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Unformatted text preview: CHAPTER 4 TREES 1 Preliminaries 1. Terminology Lineal Tree Pedigree Tree ( binary tree ) 1/16 1 Preliminaries Definition A tree is a collection of nodes. The collection can be empty; otherwise, a tree consists of (1) a distinguished node r , called the root ; (2) and zero or more nonempty (sub)trees T 1 , , T k , each of whose roots are connected by a directed edge from r . Note: Subtrees must not connect together. Therefore every node in the tree is the root of some subtree. There are edges in a tree with N nodes. Normally the root is drawn at the top. Note: Subtrees must not connect together. Therefore every node in the tree is the root of some subtree. There are edges in a tree with N nodes. Normally the root is drawn at the top. N 1 2/16 A C B D G F E H I J M L K degree of a node ::= number of subtrees of the node. For example, degree(A) = 3, degree(F) = 0. degree of a tree ::= For example, degree of this tree = 3. { } ) node ( degree max tree node leaf ( terminal node ) ::= a node with degree 0 (no children). parent ::= a node that has subtrees. children ::= the roots of the subtrees of a parent. siblings ::= children of the same parent. 1 Preliminaries 3/16 1 Preliminaries A C B D G F E H I J M L K ancestors of a node ::= all the nodes along the path from the node up to the root. descendants of a node ::= all the nodes in its subtrees. depth of n i ::= length of the unique path from the root to n i . Depth(root) = 0. height of n i ::= length of the longest path from n i to a leaf....
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 Spring '09
 JilinWang
 Computer Science

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