How to generate all possible combinations?

Question

I\'m currently trying to make a Set of all possible combinations from an Array of Strings, were each element contains only one letter.

Answer 1

This is quite similar to @vacawama's answer, but hopefully different enough that it deserves a separate answer :)

Here, an array with all combinations is built (explaining comments inline):

func combinations(array : [String]) -> [String] {

    // Recursion terminates here:
    if array.count == 0 { return [] }

    // Concatenate all combinations that can be built with element #i at the
    // first place, where i runs through all array indices:
    return array.indices.flatMap { i -> [String] in

        // Pick element #i and remove it from the array:
        var arrayMinusOne = array
        let elem = arrayMinusOne.removeAtIndex(i)

        // Prepend element to all combinations of the smaller array:
        return [elem] + combinations(arrayMinusOne).map { elem + $0 }
    }
}

Then you can filter the strings with at least two letters, and convert it to a Set:

let c = Set(combinations(["A", "B", "C"]).filter { $0.characters.count >= 2 })
print(c)
// ["BA", "AC", "ABC", "AB", "BCA", "CB", "BC", "CAB", "ACB", "CA", "CBA", "BAC"]

I made a simple performance comparison (compiled in Release mode on a Macbook Pro):

let array = ["A", "B", "C", "D", "E", "F", "G"]

let t1 = NSDate()
let c1 = Set(combinations(array).filter { $0.characters.count >= 2 })
let t2 = NSDate()
let c2 = permute(array)
let t3 = NSDate()

print(c1 == c2) // true
print(t2.timeIntervalSinceDate(t1))
print(t3.timeIntervalSinceDate(t2))

The result depends on the size of the input array, but @vacawama's updated method is the fastest:

# of array   This      vacawama's   vacawama's
elements:    method:   1st method:  2nd method:

  2          0.00016   0.00005      0.00001
  3          0.00043   0.00013      0.00004
  4          0.00093   0.00062      0.00014
  5          0.00335   0.00838      0.00071
  6          0.01756   0.24399      0.00437
  7          0.13625   11.90969     0.03692