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This chapter provides definitions and properties of binary trees, including tree terminology, binary trees, full and complete binary trees, binary tree traversals, and binary search trees. Learn about the structure and characteristics of binary trees and their applications.
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Defn: A tree can be defined in one of the following different, but equivalent, manners: a connected graph with no cycles. a directed acyclic graph with one node from which all other nodes are reachable. Example: A B C D E F G
A B C^ D E F G Defn: In a tree, the node from which all other nodes are reachable is called the root. Defn: The children of a node X are all of the nodes you can access from X by following one edge. Defn: The parent of a node X is the node of which X is a child. Defn: The siblings of a node X are all other children with the same parent as X. Defn: The descendants of a node X are all of the nodes reachable from X.
Defn: A binary tree is a tree in which every node has at most two children. Example: A B C D (^) E F G H Defn: A strictly binary tree is a tree in which every node has either 0 or 2 children.
Defn: A binary tree of depth k is called full if it contains all possible nodes at depth k. Example: A full tree of depth 2 A B C D (^) E F G H Defn: A complete binary tree is an almost full binary tree except that it may be missing nodes at the right-hand side of the lowest level. Example: A complete tree A B C D (^) E F
Defn: A tree traversal is a method of traveling from node to node through a tree, visiting every node. There are three types of traversals :
1. Preorder preorder (node): visit the node preorder(node’s left subtree) preorder(node’s right subtree) 2. Inorder inorder (node): inorder(node’s left subtree) visit the node inorder(node’s right subtree) 3. Postorder postorder (node): postorder(node’s left subtree) postorder(node’s right subtree) visit the node
Example: Tree Traversals A B C D (^) E F G Preorder: A, B, D, E, G, C, F Inorder: D, B, G, E, A, C, F Postorder: D, G, E, B, F, C, A
