Average case. Run empirical studies to estimate the average and standard deviation of the number of compares used for search hits and for search misses in a BST built by running 100 trials of the experiment of inserting N random keys into an initially empty tree, for N = 104, 105, and 106. Compare your results against the formula for the average given in exercise3.2.35.
Exercise 3.2.35:
Refined analysis. Refine the mathematical model to better explain the experimental results in the table given in the text. Specifically, show that the average number of compares for a successful search in a tree built from random keys approaches the limit 2 ln N + 2γ - 3 ≈ 1.39 lg N - 1.85 as N increases, where γ = .57721… is Euler’s constant. Hint: Referring to the quicksort analysis in section2.3, use the fact that the integral of 1/x approaches ln N + γ.
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