Generating all permutations of a given string

Question

What is an elegant way to find all the permutations of a string. E.g. permutation for ba, would be ba and ab, but what about longer st

Answer 1

This can be done iteratively by simply inserting each letter of the string in turn in all locations of the previous partial results.

We start with [A], which with B becomes [BA, AB], and with C, [CBA, BCA, BAC, CAB, etc].

The running time would be O(n!), which, for the test case ABCD, is 1 x 2 x 3 x 4.

In the above product, the 1 is for A, the 2 is for B, etc.

Dart sample:

void main() {

  String insertAt(String a, String b, int index)
  {
    return a.substring(0, index) + b + a.substring(index);
  }

  List Permute(String word) {

    var letters = word.split('');

    var p_list = [ letters.first ];

    for (var c in letters.sublist(1)) {

      var new_list = [ ];

      for (var p in p_list)
        for (int i = 0; i <= p.length; i++)
          new_list.add(insertAt(p, c, i));

      p_list = new_list;
    }

    return p_list;
  }

  print(Permute("ABCD"));

}