Split all other elements in the set into those greater than or equal to x and those less than x.  
Its average time complexity is of the order n log(n).  To execute it, arbitrarily choose an element x in the set.  Split all other elements in the set into those greater than or equal to x and those less than x.  Apply the same function recursively to the newly generated subsets until each subset has just one member.  You have just performed, for 10 points, what sorting algorithm?
Its average time complexity is of the order n log(n).  To execute it, arbitrarily choose an element x in the set.  
Quicksort