  We characterize the class of cycle decompositions that can achieve all Young
tableau shapes (except the trivial ones with a single row or a single column)
under the Robinson--Schensted--Knuth (RSK) correspondence, a property that we
call RSK-completeness. We prove that for even $n$, cyclic permutations comprise
the only fixed cycle decomposition that is RSK-complete. For odd $n$, cyclic
permutations and almost cyclic permutations which have a cycle of length $n-1$
are the only RSK-complete cycle decompositions.
