So binary MSD radix sort is also just called "binary quicksort" by some authors; they are substantially the same algorithm. How can I explain?
If you really want to replicate the exact swaps and pivoting in the most common form of quicksort, what your fingers will actually do, looks like this.
1. Cut the to-be-sorted deck-portion in half so that you can peek at the first, last, and middle card. Choose the median and swap it to the back of the deck.
2. The deck now sits in your left hand and your right hand conceptually contains two empty stacks of cards, the one between thumb and forefinger is a stack <= to pivot, and between forefinger and ring finger is the stack > pivot.
3. You are permitted two operations: (a) deal a card > pivot from the left hand onto the back of the second stack, or (b) deal a card <= pivot from the left hand onto the back of the first stack, but to make it a conceptual swap you now have to pick the card from the top of the second stack and put it on the back of the second stack.
4. Process the whole left hand this way; at the end the pivot you selected will be at the back of the first stack in your right hand. Separate it out and recurse on the two remaining stacks.
So if you do this enough you'll start to appreciate these two things:
- "with cards I don't really need to rotate that second stack card by card whenever I add to that first stack -- that's not affecting correctness, it's just needed for array sorts to be in-place"
and similarly
- "with cards I sometimes get these really stupid starts where like the median is 10 of spades and I'm going to split this like 9-1-42, eff it I'm just going to pretend that the median was the king of clubs, that's what I needed to split the damn deck in half."
and those are the optimizations performed in the above description of quicksort.