Max element of a list with a custom ordering function

I need a function to find max element of a list according to some custom ordering function, assuming that the function implements a total order (elements being compared might not even be numbers). Unlike Sort, the predefined Max function does not accept a custom ordering function. A naïve solution would be to use Sort[list, p]〚1〛, but this would unnecessarily sort the whole list, while I only need to find the first element.

I ended up defining

max[list_, p_] := list[[Ordering[list, 1, p][[1]] ]];

and it works fine from performance point of view. But I wonder if there is a more simple or natural way to do this task. Is there a predefined function solving this problem that I missed?

Answer

If your operation can be converted to a canonical ranking rather than a pairwise comparison then you can use MaximalBy introduced in version 10.

If not a good approach to a single pass through a list is Fold. Here is a function using that:

foldMax[list_, p_] := Fold[If[p[##], ##] &, list]

This proves to be faster in some cases than using Ordering (in your function):

x = RandomReal[9, 5000000];

max[x, Less]     // AbsoluteTiming
foldMax[x, Less] // AbsoluteTiming

{1.209069, 4.32482*10^-6}

{0.430025, 4.32482*10^-6}