Special Binary Tree

What is the name of the binary tree (or the family of the binary trees), that is balanced, and has the minimum number of nodes possible for its height?

Well this is special ki开发者_开发问答nd of tree not the AVL tree.

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if the binary tree is balanced then, it height is a function of its nodes (n). height = log₂n. so a balanced tree don't have a range of heights.

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The minimum number of nodes a completely balanced binary tree can have for height d is 2^(d-1)+1. As far as i know this type doesn't have a name.

The maximal number of nodes is 2^d. This is called a complete tree. All layers are completely full and each node has either 2 or zero childern(implied).

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Red-black tree?

Any one from http://en.wikipedia.org/wiki/Self-balancing_binary_search_tree#Implementations?

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The name of the binary tree (or the family of the binary trees), that has the minimum number of nodes possible for its height is a linked list :D