Question

Let T be a proper binary tree. Given a node v ∈ T, the imbalance of v, denoted imbalance(v), is defined as the difference, in absolute value, between the number of leaves of the left subtree of v and the number of leaves of the right subtree of v. (If v is a leaf, then imbalance(v) is defined to be 0.) Define imbalance(T) = maxv∈T imbalance(v).

(a) Provide an upper bound to the imbalance of a proper binary tree with n nodes, and exhibit a proper binary tree whose imbalance matches such an upper bound.

(b) Draw a proper binary tree T for which imbalance(T) = imbalance(v) and v is not the root of T.

(c) Design an efficient algorithm to compute imbalance(T), and determine its complexity.

Answer 1

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