A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator obey two of the properties of a total order:
- if a ≤ b and b ≤ c then a ≤ c (transitivity)
- for all a and b, either a ≤ b or b ≤ a (totalness or trichotomy).
It is possible that both a ≤ b and b ≤ a; in this case either may come first in the sorted list. In a stable sort, the input order determines the sorted order in this case.
A metaphor for thinking about comparison sorts is that someone has a set of unlabelled weights and a balance scale. Their goal is to line up the weights in order by their weight without any information except that obtained by placing two weights on the scale and seeing which one is heavier (or if they weigh the same).
Read more about Comparison Sort: Examples, Performance Limits and Advantages of Different Sorting Techniques, Number of Comparisons Required To Sort A List
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“Envy and jealousy are the private parts of the human soul. Perhaps the comparison can be extended.”
—Friedrich Nietzsche (1844–1900)
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That’s all. Of course, there may be some sort of sequel but it is not known to me. In such cases instead of getting bogged down in guesswork, I repeat the words of the merry king in my favorite fairy tale: Which arrow flies for ever? The arrow that has hit its mark.”
—Vladimir Nabokov (1899–1977)