Paparan mengenai Binary Search Tree (BST) - Algoritma dan Struktur Data. Disusun oleh Achmad Solichin, dirangkum dari berbagai sumber.

1. BINARY SEARCH TREE
(BST)
Algoritma dan Struktur
Data
Dr. Achmad Solichin,
S.Kom, M.T.I

2. REMEMBER: TREE TERMINOLOGY
2
A
E
B
D F
C
G
IH
LJ MK N
Node / Vertex
Edges
Root
Leaves
Left subtree
Right subtree

3. EXAMPLE TREE CALCULATIONS
3
A
E
B
D F
C
G
IH
LJ MK N
A
Recall: Height of a tree is the
maximum number of edges from
the root to a leaf.
Height =
0
A
B Height =
1
What is the height of this tree?
What is the depth of node G?
What is the depth of node L?
Depth =
2
Depth =
4
Height =
4

4. BINARY TREE
4
• Binary tree: Each node has at most 2 children (branching
factor 2)
• Binary tree is
• A root (with data)
• A left subtree (may be empty)
• A right subtree (may be empty)
• Special Cases

5. BINARY SEARCH TREE (BST) DATA
STRUCTURE
4
121062
115
8
14
13
7 9
Structure property (binary tree)
 Each node has  2 children
 Result: keeps operations simple
Order property
 All keys in left subtree smaller
than node’s key
 All keys in right subtree larger
than node’s key
 Result: easy to find any given key
5
A binary search tree is a type of binary tree
(but not all binary trees are binary search trees!)

6. ARE THESE BST ?
3
1171
84
5
4
181062
115
8
20
21
7
15
6

7. ARE THESE BST ?

8. INSERTION IN BST
2092
155
12
307 17
insert(13)
insert(8)
insert(31)
(New) insertions happen
only at leaves – easy!
10
8 31
13
8
Again… worst case running time is O(n),
which may happen if the tree is not
balanced.

9. INSERTION IN BST

10. SEARCHING IN BST
Find “4” !
Start with root Go to left, because 4 < 8 Go to right, because 4 > 3Go to left, because 4 < 6
and we found it

11. SEARCHING IN BST: ALGORITHM

12. OTHER BST “FINDING”
OPERATIONS
FindMin: Find minimum node
 Left-most node
FindMax: Find maximum node
 Right-most node
2092
155
12
307 1710
12

13. DELETION IN BST
2092
155
12
307 17
Why might deletion be harder than insertion?
10
13

14. DELETION IN BST
Basic idea: find the node to be removed,
then
“fix” the tree so that it is still a binary
search tree
Three potential cases to fix:
 Node has no children (leaf)
 Node has one child
 Node has two children
14

15. DELETION – THE LEAF CASE
2092
155
12
307 17
delete(17)
10
15

16. DELETION – THE ONE CHILD
CASE
2092
155
12
307 10
16
delete(15)

17. DELETION – THE ONE CHILD
CASE
2092
5
12
307 10
17
delete(15)

18. DELETION – THE TWO CHILD
CASE
3092
205
12
7
What can we replace 5 with?
10
18
delete(5)
4

19. DELETION – THE TWO CHILD
CASE
What can we replace the node with?
Options:
successor minimum node from right subtree
findMin(node.right)
predecessor maximum node from left subtree
findMax(node.left)
19

20. DELETION: THE TWO CHILD CASE
(EXAMPLE)
3092
235
12
7 10
18
1915 3225
delete(23)

21. DELETION: THE TWO CHILD CASE
(EXAMPLE)
3092
235
12
7 10
18
1915 3225
delete(23)

22. DELETION: THE TWO CHILD CASE
(EXAMPLE)
22
3092
195
12
7 10
18
1915 3225
delete(23)

23. DELETION: THE TWO CHILD CASE
(EXAMPLE)
3092
195
12
7 10
18
15 3225
Success! 
delete(23)

24. DELETION: ALGORITHM

25. BST PERFORMANCE

26. REFERENSI
 Slide by Lauren Milne, entitled “Lecture 6: Binary Search Trees”,
University of Washington
 Slide from King Abdulaziz University, entitled “Binary Search
Tree”.
 https://www.programiz.com/dsa/binary-search-tree
 https://en.wikipedia.org/wiki/Binary_search_tree

27. THANK YOU
Dr. Achmad Solichin, S.Kom. M.T.I.
Universitas Budi Luhur
achmad.solichin@budiluhur.ac.id |
http://achmatim.net