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// (c) Microsoft Corporation 2005-2009.
namespace Microsoft.FSharp.Math
type Permutation = int -> int
type permutation = int -> int
[<RequireQualifiedAccess>]
[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]
module Permutation =
let invalidArg arg msg = raise (new System.ArgumentException((msg:string),(arg:string)))
let ofFreshArray (arr:_[]) =
let arr2 = Array.zeroCreate arr.Length
for i = 0 to arr.Length - 1 do
let x = arr.[i]
if x < 0 || x >= arr.Length then invalidArg "arr" "invalid permutation"
arr2.[x] <- 1
for i = 0 to arr.Length - 1 do
if arr2.[i] <> 1 then invalidArg "arr" "invalid permutation"
(fun k -> arr.[k])
let ofArray (arr:_[]) = arr |> Array.copy |> ofFreshArray
let of_array (arr:_[]) = ofArray arr
let ofPairs (mappings: seq<int * int>) =
let p = dict mappings
(fun k -> if p.ContainsKey k then p.[k] else k)
let of_pairs (mappings: seq<int * int>) = ofPairs mappings
let swap (n:int) (m:int) =
(fun k -> if k = n then m elif k = m then n else k)
let reversal size =
if size <= 0 then invalidArg "size" "a permutation size must be positive";
(fun k -> (size - 1 - k))
let rotation size distance =
if size <= 0 then invalidArg "size" "a permutation size must be positive";
if abs distance >= size then invalidArg "distance" "the absolute value of the distance must be less than the size of the permutation";
(fun k -> (k + size + distance) % size)
let identity (k:int) = k
let inverse size p =
if size <= 0 then invalidArg "size" "a permutation size must be positive";
let arr2 = Array.zeroCreate size
for i = 0 to size - 1 do
arr2.[p i] <- i
ofFreshArray arr2
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