A very common problem in computer graphics is to approximate a complex shape with a bounding box. For a set, S, of n points in 2-dimensional space, the idea is to find the smallest rectangle, R, with sides parallel to the coordinate axes that contains all the points in S. Once S is approximated by such a bounding box, we can often speed up lots of computations that involve S. For example, if R is

completely obscured some object in the foreground, then we dont need to render any of S. Likewise, if we shoot a virtual ray and it completely misses R, then it is guarantee to completely miss S. So doing comparisons with R instead of S can often save time. But this savings is wasted if we spend a lot of time constructing R; hence, it would be ideal to have a fast way of computing a bounding box, R, for a set, S, of n points in the plane. Note that the construction of R can be reduced to two instances of the problem of simultaneously finding the minimum and the maximum in a set of n numbers; namely, we need only do this for the x-coordinates in S and then for the y-coordinates in S. Therefore, design a divide-and-conquer algorithm for finding both the minimum and the maximum element of n numbers using no more than 3n/2 comparisons.