Show that if a node in a binary search tree has two children, then its successor has no left child and its predecessor has no right child.
Answer to relevant QuestionsAn in order tree walk of an n-node binary search tree can be implemented by finding the minimum element in the tree with TREE-MINIMUM and then making n-1 calls to TREESUCCESSOR. Prove that this algorithm runs in Θ (n) ...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 ...Show 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).Show how to compute the length of an LCS using only 2 · min (m, n) entries in the c table plus O (1) additional space. Then show how to do this using min (m, n) entries plus O (1) additional space.The procedure BUILD-MAX-HEAP in Section 6.3 can be implemented by repeatedly using MAX-HEAP-INSERT to insert the elements into the heap. Consider the following implementation: BUILD-MAX-HEAP'(A) 1 heap-size [A] ← ...
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