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A detailed examination of binary search trees reveals that the probability of making precisely i comparisons in placing the (n−1)th item in the tree is related to the (n−i)th symmetric function of the integers 1, …, n. A recurrence relation for the moments of this distribution of comparisons is derived, and formulas for the mean number of comparisons and its variance are displayed. These are shown to be in accord with previously published values.
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W. C. Lynch (1965) studied this question.
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