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In this paper, we provide new insights and analysis for the two elementarytree-based data structures - the AVL tree and binary heap. We presented twosimple properties that gives a more direct way of relating the size of an AVLtree and the Fibonacci recurrence to establish the AVL tree's logarithmicheight. We then give a potential function-based analysis of the bottom-up heapconstruction to get a simpler and tight bound for its worst-case running-time.

A Tale of Two Trees: New Analysis for AVL Tree and Binary Heap