I suppose one of the benefits of having a poor memory is that one sometimes improves things in the course of rederiving them from an imperfect recollection.

You could also call the last version the online version, as it will ensure the partial list is random at any point in time (and can be used for inputs with indeterminate length, or to extend a random list with new elements, sample k elements etc.)

Not too sure if the enumerate is necessary. I usually dislike using it just to have an index to play around with. A similar way of doing the same thing is:

    for x in source:
        a.append(x)
        i = random.randint(0, len(a))
        a[i], a[-1] = a[-1], a[i]

Suppose I want to uniformly randomly shuffle a deck of cards in a single pass. I stick the deck on the table and call it the non-shuffled pile. My goal is to move the deck, one card at a time, into the shuffled pile. First I need to select a card, uniformly at random, to be the bottom card of the new pile, and I move it over. Then I select another card, uniformly at random from the still non-shuffled cards, and put it on top of the bottom shuffled card. I repeat this until I’ve moved all the cards, so that each card in the shuffled pile is a uniform random selection from all of the cards it could have been. And that’s it.

One can think of this as random selection, whereas the “forward” version is like random insertion of a not-random card into a shuffled pile. And for whatever reason I tend to think of the selection version first.

Separate point: One way of deriving 4 different variants of Fisher-Yates is to take a random bijection f:[n]->[n] (where [n] means {0,1,...,n}) drawn using whichever variant of the FY shuffle, and then potentially pre-composing or post-composing with the bijection reverse:[n]->[n] that sends k to n - k - 1.

For me, the reason for reaching for the “backwards” version first is that it wasn’t as clear to me that the “forward” version makes a uniform distribution.

Even after reading the article.

I appreciated the comment here about inserting a card at a random location, but that also isn’t quite right, because you swap cards not insert. Nevertheless, that did it for me.

both seem intuitive from individual perspectives

• loop counts downwards vs upwards

• the processed part of the array is a uniform sample of the whole array, or it is a segment that has been uniformly shuffled

Knuth described only the downwards sampling version, which is probably why it’s the most common.

The variants are compared quite well on wikipedia https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle