Dutch national flag on a Turing Machine

Question

I have a sequence of characters xxxxxx (with x^k and k > 0) My goal is to transform this sentence into a dutch flag, that is to say :

xxxxx -> RRWWBB xxxx -> RWBB

with R <= W <= B

All solutions that I have found, have a very high complexity. Do you have any hint/clue to help to me build a Turing machine using only one tape and one head/cursor?

Answer 1

How about dividing the task into subtasks like:

1. Change the last X to B.
2. Change the last X to W.
3. Change the first X to R.
4. Change BW to WB.

EDIT:

Here's another approach: you say you've seen algorithms that start with the colors present (out of order). So all you really need is a way to put the colors in (out of order)...