Why break up the pairs and use buckets? It seems like you simply need three passes: First pass - get the reds and insert them in order into a new array of size n (assuming we can use additional space) Second pass - get the blues and insert them in order into the array Third pass - get the yellows and insert them in order into the array
Each pass is O(n) since we have to visit each element, so the entire algorithm is O(n).
EDIT: Why three passes ? .Two passes can do it
index_red=-1 for index =0 to a.length-1 if a[index].color == "Red" swap(a,++index_red,index) index_blue=index_red for index = index_blue+1 to a.length-1 if a[index].color=="blue" swap(a,++index_blue,index)
The swap' above makes it a non-stable sort.