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 $key(a_1') \leq key(a_2') \leq \cdots \leq key(a_n')$.
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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).
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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).
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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).
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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).
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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.
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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).
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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).
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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).
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## Structural Comparison
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.
