A complete binary tree is a graph defined through the following recur- sive definition.
Basis step:A single vertex is a complete binary tree.Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the graph formed by starting with a root r, and adding an edge from r to each of the vertices r1,r2 is also a complete binary tree.The set of leaves of a complete binary tree can also be defined recursively.Basis step: The root r is a leaf of the complete binary tree with exactly one vertex r.Inductive step: The set of leaves of the tree T built from trees T1, T2 is the union of the sets of leaves of T1 and the set of leaves of T2.
The height h(T ) of a binary tree is defined in the class.Use structural induction to show that L(T), the number of leaves of a complete binary tree T , satisfies the following inequality
L(T) ≤ 2^h(T).
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