Let P = {(xi , yi) : 1 i n} be a set of n points in the plane. Assume that no two of them have the same x- or y-coordinate. We also assume that n is a positive power of 2. A point (xi , yi) is dominant if for every point (xj , yj ) P, xj > xi implies that yj < yi . Show that after sorting the points in P in increasing order of x-coordinates, which takes O(n log n) time, you can find the dominant points in an additional O(n) time. Describe your algorithm. Explain its correctness. Derive its running time. Please explain how to do this question

3. (10 points) Let P={(xi,yi):1in} be a set of n points in the plane. Assume that no two of them have the same x - or y-coordinate. We also assume that n is a positive power of 2 . A point (xi,yi) is dominant if for every point (xj,yj)P,xj>xi implies that yj