Dutch national flag on a Turing Machine

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

xxx -> RWB
xxxx -> RWBB
xxxxx -> RWWBB
xxxxxx -> RRWWBB

with R <= W <= B

All solutions that I have found, have a very high complexity.

What is an efficient approach to build a Turing machine using only one tape and one head/cursor?

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)...