We define an AVL binary search tree to be a tree with the binarysearch tree property where, for each node in the tree, the heightof its children differs by no more than 1. For this problem, assumewe have a team of biologists that keep information about DNAsequences in an AVL binary search tree using the specific weight(an integer) of the structure as the key. The biologists routinelyask questions of the type, “Are there any structures in the treewith specific weight between a and b, inclusive?” and they hope toget an answer as soon as possible. Design an efficient algorithmthat, given integers a and b, returns true if there exists a key xin the tree such that a ≤ x ≤ b, and false if no such key exists inthe tree. Describe your algorithm in pseudocode and English. Whatis the time complexity of your algorithm? Explain.
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