On the Average Height of b-Balanced Ordered Trees
نویسنده
چکیده
An ordered tree with height h is b-balanced if all its leaves have a level ` with h − b ≤ ` ≤ h, where at least one leaf has a level equal to h− b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall determine the exact asymptotic behaviour of the average height of such a tree together with the variance.
منابع مشابه
On the Average Height of b-Balanced Ordered Trees
An ordered tree with height h is b-balanced if all its leaves have a level l with h − b <= l <= h, where at least one leaf has a level equal to h − b. For large n, we shall compute asymptotic equivalents to the number of all b-balanced ordered trees with n nodes and of all such trees with height h. Furthermore, assuming that all b-balanced ordered trees with n nodes are equally likely, we shall...
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