  In this paper we describe a randomized algorithm which returns a maximal
spanning forest of an unknown {\em weighted} undirected graph making $O(n)$
$\mathsf{CUT}$ queries in expectation. For weighted graphs, this is optimal due
to a result in [Auza and Lee, 2021] which shows an $\Omega(n)$ lower bound for
zero-error randomized algorithms. %To our knowledge, it is the only regime of
this problem where we have upper and lower bounds tight up to constants. These
questions have been extensively studied in the past few years, especially due
to the problem's connections to symmetric submodular function minimization. We
also describe a simple polynomial time deterministic algorithm that makes
$O(\frac{n\log n}{\log\log n})$ queries on undirected unweighted graphs and
returns a maximal spanning forest, thereby (slightly) improving upon the
state-of-the-art.
