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Answered! We in class that the height h with minimal number of nodes (denote as N (h)) is given by the Fibonacci recurrence N…

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We in class that the height h with minimal number of nodes (denote as N (h)) is given by the Fibonacci recurrence N (h + 1) = N (h) + N (h – 1) + 1, with N (0) = 1 and N (1) = 2. Show that the height of an AVL tree in the worst-case is O (log n). F (n + 1) = 1/squareroot 5/2)^n +1 – 1/squareroot 5(1 – squareroot 5/2)^n +1

4. Worst AVL Tree, 20pts. We in class that the height h with minimal number of nodes (denote as N(h) is given by the Fibonacci recurrence N(ha 1) N(h) N(h 1) 1, with N (0) 1 and N (1) 2. Show that the height of an AVL tree in the worst-case is O log n). Hint Consider the close form of the Fibonacci recurrence n--1 n-1 1)

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