4.5 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Sorting | Obsidian::STEM | algorithm::sorting |
|
Overview
Let n \geq 0. The sorting problem refers to permuting records a_1, a_2, \ldots, a_n into a new sequence \langle a_1', a_2', \ldots, a_n' \rangle such that key(a_1') \leq key(a_2') \leq \cdots \leq key(a_n').
%%ANKI Cloze In the sorting problem, a "{record}" refers to {the entries being sorted}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
END%%
%%ANKI Cloze In the sorting problem, a "{key}" refers to {the value records are sorted by}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
END%%
%%ANKI Cloze In the sorting problem, "{satellite data}" refers to {the non-key values of records}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
END%%
%%ANKI Basic What term does Cormen et al. use to describe the record value used for sorting? Back: Keys. Reference: Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
END%%
A few key terms are used to describe properties of sorting algorithms:
- Stability
- An algorithm is stable if values that compare as equal are ordered the same in the output as they are in the input.
- In Place
- An algorithm is in place if only a constant number of input values are ever stored outside the array.
- Adaptive
- An algorithm is adaptive if it takes advantage of existing order in its input.
%%ANKI Basic What makes a sorting algorithm stable? Back: "Equal" values are ordered the same in the output as they are in the input. Reference: Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
END%%
%%ANKI Basic What is an in place sorting algorithm? Back: One in which only a constant number of input values are ever stored outside the array. Reference: Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
END%%
%%ANKI Basic What is an adaptive sorting algorithm? Back: One that takes advantage of existing order in its input. Reference: Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
END%%
Structural Comparison
The #elixir documentation makes a point that there exist two types of comparisons between data types.1 The first is structural in which comparisons are made on the underlying data structures used to describe the data types. The second is semantic which focuses on making the comparison with respect to what the data types represent.
iex> 1 < :atom # structural
true
iex> Date.compare(~D[2017-03-31], ~D[2017-04-01]) # semantic
:lt
%%ANKI Basic What are the two types of comparisons made between data types? Back: Structural and semantic. Reference: “Kernel — Elixir v1.16.1,” accessed February 2, 2024, https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison.
END%%
%%ANKI Basic What is structural comparison of two data types? Back: Comparison of the underlying data structures making up data types. Reference: “Kernel — Elixir v1.16.1,” accessed February 2, 2024, https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison.
END%%
%%ANKI Basic What is semantic comparison of two data types? Back: Comparison made with respect to what the data types represent. Reference: “Kernel — Elixir v1.16.1,” accessed February 2, 2024, https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison.
END%%
Bibliography
- Thomas H. Cormen et al., Introduction to Algorithms, 3rd ed (Cambridge, Mass: MIT Press, 2009).
- “Kernel — Elixir v1.16.1,” accessed February 2, 2024, https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison.