How to find the split in regression trees

See: http://math.uprm.edu/~wrolke/esma6665/regtree.htm (How to Grow a tree). I'm having a bit of confusion.

So we have some predicting variable X, and target Y. We want to find a value that splits X into 2 sets, that minimizes the sum of squared error. So let us say there are n data points. Then there are O(n²⁾ combinations we would need to test, but the page seems to indicate that this split can be found quickly O(n) maybe? I tried looking in "The Elements of Statistical Learning" but it says the same thing, without explaining how and only saying that it can be done very quickly.

Can anyone provide a bit of enlightenment on this matter? Is O(n²⁾ somehow considered "quick" in this case, or am I just an idiot and missing something?