The.Algorithm.Design.Manual.Springer-Verlag.1998

Binary Search Trees
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Binary Search Trees
Fast support of all dictionary operations is realized by binary search trees. A binary tree is a rooted tree
where each node contains at most two children. Each child can be identified as either a left or right child.
As shown in Figure , a binary tree can be implemented where each node has left and right pointer
fields, an (optional) parent pointer, and a data field.
Figure: Relationships in a binary search tree
A binary search tree labels each node in a binary tree with a single key such that for any node labeled x,
all nodes in the left subtree of x have keys < x while all nodes in the right subtree of x have keys > x. The
search tree labeling enables us to find where any key is. Start at the root. If it does not contain the key we
are searching for, proceed either left or right depending upon whether what we want occurs before or after
the root key. This algorithm works because both the left and right subtrees of a binary search tree are
binary search trees; the recursive structure yields a recursive algorithm. Accordingly, the dictionary Query
operation can be performed in O(h) time, where h is the height of the tree.
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