This document provides information about trees as a non-linear data structure. It includes definitions of different types of trees such as binary trees and heaps. Examples are given to illustrate tree representation and traversal methods for binary trees. Heaps are described as useful for implementing priority queues, with max and min heaps discussed.

1. TREE
1
4
Prepared by: Mir Omranudin Abhar
Email : MirOmran@Gamil.com
Spring , 2019

2. 2
• Non-Linear Data Structure
• Non- Primitive Data Structure
• Dynamic Data Structure

3. Tree
3
‫از‬ ‫تهی‬ ‫غیر‬ ‫و‬ ‫متناهی‬ ‫ای‬ ‫مجموعه‬
‫ی‬
‫چندین‬ ‫یا‬ ‫ک‬
node
‫است‬

4. Tree – example
4

5. Tree – example-1
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6. Tree – example-2
6

7. Tree – example-3
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… … .… ..
… … .… .. … … .… .. … … .… ..

8. Tree – example-4
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9. Tree Representation -> Linked list
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10. Tree Representation -> Linked list
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11. Binary -Tree
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12. Binary -Tree
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13. Complete Binary -Tree
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𝐦𝐚𝐱 𝒏𝒐𝒅𝒆 𝒊 ⇒ 𝟐𝒊−𝟏
, 𝑖 ≥ 1
𝒕𝒐𝒕𝒂𝒍 𝒏𝒐𝒅𝒆 𝒌 ⇒ 𝟐𝒌
− 𝟏 , 𝑘 ≥ 1
𝑖 ⇒ 𝑙𝑒𝑣𝑒𝑙 , 𝑘 ⇒ 𝑑𝑒𝑝𝑡ℎ

14. Binary Tree- Representation [array]
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𝑺𝒊𝒛𝒆 − 𝑨𝒓𝒓𝒂𝒚 𝒏𝒐𝒅𝒆 𝒌 ⇒ 𝟐𝒌
− 𝟏 , 𝑘 ≥ 1
𝑘 ⇒ 𝑑𝑒𝑝𝑡ℎ

15. Binary Tree- Representation [Linked list]
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16. Binary Tree- Traversing
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• Pre-Order Root Left-sub-tree Right-sub-tree
• In-Order Left-sub-tree Root Right-sub-tree
• Post-Order Left-sub-tree Right-sub-tree Root

17. Binary Tree- Traversing [Pre-Order]
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18. Binary Tree- Traversing [In-Order]
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19. Binary Tree- Traversing [Post-Order]
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20. Binary Tree- Traversing [ Class Activity ]
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• Pre-Order Root Left-sub-tree Right-sub-tree
• In-Order Left-sub-tree Root Right-sub-tree
• Post-Order Left-sub-tree Right-sub-tree Root

21. Converting Algebraic expression into
binary tree
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22. Converting Algebraic expression into
binary tree
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23. Converting Algebraic expression into
binary tree
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24. Converting Algebraic expression into
binary tree
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25. HEAP
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‫برای‬
Implement
‫کردن‬
priority Queue
‫میشود‬ ‫استفاده‬ ‫ها‬
.
‫نوع‬ ‫این‬ ‫در‬ ‫که‬ ‫عضوی‬ ‫هر‬
Queue
‫است‬ ‫اولویت‬ ‫ترین‬ ‫پائین‬ ‫یا‬ ‫باالترین‬ ‫میشود‬ ‫خارج‬ ‫ان‬ ‫از‬
.

26. Type – [HEAP ]
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1. Min Heap
Parent Node < child Node
2. Max Heap
Parent Node > child Node

27. Type – [ Max HEAP ]
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Parent Node > child Node

28. Type – [ Min HEAP ]
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Parent Node < child Node

29. [ Max HEAP ]-Example
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Parent Node > child Node
1

30. [ Max HEAP ]-Example
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1

31. [ Min HEAP ]-Example [ Class Activity ]
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2

32. [ Min HEAP ]-Example [ Class Activity ]
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2

33. [Delete Node]- [Max heap]
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34. [Delete Node]- [Max heap]
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35. Question
.1
‫در‬
‫وایبر‬
‫در‬
‫مرحله‬
exchange message
‫بین‬
‫دو‬
client
‫از‬
‫کدام‬
‫الگوریتم‬
‫بخاطر‬
encryption
‫استفاده‬
‫شده‬
‫است‬
.
‫و‬
‫معلومات‬
‫مختصر‬
‫در‬
‫ارتباط‬
‫به‬
‫ان‬
‫الگوریت‬
‫م‬
‫ارایه‬
‫دهید؟‬
.2
Multiprocessor scheduling
‫چیست؟‬
35