Why does Sattolo's algorithm produce a permutation with exactly one cycle?
On creating a single-cycle permutation from a shuffle:Take 0, 1, 2, 3, 4, 5 and shuffle it.
4, 3, 0, 5, 1, 2Now you can read out a permutation:4 → 33 → 00 → 55 → 11 → 22 → 4It will only have one cycle.