```(* get sort from vNS.ml *)

exception Repeated_Vertex;;
exception Logic_error;;
let pe vl = match let rec mpa l th = match l with
[] -> [], []
| (a, b)::c -> if th >= b then raise Repeated_Vertex;
match mpa c b with sl, l -> (b::sl, (ref false, a)::l)
in mpa (sort
(fun x y -> match (x, y) with (_, b), (_, d) -> b < d)
(let rec numr l n = match l with [] -> [] |
a::b -> (n, a)::(numr b (n + 1)) in numr vl 0))
(-1) with svl, spl ->
let ar = Array.of_list spl in
let rec dp i p = if i < 0 then p else let next = dp (i-1) in
match ar.(i) with a, n -> if !a then next (not p) else
let rec lop v = match ar.(v) with w, x ->
if !w then raise Logic_error; w := true;
if v = i then () else lop x in lop n;
next p
in dp (Array.length ar - 1) false, svl;;
(* false is even parity *)

(* test
pe [5; 3; 4; 7; 2];; (* (false, [2; 3; 4; 5; 7]) *)
pe [2; 5; 4; 7; 1];; (* (true, [1; 2; 4; 5; 7]) *)
pe [];; (* (false, []) *)
pe [4];; (* (false, [4]) *)
pe [4; 7];; (* (false, [4; 7]) *)
pe [7; 4];; (* (true, [4; 7]) *)
*)
```