69 lines
2.9 KiB
Markdown
69 lines
2.9 KiB
Markdown
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---
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title: Sorting
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TARGET DECK: Obsidian::STEM
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FILE TAGS: algorithm sorting
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tags:
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- algorithm
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- sorting
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---
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## Overview
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Let $n \geq 0$ and $S = \langle a_1, a_2, \ldots, a_n \rangle$ be a sequence. The **sorting problem** refers to permuting **keys** $a_1, a_2, \ldots, a_n$ into a new sequence $\langle a_1', a_2', \ldots, a_n' \rangle$ such that $a_1' \leq a_2' \leq \cdots \leq a_n'$.
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%%ANKI
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Basic
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What makes a sorting algorithm stable?
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Back: "Equal" values are ordered the same in the output as they are in the input.
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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: 1706925787139-->
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END%%
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%%ANKI
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Basic
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What is an in place sorting algorithm?
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Back: One in which only a constant number of input values are ever stored outside the array.
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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: 1706925787146-->
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END%%
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## Structural Comparison
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The #Elixir documentation makes a point that there exist two types of comparisons between data types.[^structural] 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.
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```elixir
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iex> 1 < :atom # structural
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true
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iex> Date.compare(~D[2017-03-31], ~D[2017-04-01]) # semantic
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:lt
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```
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%%ANKI
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Basic
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What are the two types of comparisons made between data types?
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Back: Structural and semantic.
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Reference: “Kernel — Elixir v1.16.1,” accessed February 2, 2024, [https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison](https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison).
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<!--ID: 1706913303147-->
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END%%
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%%ANKI
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Basic
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What is structural comparison of two data types?
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Back: Comparison of the underlying data structures making up data types.
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Reference: “Kernel — Elixir v1.16.1,” accessed February 2, 2024, [https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison](https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison).
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<!--ID: 1706913303155-->
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END%%
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%%ANKI
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Basic
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What is semantic comparison of two data types?
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Back: Comparison made with respect to what the data types represent.
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Reference: “Kernel — Elixir v1.16.1,” accessed February 2, 2024, [https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison](https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison).
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<!--ID: 1706913303160-->
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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).
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* “Kernel — Elixir v1.16.1,” accessed February 2, 2024, [https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison](https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison).
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[^structural]: [Structural Comparison](https://hexdocs.pm/elixir/1.16/Kernel.html#module-structural-comparison)
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