This document discusses trees and their applications in computer science. It defines different types of trees and tree traversal methods. Algorithms for tree traversal like breadth-first search and depth-first search are presented along with examples. Real-world applications of trees are explored, including B-trees, B+ trees, Huffman coding and directory trees. The document describes projects developed using B-trees and B+ trees for dictionary word search and a directory tree for file searching.

1. Analysis of Tree in Computer-
based Application
Department of Computer Science & Engineering

2. 2Department of Computer Science & Engineering
Presented By
Abhijeet Das (011132133)
Md. Kamal Ibne Sharif (011132104)
Nazmul Hyder (011131085)
Md. Al Alamin Khan (011132152)
Supervised By
Dr. Mohammad Nurul Huda
Professor
Department of Computer Science &
Engineering
United International University

3. 3Department of Computer Science & Engineering
Outline
• Definition of Tree
• Construction of a Binary Tree
• Different types of Tree Traversal
• Algorithms of Tree Traversal
• Applications of Tree
• Conclusion

4. 4Department of Computer Science & Engineering
What is Tree?

5. 5Department of Computer Science & Engineering
Different Types of Tree Traversal
• Pre-order Traversal
• In-order Traversal
• Post-order Traversal
• Level-order Traversal

6. 6Department of Computer Science & Engineering
How to Construct a Binary Tree?
6 4 9 8 10 3 5
6
4
53
9
108

7. 7Department of Computer Science & Engineering
Pre-order Traversal
Pseudocode
void preorder(BtreeNode){
if(node != NULL){
visit(node)
preorder(node->left)
preorder(node->right)
}
}
6 4 3 5 9 8 10

8. 8Department of Computer Science & Engineering
In-order Traversal
Pseudocode
void preorder(BtreeNode){
if(node != NULL){
preorder(node->left)
visit(node)
preorder(node->right)
}
}
3 4 5 6 8 9 10

9. 9Department of Computer Science & Engineering
Post-order Traversal
Pseudocode
void preorder(BtreeNode){
if(node != NULL){
preorder(node->left)
preorder(node->right)
visit(node)
}
}
3 5 4 8 10 9 6

10. 10Department of Computer Science & Engineering
Level-order Traversal
Pseudocode
while(!q.isEmpty()){
levelNodes = q.size();
while(levelNodes>0){
Node n = (Node)q.remove();
System.out.print(" " + n.data);
if(n.left!=null) q.add(n.left);
if(n.right!=null) q.add(n.right);
levelNodes--;
}
System.out.println("");
}
6 4 9 3 5 8 10

11. 11Department of Computer Science & Engineering
Algorithms of Tree Traversal
• Breadth-first search tree
• Depth-first search tree
• Heap tree

12. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A
Output:

13. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G
Output: A

14. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G
Output: A

15. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G
Output: A B

16. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G
Output: A B

17. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G C
Output: A B G

18. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G C
Output: A B G

19. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A CB G

20. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A CB G

21. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A CB G D

22. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A CB G D

23. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A C EB G D

24. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A C EB G D

25. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A C EB G D F

26. 12Department of Computer Science & Engineering
Breadth-first search tree
A
B D
G F
C E
Queue: A B G EC D F
Output: A C EB G D F
Queue is empty

27. 13Department of Computer Science & Engineering
Pseudocode of Breadth-first search tree

28. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
S
Stack
Output: S

29. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C A
S
Stack
Output: S A

30. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C A
D
S
Stack
Output: S A D

31. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
B
A
D
S
Stack
Output: S A D B

32. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
B
A
D
S
Stack
Output: S A D B

33. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
C
B
A
D
S
Stack
Output: S A D B C

34. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
C
B
A
D
S
Stack
Output: S A D B C

35. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
C
B
A
D
S
Stack
Output: S A D B C

36. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
C
B
A
D
S
Stack
Output: S A D B C

37. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
C
B
A
D
S
Stack
Output: S A D B C

38. 14Department of Computer Science & Engineering
Depth-first Search tree
S
A B
D
C
C
B
A
D
S
Stack
Output: S A D B C
Stack is empty

39. 15Department of Computer Science & Engineering
Pseudocode of Depth-first Search tree

40. 16Department of Computer Science & Engineering
Heap tree
45 33 3 17 25 80
45
33 3
2517 80
80
33 45
2517 3
Heap Tree Max Heap

41. 17Department of Computer Science & Engineering
80
33
17 325
45
80

42. 17Department of Computer Science & Engineering
3
33
17 25
45
80

43. 17Department of Computer Science & Engineering
3
33
17 25
45
80

44. 17Department of Computer Science & Engineering
45
33
17 25
3
80

45. 17Department of Computer Science & Engineering
45
33
17 25
3
80 45

46. 17Department of Computer Science & Engineering
25
33
17
3
80 45

47. 17Department of Computer Science & Engineering
33
25
17
3
80 45

48. 17Department of Computer Science & Engineering
33
25
17
3
80 45 33

49. 17Department of Computer Science & Engineering
17
25 3
80 45 33

50. 17Department of Computer Science & Engineering
25
17 3
80 45 33

51. 17Department of Computer Science & Engineering
25
17 3
80 45 2533

52. 17Department of Computer Science & Engineering
3
17
80 45 2533

53. 17Department of Computer Science & Engineering
17
3
80 45 2533

54. 17Department of Computer Science & Engineering
17
3
80 45 172533

55. 17Department of Computer Science & Engineering
3
80 45 17 32533

56. 18Department of Computer Science & Engineering
Pseudocode of Heap tree

57. 19Department of Computer Science & Engineering
Applications of Tree
• B-Tree
• B+ Tree
• Huffman Coding
• Directory Tree Search

58. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
40

59. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
10 40

60. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
10 40 50

61. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
10 40
50
60

62. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
10 20 40
50
60

63. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
40
30 50
60 7010 20

64. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
35 40
30 50
60 70 7510 20

65. 20Department of Computer Science & Engineering
B-Tree
M=4
40 10 50 60 20 30 70 35 75 80
35 40
30 50 75
60 7010 20 80

66. 21Department of Computer Science & Engineering
Pseudocode of B-Tree insertion

67. 22Department of Computer Science & Engineering
Uses of B-Tree in Real Life Applications
• Search Optimization
• Dictionary
• Phonebook
• Database System
We developed a dictionary word search application using B-Tree.

68. 23Department of Computer Science & Engineering
Pseudocode of dictionary word search using B-Tree

69. 24Department of Computer Science & Engineering
B+ Tree
M=4
40 10 50 60 20 30 70 35 75 80
40

70. 24Department of Computer Science & Engineering
B+ Tree
M=4
40 10 50 60 20 30 70 35 75 80
10 40 50

71. 24Department of Computer Science & Engineering
B+ Tree
M=4
40 10 50 60 20 30 70 35 75 80
10 40
50
50 60

72. 24Department of Computer Science & Engineering
B+ Tree
M=4
40 10 50 60 20 30 70 35 75 80
10 20 40
50
50 60

73. 24Department of Computer Science & Engineering
B+ Tree
M=4
40 10 50 60 20 30 70 35 75 80
30 40
30 50
50 60 7010 20

74. 24Department of Computer Science & Engineering
B+ Tree
M=4
40 10 50 60 20 30 70 35 75 80
30 35 40
30 50
50 60 7010 20

75. 24Department of Computer Science & Engineering
B+ Tree
M=4
40 10 50 60 20 30 70 35 75 80
30 35 40
30 50 70
50 6010 20 70 75 80

76. 25Department of Computer Science & Engineering
Uses of B+ Tree in Real Life Applications
• Search Optimization
• Dictionary
• Phonebook
• Database System
We also developed a dictionary word search application using B+ Tree.

77. 26Department of Computer Science & Engineering
Pseudocode of dictionary word search using B+ Tree

78. 27Department of Computer Science & Engineering
Huffman Coding

79. 27Department of Computer Science & Engineering
Huffman Coding
=100 words
=100*3=300bit
=45.1+13.3+12.3+16.3+9.4+5.4=224bit

80. 28Department of Computer Science & Engineering
Pseudocode of Huffman Tree Construction

81. 29Department of Computer Science & Engineering
Uses of Huffman Coding in Real life application
• Data Compression

82. 30Department of Computer Science & Engineering
Our Applications
• Dictionary word search using B-Tree
• Dictionary Word search using B+ Tree
• Directory Search using Binary Search Tree

83. 31Department of Computer Science & Engineering
Conclusion
In real life there are so many computer based application
uses tree data structure such as,
• Folder in Operating System
• Linux file System
• HTML Document Object Model(DOM)
• Network Routing
• Syntax Tree in Compiler
• Auto Corrector and Spell Checker