If T is a binary tree that has t leaves and height h, then t and h are related by the inequality .
To fill the blank in the statement, “If is a binary tree that has leaves and height , then and are related by the inequality ______.”
is a binary tree with number of leaves and the height is .
If this rooted tree is a binary tree, in a particular level the maximum number of vertices we obtain is to the power of the level number. For an example, consider the level number one of a binary tree. Then, the parent vertex would be the root and the maximum number of children is . Hence,
By the height of a rooted tree we denote the maximum number of levels
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