7.1-tree_intro

# 7.1-tree_intro - Height of a tree T’s root • Level of a...

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CMPT 225 Introduction to Trees

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CMPT 225 What is a Tree – In Real World?
CMPT 225 What is a Tree – as a Data Structure? • Hierarchical • Sequential access • Definition: A set of zero (empty tree) or more “nodes” partitioned into a root “node” and subtrees (of the root) NOTE: “node” != class Node of our linked list

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CMPT 225 Tree Classification • Classify or name trees by potential maximum # of children (or subtrees) a node of the tree can have • Example:
CMPT 225 Terminology - 1 Root Node Edge Leaf See textbook @ pages __________ Parent Child Sibling Ancestor Descendant

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CMPT 225 Terminology - 2 • Path length: # of nodes in path. From node N 1 to another node N k , path length is K. • Height of a node N: Length of longest path from node N to a leaf. • Height of a tree T:

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Unformatted text preview: Height of a tree T’s root. • Level of a node N: If node N is the root of tree T, then node N is at level 1, otherwise level++ every time we reach root of subtree of node N. CMPT 225 Terminology - 3 • Empty tree • Full tree of height H: - All nodes at level < H have max # of children - Nodes @ level H have 0 children ( they are leaves ) • Complete tree of height H: is a tree that is full all the way down to level H-1 with level H filled in from left to right without any gap. CMPT 225 Terminology - 4 • Subtree: • Recursive Nature of Trees • Balanced tree: A N-ary tree in which all N subtrees of any nodes have height that differ by at most 1. CMPT 225 Bin-ary Tree • Definition: N-ary tree where N = 2 • Property: If binary tree T has height H then T has between H and 2 H-1 nodes...
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7.1-tree_intro - Height of a tree T’s root • Level of a...

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