Lazy Evaluation and Time Complexity

Question

I was looking around stackoverflow Non-Trivial Lazy Evaluation, which led me to Keegan McAllister\'s presentation: Why learn Haskell. In slide 8, he shows the minimum functi

Answer 1

One interesting way of seeing this in practice is to trace the comparison function.

import Debug.Trace
import Data.List

myCmp x y = trace (" myCmp " ++ show x ++ " " ++ show y) $ compare x y

xs = [5,8,1,3,0,54,2,5,2,98,7]

main = do
    print "Sorting entire list"
    print $ sortBy myCmp xs

    print "Head of sorted list"
    print $ head $ sortBy myCmp xs

First, notice the way in which the output of the entire list is interleaved with the trace messages. Second, notice how the trace messages are similar when merely computing the head.

I've just run this through Ghci, and its not exactly O(n): it takes 15 comparisons to find the first element, not the 10 that ought to be required. But its still less than O(n log n).

Edit: as Vitus points out below, taking 15 comparisons instead of 10 is not the same as saying its not O(n). I just meant that it takes more than the theoretical minimum.