(definition)

**Definition:**
The (weight) balance of a tree is the number of *leaves* of the left subtree of a tree, denoted |T_{l}|, divided by the total number of leaves of the tree. Formally, ρ(T) = |T_{l}|/|T|.

**Also known as** root balance.

**See also**
*BB(α) tree*, *height-balanced tree*, *right rotation*, *left rotation*, *relaxed balance*.

*Note:
The balance of a node is the balance of the (sub)tree rooted at that node. After Johann Blieberger <blieb@auto.tuwien.ac.at>, Discrete Loops and Worst Case Performance, page 22.*

Author: PEB

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Entry modified 20 December 2004.

HTML page formatted Mon Feb 2 13:10:39 2015.

Cite this as:

Paul E. Black, "balance", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 20 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/balance.html