
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Basic
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How do you determine the input size used to measure an algorithm's running time?
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Back: This depends entirely on the specific problem/algorithm.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707334419356-->
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END%%
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%%ANKI
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Basic
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What *concrete* measure is typically used to measure running time?
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Back: The number of primitive operations executed.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707334419359-->
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END%%
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%%ANKI
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Basic
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What *abstract* measure is typically used to measure running time?
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Back: It's order of growth.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707344177499-->
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END%%
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%%ANKI
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Basic
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Why does Cormen et al. state the scope of average-case analysis is limited?
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Back: What constitutes an "average" input isn't always clear.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707334419363-->
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END%%
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%%ANKI
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Basic
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What about running time are algorithm designers mostly interested in?
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Back: It's order of growth.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707344177503-->
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END%%
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%%ANKI
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Basic
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How does order of growth relate to running time?
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Back: Order of growth measures how quickly running time grows with respect to input size.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707344177506-->
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END%%
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%%ANKI
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Basic
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Why are lower-ordered terms ignored when determining order of growth?
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Back: They become less significant as input size grows.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707344177510-->
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END%%
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%%ANKI
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Basic
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Why are leading coefficients ignored when determining order of growth?
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Back: They become less significant as input size grows.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707344177513-->
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END%%
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%%ANKI
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Basic
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Polynomials describing order of growth usually have what two parts ignored?
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Back: Coefficients and lower-ordered terms.
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Reference: Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009).
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<!--ID: 1707344177515-->
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END%%
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## References
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* Thomas H. Cormen et al., *Introduction to Algorithms*, 3rd ed (Cambridge, Mass: MIT Press, 2009). |