TREES

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# TREES - PowerPoint PPT Presentation

TREES. Tree. Minimal Terdiri dari 1 node (simpul). node. root. m – ary Tree. leaf. leaf. Branch. binary. Binary Tree. Binary juga disebut 2-ary Tree Yaitu Tree dengan anak &lt;=2. +. A. B. Representasi Infix pada Tree. 1. Infix A+B. 2. Infix A * B ^ C – D. -. D. *. A. ^. B.

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## PowerPoint Slideshow about ' TREES' - gail-huber

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### TREES

Tree
• Minimal Terdiri dari 1 node (simpul)

node

root

m – ary Tree

leaf

leaf

Branch

binary

Binary Tree

Binary juga disebut 2-ary Tree

Yaitu Tree dengan anak <=2

+

A

B

1. Infix A+B

2. Infix A * B ^ C – D

-

D

*

A

^

B

C

+

/

A

D

B

E

3. Infix (A+B) * C + D / E

+

*

C

Tree Level
• Tree dibawah

N0

Level 0

N3

Level 1

N1

N2

Level 2

N5

N4

N6

N7

N8

N9

N10

N11

Level 3

Tree Level
• Keterangan

Root = N0

Leaf = N4,N5,N6,N7,N9,N10,N11

Branch node = N1,N2,N3,N8

T1 = N1,N4,N5,N6

T2 = N2,N7

T3 = N3,N8,N9,N10,N11

Depth = Max Level

N0

N3

N1

N9

N8

N4

N5

N6

N10

N11

N2

N7

Representasi Tree

1. Diagram Venn

Representasi Tree

2. Pedigree Chart

N0

N3

N1

N2

N5

N4

N6

N7

N8

N9

N10

N11

N4

N5

N1

N6

N0

N2

N7

N10

N8

N3

N11

N9

Representasi Tree

3. Linear chart

Representasi Tree

4. Nested Parentheses

(N0(N1(N4)(N5)(N6))(N2(N7))

(N3(N8(N10)(N11))(N9)))

N0

N1

N4

N5

N6

N2

N7

N3

N8

N10

N11

N9

Representasi Tree

5. Bar Chart

Representasi Tree

6. Level-Number Chart

1 N0

2 N1

3 N4

3 N5

3 N6

2 N2

3 N7

2 N3

3 N8

4 N10

4 N11

3 N9

A

A

B

B

A

A

=

B

B

General Tree Vs Binary Tree
• General Tree
• Binary Tree

A

B

C

D

E

F

G

J

K

H

I

Binary Tree dalam Array
• Representasi Binary Tree pada Array

Anak kiri = 2n

Anak Kanan = 2n+1

n = index saat ini

Konversi General Tree ke Binary Tree
• Langkah-langkah konversi:
• menghapus semua cabang (branch) yang terhubung pada setiap node, kecuali cabang yang paling kiri. Selanjutnya menghubungkan semua node pada level yang sama dengan branch
• mengubah menjadi binary-tree, di mana branch kiri adalah branch yang vertical & branch kanan adalah branch yang horizontal.

Data

L – Child

R – Child

L

R

D

Print Data

• Traversal Inorder : L D R
• Traversal Preorder : D L R
• Traversal Postorder : L R D

B

A

A

B

C

C

D

E

• Inorder = A B C
• Preorder = B A C
• Postorder = A C B
• Inorder = D B E A C
• Preorder = A B D E C
• Postorder = D E B C A

A

A

A

B

B

C

D

B

C

D

E

C

E

F

G

F

D

E

F

G

G

Inorder : E FG B C D A

Preorder : A B E F G C D

Postorder : G F E D C B A

Soal

Gambarkan Binary Tree yang dimaksud

• Traversal Preorder : ABCDEFGHI
• Traversal Inorder : CDEBFAIHG
• Traversal Postorder: EDACGFBH, jumlah child untuk masing-masing node adalah: A = 1; B = 2; C = 0; D = 1; E = 0; F = 1; G = 0; H = 2