# Copyright (C) 2022 Exaloop Inc. <https://exaloop.io>
# Parts of this file: https://github.com/orlp/pdqsort
# License:
#    Copyright (c) 2021 Orson Peters <orsonpeters@gmail.com>
#
#    This software is provided 'as-is', without any express or implied warranty. In no event will the
#    authors be held liable for any damages arising from the use of this software.
#
#    Permission is granted to anyone to use this software for any purpose, including commercial
#    applications, and to alter it and redistribute it freely, subject to the following restrictions:
#
#    1. The origin of this software must not be misrepresented; you must not claim that you wrote the
#    original software. If you use this software in a product, an acknowledgment in the product
#    documentation would be appreciated but is not required.
#
#    2. Altered source versions must be plainly marked as such, and must not be misrepresented as
#    being the original software.
#
#    3. This notice may not be removed or altered from any source distribution.

def _med3(
    a: int, b: int, c: int, d: Array[T], k: Callable[[T], S], T: type, S: type
) -> int:
    if k(d[a]) < k(d[b]):
        return b if (k(d[b]) < k(d[c])) else (c if k(d[a]) < k(d[c]) else a)
    else:
        return (
            b
            if not (k(d[b]) < k(d[c]) or k(d[b]) == k(d[c]))
            else (c if not (k(d[a]) < k(d[c]) or k(d[a]) == k(d[c])) else a)
        )

def _swap(i: int, j: int, a: Array[T], T: type):
    a[i], a[j] = a[j], a[i]

def _vecswap(i: int, j: int, n: int, a: Array[T], T: type):
    while n > 0:
        _swap(i, j, a)
        i += 1
        j += 1
        n -= 1

def _qsort(
    arr: Array[T], frm: int, cnt: int, key: Callable[[T], S], T: type, S: type
):
    if cnt <= 7:
        i = frm + 1
        while i < frm + cnt:
            j = i
            while j > frm and not (
                key(arr[j - 1]) < key(arr[j]) or key(arr[j - 1]) == key(arr[j])
            ):
                _swap(j, j - 1, arr)
                j -= 1
            i += 1
        return

    mid = cnt // 2
    lo = frm
    hi = frm + cnt - 1

    if cnt > 40:
        s = cnt // 8
        lo = _med3(lo, lo + s, lo + 2 * s, arr, key)
        mid = _med3(mid - s, mid, mid + s, arr, key)
        hi = _med3(hi - 2 * s, hi - s, hi, arr, key)
    mid = _med3(lo, mid, hi, arr, key)

    _swap(frm, mid, arr)
    a = frm
    b = a
    c = frm + cnt - 1
    d = c

    while True:
        while b <= c and (
            key(arr[b]) < key(arr[frm]) or key(arr[b]) == key(arr[frm])
        ):
            if key(arr[b]) == key(arr[frm]):
                _swap(a, b, arr)
                a += 1
            b += 1

        while c >= b and not key(arr[c]) < key(arr[frm]):
            if key(arr[c]) == key(arr[frm]):
                _swap(c, d, arr)
                d -= 1
            c -= 1

        if b > c:
            break
        _swap(b, c, arr)
        b += 1
        c -= 1

    hi = frm + cnt
    span = min(a - frm, b - a)
    _vecswap(frm, b - span, span, arr)

    span = min(d - c, hi - d - 1)
    _vecswap(b, hi - span, span, arr)

    span = b - a
    if span > 1:
        _qsort(arr, frm, span, key)

    span = d - c
    if span > 1:
        _qsort(arr, hi - span, span, key)

def qsort_array(
    collection: Array[T], size: int, key: Callable[[T], S], T: type, S: type
):
    """
    Pattern-defeating Quicksort
    By Orson Peters, published at https://github.com/orlp/pdqsort

    Sorts the array inplace.
    """
    _qsort(collection, 0, size, key)

def qsort_inplace(
    collection: List[T], key: Callable[[T], S], T: type, S: type
):
    """
    Pattern-defeating Quicksort
    By Orson Peters, published at https://github.com/orlp/pdqsort

    Sorts the list inplace.
    """
    qsort_array(collection.arr, collection.len, key)

def qsort(collection: List[T], key: Callable[[T], S], T: type, S: type) -> List[T]:
    """
    Pattern-defeating Quicksort
    By Orson Peters, published at https://github.com/orlp/pdqsort

    Returns a sorted list.
    """
    collection = collection[:]
    qsort_inplace(collection, key)
    return collection
