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MINISTRY OF EDUCATION & HIGHER EDUCATION COLLEGE OF SCIENCE AND TECHNOLOGY KHANYOUNIS- PALESTINE DATA STRUCTURE Information Technology , 3’rd Semester Using C# Lecture 13: Trees Presented By: Mahmoud Rafeek Alfarra Outline Classification of Data Structures The definition of a tree Terminology of Tree Binary Trees Binary Search Tree Emank X Mezank !! Classification of Data Structures 3 Classification Linear Hierarchical Presented & Prepared by: Mahmoud R. Alfarra The definition of a tree 4 A tree is a set of nodes connected by edges. An example of a tree is a company’s organization chart Presented & Prepared by: Mahmoud R. Alfarra The definition of a tree 5 The purpose of an organization chart is to communicate to the viewer the structure of the organization. root node internal nodes leaf nodes Presented & Prepared by: Mahmoud R. Alfarra Terminology of Tree 6 Tree: A collection of data whose entries have a hierarchical organization Node: An entry in a tree Root node: The node at the top Terminal or leaf node: A node at the bottom Presented & Prepared by: Mahmoud R. Alfarra Terminology of Tree 7 Parent: The node immediately above a specified node Child: A node immediately below a specified node Ancestor: Parent, parent of parent, etc. Descendent: Child, child of child, etc. Siblings: Nodes sharing a common parent Presented & Prepared by: Mahmoud R. Alfarra Terminology of Tree 8 Binary tree: A tree in which every node has at most two children Depth: The number of nodes in longest path from root to leaf Presented & Prepared by: Mahmoud R. Alfarra Terminology of Tree 9 Presented & Prepared by: Mahmoud R. Alfarra Binary Trees 10 Tree nodes contain two or more links Most of other data structures we have discussed only contain one In Binary trees All nodes contain two links None, one, or both of which may be NULL The root node is the first node in a tree. Each link in the root node refers to a child A node with no children is called a leaf node Presented & Prepared by: Mahmoud R. Alfarra Binary Trees 11 Allow the head (and the rear) to be moving targets B A D C Presented & Prepared by: Mahmoud R. Alfarra Binary Tree Definitions 12 Leaf: node that has no left and right children Parent: node with at least one child node Level of a node: number of branches on the path from root to node Height of a binary tree: number of nodes no the longest path from root to node Presented & Prepared by: Mahmoud R. Alfarra Binary search trees 14 5 10 2 5 10 45 30 5 45 30 2 25 45 2 10 25 30 25 Not a binary search tree Binary search trees Presented & Prepared by: Mahmoud R. Alfarra !! Emank X Mezank أعظم أسبـاب النجاة استعن ابهلل Next Lecture Examples (Implementation of tree and then Practices )