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10/22/10
19:10:12
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24
CS 61B: Lecture 24
Friday, October 22, 2010
Today’s reading:
ROOTED TREES
============
A _tree_ consists of a set of nodes and a set of edges that connect pairs of
nodes.
A tree has the property that there is exactly one path (no more, no
less) between any two nodes of the tree.
A _path_ is a connected sequence of
zero or more edges.
In a _rooted_ tree, one distinguished node is called the _root_.
Every node c,
except the root, has exactly one _parent_ node p, which is the first node
traversed on the path from c to the root.
c is p’s _child_.
The root has no
parent.
A node can have any number of children.
Some other definitions:
 A _leaf_ is a node with no children.
 _Siblings_ are nodes with the same parent.
 The _ancestors_ of a node d are the nodes on the path from d to the root.
These include d’s parent, d’s parent’s parent, d’s parent’s parent’s
parent, and so forth up to the root.
Technically, the ancestors of d also
include d itself, which makes you wonder about d’s sex life.
The root is
an ancestor of every node in the tree.
 If a is an ancestor of d, then d is a _descendant_ of a.
 The _length_ of a path is the number of edges in the path.
 The _depth_ of a node n is the length of the path from n to the root.
(The
depth of the root is zero.)
 The _height_ of a node n is the length of the path from n to its deepest
descendant.
(The height of a leaf node is zero.)
 The height of a tree is the depth of its deepest node = height of the root.
 The _subtree_ rooted at node n is the tree formed by n and its descendants.
 A _binary_tree_ is a tree in which no node has more than two children, and
every child is either a _left_child_ or a _right_child_, even if it’s the
only child its parent has.
A commonly encountered application of trees is the directory structure of a
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This note was uploaded on 01/10/2012 for the course CS 61B taught by Professor Canny during the Fall '01 term at University of California, Berkeley.
 Fall '01
 Canny
 Data Structures

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