  We study the problem of estimating the edit distance between two
$n$-character strings. While exact computation in the worst case is believed to
require near-quadratic time, previous work showed that in certain regimes it is
possible to solve the following {\em gap edit distance} problem in sub-linear
time: distinguish between inputs of distance $\le k$ and $>k^2$. Our main
result is a very simple algorithm for this benchmark that runs in time $\tilde
O(n/\sqrt{k})$, and in particular settles the open problem of obtaining a truly
sublinear time for the entire range of relevant $k$.
  Building on the same framework, we also obtain a $k$-vs-$k^2$ algorithm for
the one-sided preprocessing model with $\tilde O(n)$ preprocessing time and
$\tilde O(n/k)$ query time (improving over a recent $\tilde O(n/k+k^2)$-query
time algorithm for the same problem [GRS'20].
