Sorting algorithms/Permutation sort
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Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
Permutation sort.
Pseudocode:
while not InOrder(list) do nextPermutation(list);
C++
Since next_permutation already returns whether the resulting sequence is sorted, the code is quite simple:
<lang cpp>
- include <algorithm>
template<typename ForwardIterator>
void permutation_sort(ForwardIterator begin, ForwardIterator end)
{
while (std::next_permutation(begin, end))
{
// -- this block intentionally left empty --
}
} </lang>
D
<lang d>module permsort ; import std.stdio ;
bool isSorted(T)(inout T[] a) { // test if a is already sorted
if(a.length <= 1) return true ; // 1-elemented/empty array is defined as sorted for(int i = 1 ; i < a.length ; i++) if(a[i] < a[i-1]) return false ; return true ;
}
Permutator!(T) Perm(T)(T[] x) { return Permutator!(T)(x) ; } struct Permutator(T) { // permutation iterator
T[] s ;
alias int delegate(inout T[]) DG ;
void swap(int i, int j) { T tmp = s[i] ; s[i] = s[j] ; s[j] = tmp ; }
int opApply(DG dg) { return perm(0, s.length, dg) ; }
int perm(int breaked, int n, DG dg) {
if(breaked) return breaked ;
else if(n <= 1) breaked = dg(s) ;
else {
for(int i = 0 ; i < n ; i++) {
if((breaked = perm(breaked, n - 1, dg)) != 0) break ;
if(0 == (n % 2)) swap(i, n-1) ; else swap(0, n-1) ;
}
}
return breaked ;
}
}
T[] permsort(T)(T[] s) {
foreach( p ; Perm(s))
if(isSorted(p))
return p.dup ;
assert(false, "Should not be here") ;
}
void main() {
auto p = [2,7,4,3,5,1,0,9,8,6] ;
writefln("%s", permsort(p)) ;
writefln("%s", p) ; // sort is in place
writefln("%s", permsort(["rosetta"])) ; // test with one element
writefln("%s", permsort(cast(int[])[])) ; // test empty array
}</lang>
Haskell
<lang Haskell> import Control.Monad
permutationSort l = head [p | p <- permute l, sorted p]
sorted (e1 : e2 : r) = e1 <= e2 && sorted (e2 : r) sorted _ = True
permute = foldM (flip insert) []
insert e [] = return [e] insert e l@(h : t) = return (e : l) `mplus`
do { t' <- insert e t ; return (h : t') }
</lang>
Icon
Partly from here <lang icon>procedure do_permute(l, i, n)
if i >= n then
return l
else
suspend l[i to n] <-> l[i] & do_permute(l, i+1, n)
end
procedure permute(l)
suspend do_permute(l, 1, *l)
end
procedure sorted(l)
local i
if (i := 2 to *l & l[i] >= l[i-1]) then return &fail else return 1
end
procedure main()
local l
l := [6,3,4,5,1]
|( l := permute(l) & sorted(l)) \1 & every writes(" ",!l)
end</lang>
OCaml
Like the Haskell version, except not evaluated lazily. So it always computes all the permutations, before searching through them for a sorted one; which is more expensive than necessary; unlike the Haskell version, which stops generating at the first sorted permutation. <lang ocaml>let rec sorted = function
| e1 :: e2 :: r -> e1 <= e2 && sorted (e2 :: r) | _ -> true
let rec insert e = function
| [] -> e | h :: t as l -> (e :: l) :: List.map (fun t' -> h :: t') (insert e t)
let permute xs = List.fold_right (fun h z -> List.concat (List.map (insert h) z))
xs [[]]
let permutation_sort l = List.find sorted (permute l)</lang>
Prolog
<lang prolog>permutation_sort(L,S) :- permutation(L,S), sorted(S).
sorted([]). sorted([_]). sorted([X,Y|ZS]) :- X =< Y, sorted([Y|ZS]).
permutation([],[]). permutation([X|XS],YS) :- permutation(XS,ZS), select(X,YS,ZS).</lang>
Python
<lang python>from itertools import permutations
in_order = lambda s: all(x <= s[i+1] for i,x in enumerate(s[:-1])) perm_sort = lambda s: (p for p in permutations(s) if in_order(p)).next()</lang>
Scheme
<lang scheme> (define (insertions e list)
(if (null? list)
(cons (cons e list) list)
(cons (cons e list)
(map (lambda (tail) (cons (car list) tail))
(insertions e (cdr list))))))
(define (permutations list)
(if (null? list)
(cons list list)
(apply append (map (lambda (permutation)
(insertions (car list) permutation))
(permutations (cdr list))))))
(define (sorted? list)
(cond ((null? list) #t)
((null? (cdr list)) #t)
((<= (car list) (cadr list)) (sorted? (cdr list)))
(else #f)))
(define (permutation-sort list)
(let loop ((permutations (permutations list)))
(if (sorted? (car permutations))
(car permutations)
(loop (cdr permutations)))))
</lang>
Tcl
using package struct::list form
. The firstperm procedure returns the lexicographically first permutation of the input list.
<lang tcl>package require struct::list
proc permutationsort {list} {
return [struct::list firstperm $list]
}</lang>