Paul Erdos talked about the "Book" where God keeps the most elegant proof of each mathematical theorem. This even inspired a book (which I believe is now in its 4th edition): Proofs from the Book.
If God had a similar book for algorithms, what algorithm(s) do you think would be a candidate(s)?
If possible, please also supply a clickable reference and the key insight(s) which make it work.
Only one algorithm per answer, please.