9.4 a. Construct a two-tree that is not complete. b. Construct a complete tree that is not a two-tree. c. Construct a complete two-tree that is not full. d. How many leaves are there in a two-tree with 17 elements? e. How many leaves are there in a two-tree with 731 elements? f. A non-empty two-tree must always have an odd number of elements. Why? Hint: Use the Binary Tree Theorem and the fact that the number of leaves must be an integer. g. How many elements are there in a full binary tree of height 4? h. How many elements are there in a full binary tree of height 12? i. Use induction (original form) on the height of the tree to show that any full binary tree is a two tree. j. Use the results from part i and the Binary Tree Theorem to determine the number of leaves in a full binary tree with 63 elements. k. Construct a complete two-tree that is not full, but in which the heights of the left and right subtrees are equal. | |
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