How can I sort multiple arrays based on the sorted order of another array

I have multiple arrays, and I want to sort all of them based on the sorted order of one of them, like so:

var myArr = ["b", "a", "c"]
var myArr2 = ["letter b", "letter a", "letter c"]
var myArr3 = ["b is the second letter", "a is the first letter", "c is the third letter"]

func sortMultipleArraysBasedOnOne(alphabeticallyArray:Array, arrays:[Array]){
  //order myArr alphabetically
  for array in arrays{
    //change all arrays indexes like in myArr
  }
}

sortMultipleArraysBasedOnOne(myArr, [myArr2, myArr3])

I expect after function execution the arrays will be like this:

myArr = ["a", "b", "c"]
myArr2 = ["letter a", "letter b", "letter c"]
myArr3 = ["a is the first letter", "b is the second letter", "c is the third letter"]

You can do this by first sorting an array of the keying array’s indices by the values they index, then generating new arrays based on those sorted indices, using PermutationGenerator:

let myArr = ["b", "a", "c"]
let myArr2 = ["letter b", "letter a", "letter c"]
let myArr3 = ["b is the second letter", "a is the first letter", "c is the third letter"]

func sortByKeyArray(keyArray: [String], valuesArrays: [[String]]) -> [[String]] {

    precondition(reduce(valuesArrays, true) { $0.0 && ($0.1.count == keyArray.count)},
        "Arrays all need to be the same length")


    let permutation = sorted(indices(keyArray)) {
        keyArray[$0] < keyArray[$1]
    }

    return valuesArrays.map {
        Array(PermutationGenerator(elements: $0, indices: permutation))
    }
}

sortByKeyArray(myArr, [myArr2, myArr3])
// returns [["letter a", "letter b", "letter c"], ["a is the first letter", "b is the second letter", "c is the third letter"]]

If you want to make this generic on any kind of collection (but still returning an array, in the same style as the std lib collection algos):

func sortByKeyingCollection<C: CollectionType, D: SequenceType 
  where D.Generator.Element == C, 
        C.Index: RandomAccessIndexType, 
        C.Generator.Element: Comparable>
(key: C, values: D) -> [[C.Generator.Element]] {

    let permutation = sorted(indices(key)) {
        key[$0] < key[$1]
    }

    return map(values) {
        Array(PermutationGenerator(elements: $0, indices: permutation))
    }
}

And a version that takes a custom comparator:

func sortByKeyingCollection<C: CollectionType, D: SequenceType where D.Generator.Element == C, C.Index: RandomAccessIndexType>(key: C, values: D, isOrderedBefore: (C.Generator.Element,C.Generator.Element)->Bool) -> [[C.Generator.Element]] {

    let permutation = sorted(indices(key)) {
        isOrderedBefore(key[$0],key[$1])
    }

    return map(values) {
        Array(PermutationGenerator(elements: $0, indices: permutation))
    }
}


sortByKeyingCollection(myArr, [myArr2, myArr3], >)
sortByKeyingCollection(myArr, [myArr2, myArr3], lexicographicalCompare)
sortByKeyingCollection(myArr, [myArr2, myArr3]) { dropFirst($0) < dropFirst($1) }