Observe that whenever the size field of a node is referenced in either OS-SELECT or OSRANK, it is used only to compute the rank of the node in the sub tree rooted at that node. Accordingly, suppose we store in each node its rank in the sub tree of which it is the root. Show how this information can be maintained during insertion and deletion. (Remember that these two operations can cause rotations.)
Answer to relevant QuestionsShow how to use an order-statistic tree to count the number of inversions (see Problem 2-4) in an array of size n in time O (n lg n).VLSI databases commonly represent an integrated circuit as a list of rectangles. Assume that each rectangle is rectilinearly oriented (sides parallel to the x- and y-axis), so that a representation of a rectangle consists of ...Let A[1 ¬ n] be an array of n distinct numbers. If i < j and A[i] > A[j], then the pair (i, j) is called an inversion of A. a. List the five inversions of the array ¬2, 3, 8, 6, 1¬. b. What array with elements from the ...a. Suppose that each leaf of TA is labeled with the probability that it is reached given a random input. Prove that exactly n! Leaves are labeled 1/n! And that the rest are labeled 0.b. Let D(T) denote the external path ...During the course of an algorithm, we sometimes find that we need to maintain past versions of a dynamic set as it is updated. Such a set is called persistent. One way to implement a persistent set is to copy the entire set ...
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