# Question

Show that any arbitrary n-node binary search tree can be transformed into any other arbitrary n-node binary search tree using O (n) rotations. (Hint: First show that at most n - 1 right rotation suffices to transform the tree into a right-going chain.)

## Answer to relevant Questions

Suppose that the black-height of each of the sub trees α, β, γ, δ, ε in Figures 13.5 and 13.6 is k. Label each node in each figure with its black-height to verify that property 5 is preserved by the ...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 ...Let R(i, j) be the number of times that table entry m[i, j] is referenced while computing other table entries in a call of MATRIX-CHAIN-ORDER. Show that the total number of references for the entire table isGive asymptotic upper and lower bounds for T(n) in each of the following recurrences. Assume that T(n) is constant for n ≤ 2. Make your bounds as tight as possible, and justify your answers. Given a set of n numbers, we wish to find the i largest in sorted order using a comparison based algorithm. Find the algorithm that implements each of the following methods with the best asymptotic worst-case running time, ...Post your question

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