Given a suffix array of a string $w$, it's possible to construct the Burrows-Wheeler transform of $w$ by subtracting one from the indices of the suffix array (wrapping around if necessary), then outputting the characters in $w$ that appear in that position.However, to the best of my knowledge, there doesn't seem to be an algorithm to directly construct a suffix array for $w$ given the Burrows-Wheeler transform of the string $w$. It's still possible to do so in linear time by inverting the transform to get back $w$ and then constructing the suffix array directly, but that doesn't make any use of the transformed array.Is there a fundamental reason why the reverse direction would be harder than the forward direction?Thanks!
Asymmetry in converting Burrows-Wheeler transform to suffix array?
ds.algorithms;ds.data structures