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The quicksort algorithm in Haskell
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$begingroup$
I am learning Haskell programming language mainly from this source. And there I have encouraged with "an elegant" realization of the quicksort sorting algorithm (the Quick, sort! section). Here it is:
Book's implementation
quicksort :: ( Ord a ) = > [ a ] -> [ a ]
quicksort [] = []
quicksort ( x : xs ) =
let smallerSorted = quicksort [ a | a <- xs , a <= x ]
biggerSorted = quicksort [ a | a <- xs , a > x ]
in smallerSorted ++ [ x ] ++ biggerSorted
The problem with this implementation (as I think) is doubled number of comparisons inside the let binding every time. Isn't the fact that those of a's that already in the smallerSorted list cannot be in the biggerSorted list, so we don't need to compare x with them anymore.
In order to "improve" the above approach I have written my own implementation, where I use auxiliary local function split that splits a list into two parts: less than (or equal to) x and greater than x.
My implementation
quick_sort :: (Ord a) => [a] -> [a]
quick_sort [] = [] --edge condition
quick_sort (x : xs) = --general condition
let (lt, gt) = split x xs
in (quick_sort lt) ++ [x] ++ (quick_sort gt)
where
--split function is used to split a list
--into two sublists: one for elements
--less or equal (lt) than some value - x
--and one for those that greater (gt) than x
--NOTE: split function is also recursive
split x [] = ([], []) --edge condition
split x (h : hs) --general condition
| h <= x =
let (lt, gt) = split x hs
in ( (h : lt), gt )
| otherwise =
let (lt, gt) = split x hs
in ( lt, (h : gt) )
P.S.
For a while I am not able to compare two approaches, but on the worst cases (when list to sort is already sorted) it seems that my implementation is a bit slower.
sorting haskell recursion complexity
asked yesterday
LRDPRDXLRDPRDX
2346
$endgroup$
add a comment |
$begingroup$
I am learning Haskell programming language mainly from this source. And there I have encouraged with "an elegant" realization of the quicksort sorting algorithm (the Quick, sort! section). Here it is:
Book's implementation
quicksort :: ( Ord a ) = > [ a ] -> [ a ]
quicksort [] = []
quicksort ( x : xs ) =
let smallerSorted = quicksort [ a | a <- xs , a <= x ]
biggerSorted = quicksort [ a | a <- xs , a > x ]
in smallerSorted ++ [ x ] ++ biggerSorted
The problem with this implementation (as I think) is doubled number of comparisons inside the let binding every time. Isn't the fact that those of a's that already in the smallerSorted list cannot be in the biggerSorted list, so we don't need to compare x with them anymore.
In order to "improve" the above approach I have written my own implementation, where I use auxiliary local function split that splits a list into two parts: less than (or equal to) x and greater than x.
My implementation
quick_sort :: (Ord a) => [a] -> [a]
quick_sort [] = [] --edge condition
quick_sort (x : xs) = --general condition
let (lt, gt) = split x xs
in (quick_sort lt) ++ [x] ++ (quick_sort gt)
where
--split function is used to split a list
--into two sublists: one for elements
--less or equal (lt) than some value - x
--and one for those that greater (gt) than x
--NOTE: split function is also recursive
split x [] = ([], []) --edge condition
split x (h : hs) --general condition
| h <= x =
let (lt, gt) = split x hs
in ( (h : lt), gt )
| otherwise =
let (lt, gt) = split x hs
in ( lt, (h : gt) )
P.S.
For a while I am not able to compare two approaches, but on the worst cases (when list to sort is already sorted) it seems that my implementation is a bit slower.
sorting haskell recursion complexity
asked yesterday
LRDPRDXLRDPRDX
2346
$endgroup$
add a comment |
$begingroup$
I am learning Haskell programming language mainly from this source. And there I have encouraged with "an elegant" realization of the quicksort sorting algorithm (the Quick, sort! section). Here it is:
Book's implementation
quicksort :: ( Ord a ) = > [ a ] -> [ a ]
quicksort [] = []
quicksort ( x : xs ) =
let smallerSorted = quicksort [ a | a <- xs , a <= x ]
biggerSorted = quicksort [ a | a <- xs , a > x ]
in smallerSorted ++ [ x ] ++ biggerSorted
The problem with this implementation (as I think) is doubled number of comparisons inside the let binding every time. Isn't the fact that those of a's that already in the smallerSorted list cannot be in the biggerSorted list, so we don't need to compare x with them anymore.
In order to "improve" the above approach I have written my own implementation, where I use auxiliary local function split that splits a list into two parts: less than (or equal to) x and greater than x.
My implementation
quick_sort :: (Ord a) => [a] -> [a]
quick_sort [] = [] --edge condition
quick_sort (x : xs) = --general condition
let (lt, gt) = split x xs
in (quick_sort lt) ++ [x] ++ (quick_sort gt)
where
--split function is used to split a list
--into two sublists: one for elements
--less or equal (lt) than some value - x
--and one for those that greater (gt) than x
--NOTE: split function is also recursive
split x [] = ([], []) --edge condition
split x (h : hs) --general condition
| h <= x =
let (lt, gt) = split x hs
in ( (h : lt), gt )
| otherwise =
let (lt, gt) = split x hs
in ( lt, (h : gt) )
P.S.
For a while I am not able to compare two approaches, but on the worst cases (when list to sort is already sorted) it seems that my implementation is a bit slower.
sorting haskell recursion complexity
asked yesterday
LRDPRDXLRDPRDX
2346
$endgroup$
I am learning Haskell programming language mainly from this source. And there I have encouraged with "an elegant" realization of the quicksort sorting algorithm (the Quick, sort! section). Here it is:
Book's implementation
quicksort :: ( Ord a ) = > [ a ] -> [ a ]
quicksort [] = []
quicksort ( x : xs ) =
let smallerSorted = quicksort [ a | a <- xs , a <= x ]
biggerSorted = quicksort [ a | a <- xs , a > x ]
in smallerSorted ++ [ x ] ++ biggerSorted
The problem with this implementation (as I think) is doubled number of comparisons inside the let binding every time. Isn't the fact that those of a's that already in the smallerSorted list cannot be in the biggerSorted list, so we don't need to compare x with them anymore.
In order to "improve" the above approach I have written my own implementation, where I use auxiliary local function split that splits a list into two parts: less than (or equal to) x and greater than x.
My implementation
quick_sort :: (Ord a) => [a] -> [a]
quick_sort [] = [] --edge condition
quick_sort (x : xs) = --general condition
let (lt, gt) = split x xs
in (quick_sort lt) ++ [x] ++ (quick_sort gt)
where
--split function is used to split a list
--into two sublists: one for elements
--less or equal (lt) than some value - x
--and one for those that greater (gt) than x
--NOTE: split function is also recursive
split x [] = ([], []) --edge condition
split x (h : hs) --general condition
| h <= x =
let (lt, gt) = split x hs
in ( (h : lt), gt )
| otherwise =
let (lt, gt) = split x hs
in ( lt, (h : gt) )
P.S.
For a while I am not able to compare two approaches, but on the worst cases (when list to sort is already sorted) it seems that my implementation is a bit slower.
sorting haskell recursion complexity
sorting haskell recursion complexity
asked yesterday
LRDPRDXLRDPRDX
2346
asked yesterday
LRDPRDXLRDPRDX
2346
asked yesterday
LRDPRDXLRDPRDX
2346
asked yesterday
LRDPRDXLRDPRDX
2346
asked yesterday
LRDPRDXLRDPRDX
2346
2346
add a comment |
add a comment |
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