4aa74d9c0b
Defines `mergeSort`, a naive stable merge sort algorithm, replaces it via a `@[csimp]` lemma with something faster at runtime, and proves the following results: * `mergeSort_sorted`: `mergeSort` produces a sorted list. * `mergeSort_perm`: `mergeSort` is a permutation of the input list. * `mergeSort_of_sorted`: `mergeSort` does not change a sorted list. * `mergeSort_cons`: proves `mergeSort le (x :: xs) = l₁ ++ x :: l₂` for some `l₁, l₂` so that `mergeSort le xs = l₁ ++ l₂`, and no `a ∈ l₁` satisfies `le a x`. * `mergeSort_stable`: if `c` is a sorted sublist of `l`, then `c` is still a sublist of `mergeSort le l`.
553 B
553 B
mergeSortBenchmark
Benchmarking List.mergeSort.
Run lake exe mergeSort k to run a benchmark on lists of size k * 10^5.
This reports the average time (in milliseconds) to sort:
- an already sorted list
- a reverse sorted list
- an almost sorted list
- and a random list with duplicates
Run python3 bench.py to run this for k = 1, .., 10, and calculate a best fit
of the model A * k + B * k * log k to the observed runtimes.
(This isn't really what one should do:
fitting a log to data across a single order of magnitude is not helpful.)