At a glance, it may result in TLE (Time Limit Exceeded), but the constant factor is small enough.
at a galance：第一眼看去；constant factor：常数因素。

By varying the parameters like the number and size of rectangular regions and the density, we can generate strong test cases for some extent.
parameter参数；rectangular矩形；region区域，行政区，境界；density密度；for some extent一定程度上。

This can be achieved by managing the number of Christmas trees on each y coordinate while inspecting them in the increasing order of their x coordinates.
coordinate坐标，使协调，配位（Coordination compound配位化合物）；inspect检查。

Roughly speaking, we will have to find the segment sum when...
roughly speaking粗略地说。

We consider solving it with parallel binary search. It is sufficient to solve the following problem.
parallel同时发生的，并行的，相似的，并联的（parallel binary search整体二分）；sufficient充足的。

Therefore, the original problem has been solved in a total of ... time.
therefore因此；original最初的，有独创性的，原文，独特的人；in a total of...总量为……。