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* Introduced InsertionSort algorithm. * Added shared sorting definitions for ascending and descending orders. * Updated MergeSort to reflect changes in sorting definitions.
…ofs for insertionSort
…SectionVars false`
Collaborator
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Note that #275 also contains an insertionSort algorithm. |
eric-wieser
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Feb 24, 2026
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| /-- A list is sorted (ascending/increasing) if it satisfies the `Pairwise (· ≤ ·)` predicate. | ||
| -/ | ||
| abbrev IsSortedAscending (l : List α) : Prop := List.Pairwise (· ≤ ·) l | ||
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| /-- A list is sorted (descending/decreasing) if it satisfies the `Pairwise (· ≥ ·)` predicate. | ||
| -/ | ||
| abbrev IsSortedDescending (l : List α) : Prop := List.Pairwise (· ≥ ·) l | ||
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| /-- A list is strictly sorted (ascending/increasing) | ||
| if it satisfies the `Pairwise (· < ·)` predicate. | ||
| -/ | ||
| abbrev IsStrictlySortedAscending (l : List α) : Prop := List.Pairwise (· < ·) l | ||
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| /-- A list is strictly sorted (descending/decreasing) | ||
| if it satisfies the `Pairwise (· > ·)` predicate. | ||
| -/ | ||
| abbrev IsStrictlySortedDescending (l : List α) : Prop := List.Pairwise (· > ·) l |
Collaborator
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Mathlib already has List.SortedLE and List.SortedGE and List.SortedLT and List.SortedGT for this purpose.
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I would refactor this, thank you for your suggestions. Originally Sorrachai included AscSorted in Merge Sort, hence I think we could bring it to a separated module and extend it with more concepts
Author
My bad for not looking at the PR. Let me check for other PR as well, since there have been people worked on this before me. Edit: I'll be waiting for 275's status. I hope that my proof of best/worst case can still possibly be useful in later updates. |
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Implement the insertion sort algorithm with few changes to existing merge sort code (generalize some parts)