This presentation focuses on the motivation of using a binary search tree. (Course Homework)

1. Binary Search Tree
Siwei Ma

2. A sorted list
3 21 38 40 62 75 87

3. Binary Search for sorted list
3 21 38 40 62 75 87
Try to find 38

4. Binary Search for sorted list
3 21 38 40 62 75 87
Try to find 38
Time complexity: O(log n)

5. Insertion into a list is expensive
3 21 38 40 62 75 87
30

6. Insertion into a list is expensive
3 21 38 40 62 75 87
30
Move all to the next location

7. Insertion into a list is expensive
3 21 30 38 40 62 75 87
Time complexity: O(n)

8. Linked list
3
Next:
21
Next:
38
Next:
40
Next:
62
Next:
75
Next:
A linked list

9. Easy insertion in linked list
3
Next:
21
Next:
38
Next:
40
Next:
62
Next:
75
Next:
30
Next:

10. Easy insertion in linked list
3
Next:
21
Next:
38
Next:
40
Next:
62
Next:
75
Next:
30
Next:
Time complexity: O(1)

11. They all have own advantages
Search Insertion
(sorted) list
Linked list
O(log n) O(n)
O(1)O(n)

12. Binary search tree
3 21 38 40 62 75 87
Try to re-construct the data structure

13. 40
Next:
21
Next:
3
Next:
38
Next:
62
Next:
87
Next:
75
Next:
3 21 38 40 62 75 87

14. 40
Next:
21
Next:
3
Next:
38
Next:
62
Next:
87
Next:
75
Next:
3 21 38 40 62 75 87

15. Binary search tree
40
Next:
21
Next:
3
Next:
38
Next:
62
Next:
87
Next:
75
Next:

16. Binary search tree
40
Next:
21
Next:
3
Next:
38
Next:
62
Next:
87
Next:
75
Next:
Try to find 38

17. Search
40
Next:
21
Next:
3
Next:
38
Next:
62
Next:
87
Next:
75
Next:
Try to find 38

18. Search
40
Next:
21
Next:
3
Next:
38
Next:
62
Next:
87
Next:
75
Next:
Try to find 38

19. Binary search tree
40
Next:
21
Next:
3
Next:
38
Next:
62
Next:
87
Next:
75
Next:

20. Summary
Search Insertion
(sorted) list
Linked list
O(log n) O(n)
O(1)O(n)
Binary search tree O(log n) O(log n)

21. More trees on road!