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6 Let S be a set of n points in the plane with distinct integer

6 Let S be a set of n points in the plane with distinct integer x- and y-coordinates. Let T be a complete binary tree storing the points from S at its external nodes, such that the points are ordered left to right by increasing x-coordinates. For each node v in T, let S(v) denote the subset of S consisting of points stored in the subtree rooted at v. For the root r of T, define top(r) to be the point in S = S(r) with maximal y-coordinate. For every other node v, define top(r) to be the point in S with highest y-coordinate in S(v) that is not also the highest y-coordinate in S(u), where u is the parent of v in T (if such a point exists). Such labeling turns T into a priority search tree. Describe a linear-time algorithm for turning T into a priority search tree. Implement this approach.

Hint
ManagementTime complexity approximates an algorithm’s performance regardless of the machine it runs on. One can get time complexity by counting operations executed by one’s code. Acknowledging constant, linear, quadratic, polynomial, logarithmic, linearithmic, exponential, and factorial times is important for every programmer.  ...

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