9.13 Let t be a nonempty binary tree. Use the Strong Form of the Principle of Mathematical Induction to prove each of the following parts of the Binary Tree Theorem: a. n(t ) + 1 2.0 ≤ 2height(t ) b. If t is a two-tree, then leaves(t ) = n(t ) + 1 / 2.0 c. If t is a full tree, then n(t ) + 1 / 2.0 = 2height(t ) Hint: The outline of the proof is the same as in Example A2.5 of Appendix 2. | |
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