The Department of Computer Science & Engineering

CSE 116
Introduction To Computer Science for Majors 2
Lecture B
Lecture Notes
Stuart C. Shapiro
Spring, 2003


Riley Chapter 9

Trees are mutable, unbounded collections, with a nonlinear notion of sequence.

A tree may be empty, or may have one or more nodes, one of which is its root. Every node has a mutable, either bounded or unbounded, either ordered or unordered, possibly empty, collection of children. (Having collections of children that are bounded or unbounded, ordered or unordered, is a property of the tree as a whole.) If a node, n has a child m, then n is the parent of m. Every node, other than the root, has exactly one parent. There is exactly one path between the root and any node. A node with no children is called a leaf, or leaf node. The path between the root and a leaf is called a branch. A node with one or more child is called a branch node.

If a node, n is on the path between the root and a node m, then n is an ancestor of n and m is a descendant of n. Nodes with a common parent are siblings. The length of a path between a node and one of its descendants counts the number of nodes on the path less one.

The level of a node is the length of the path from it to the root. The height of a tree is the maximum level of any of its nodes.

Every node is the root of its own subtree, consisting of it and all its descendants.

Recursively, a tree is either empty, or consists of one root node with zero or more subtrees.

For most trees, every node has some value, although some trees have only their leaves having values.

Implementation note for trees
A tree has one or more instance variables for its value(s), and an instance variable for a collection of its children, each of which is a tree.


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