Detect whether a custom post type is odd or even

I have a custom post type - let's assume it's called fruit

If I then have a list of fruits, ordered by date:

Apple
Orange
Mango
Pineapple
Orange

If I load the Mango page for example via single.php I want to know whether it's an odd or an even post so I can use some slightly different CSS classes in the template.

I could get all posts of type fruit in date order and cycle through them to find this out, but this seems incredibly wasteful.

Is there a better way?