Re: [Haskell-cafe] Where is "minimumsBy"?

28 Sep 2018

      You can read a recent implementation of sortBy at
https://github.com/ghc/ghc/blob/ghc-8.6.1-release/libraries/base/Data/OldLis...

It often helps to work with a concrete example, such as:

head (sort [5, 4, 6, 3, 7, 1])

Expanding that a bit we get:

head (mergeAll (sequences [5, 4, 6, 3, 7, 1]))

sequences is linear time, it breaks the list up into monotonically
increasing sublists (up to n/2 of them) with pairwise comparisons. It
doesn't all get evaluated right away, but nothing "interesting" is
happening there so let's show it fully evaluated.

head (mergeAll [[4, 5], [3, 6], [1, 7]])

Expanding that we get

head (mergeAll (mergePairs [[4, 5], [3, 6], [1, 7]])))
head (mergeAll (merge [4, 5] [3, 6] : [1, 7] : []))
head (mergeAll (mergePairs (merge [4, 5] [3, 6] : [1, 7] : [])))
head (mergeAll (merge (merge [4, 5] [3, 6]) [1, 7] : [])))
head (merge (merge [4, 5] [3, 6]) [1, 7])
head (merge (3 : merge [4, 5] [6]) [1, 7])
head (1 : merge (3 : merge [4, 5] [6]) [7])
1

This phase is linear time in the worst case, we only compare the first
element of each sublist once to find the least element. Having a constant
number of phases that are linear (two in this case) is still linear. It
would be linearithmic time if we were to fully evaluate the whole sort, but
laziness gets to leave a lot of that work unevaluated.

-bob

On Thu, Sep 27, 2018 at 10:16 PM Christian Sternagel 
wrote:
...
That is interesting. Is anybody aware of a more detailed justification
of how lazy evaluation makes this happen? - chris
On 09/26/2018 11:38 PM, Bob Ippolito wrote:
...
Haskell’s sort algorithm is linear complexity when only evaluating the
front of the list. See also
https://ro-che.info/articles/2016-04-02-descending-sort-haskell which
includes some measurements.
On Wed, Sep 26, 2018 at 10:30 David Feuer mailto:david.feuer@gmail.com> wrote:
Laziness does not make the complexity work out fine. Sorting is
    still O(n log n), which isn't needed here.
On Wed, Sep 26, 2018, 10:22 AM Tom Ellis
    mailto:tom-lists-haskell-cafe-2017@jaguarpaw.co.uk> wrote:
Hopefully laziness makes the complexity work out fine.
        Nonetheless I don't
        like relying on laziness for the correct complexity and it would
        still be
        nice to have an explicit version.
On Wed, Sep 26, 2018 at 10:13:21AM -0400, Brandon Allbery wrote:
        > Not exactly that, but you can use groupBy fst . sort, then the
        head of the
        > result list is your "minimumsBy" result.
        >
        > On Wed, Sep 26, 2018 at 6:28 AM Tom Ellis <
        > tom-lists-haskell-cafe-2017@jaguarpaw.co.uk
        mailto:tom-lists-haskell-cafe-2017@jaguarpaw.co.uk> wrote:
        > > Data.List.minimumBy :: Foldable t => (a -> a -> Ordering) ->
        t a -> a
        > >
        > >
        > >
https://www.stackage.org/haddock/lts-12.1/base-4.11.1.0/Data-List.html#v:min...
...
> >
        > > but there are many cases where that's quite unhelpful.
        Actually what we
        > > want is more like
        > >
        > >     minimumsBy :: ... => (a -> a -> Ordering) -> t a -> [a]
        > >
        > > There can be many distinct minimizers.  For example when I
        want to get the
        > > collection of the youngest people from [(Age, Person)] I want
        > >
        > >     minimumsBy (compare `on` fst) [(12, alice), (15,
        balaji), (12, cho)]
        > >
        > > to return
        > >
        > >     [(12, alice), (12, cho)]
        > >
        > > Does "minimumsBy" exist somewhere reasonably standard?
        Hoogle doesn't
        > > throw
        > > up anything obvious
        > >
        > >
        > >
https://www.stackage.org/lts-12.1/hoogle?q=%28a+-%3E+a+-%3E+Ordering%29+-%3E...
...
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