  We present an optimal, linear-time algorithm for the following version of
terrain guarding: given a 1.5D terrain and a horizontal line, place the minimum
number of guards on the line to see all of the terrain. We prove that the
cardinality of the minimum guard set coincides with the cardinality of a
maximum number of ``witnesses'', i.e., terrain points, no two of which can be
seen by a single guard. We show that our results also apply to the Art Gallery
problem in ``monotone mountains'', i.e., $x$-monotone polygons with a single
edge as one of the boundary chains. This means that any monotone mountain is
``perfect'' (its guarding number is the same as its witness number); we thus
establish the first non-trivial class of perfect polygons.
