## En 1. What is a GRAPH? 2. The computer handles 3. Speeding up operations using graphs ## Ja 1. グラフ構造とは 2. コンピュータ上でグラフを表す 3. グラフを用いて高速に計算する

1. GRAPHICAL
STRUCTURES
in our lives
xryuseix

2. xryuseix
Algorithem and Data Structure
RiPPro (leader), RiST (sub-Leader)
HELLO!
2
Username :
Good At :
G r o u p :
Self-introduction

3. Presentation Theme
“All events in our lives can be
represented by a GRAPHICAL STRUCTURE.”
3

4. Contents
4
1. What is a GRAPH?
2. The computer handles
3. Speeding up operations using graphs
4. Conclusion

5. What is a GRAPH?
Learn the basics of graph structure.
5
1

6. Elements of a graph
6
Elements
Node(Vertex) Edge

7. Define a graph
7
Definition
NEXT :
Concrete Example

8. Example of a graph
8
Example of Graph

9. 9
Example of Graph(1)
https://www.irasutoya.com/
Example of a graph

10. 10
Example of Graph(2)
https://www.irasutoya.com/
Follow
FollowFollow
Follow
Example of a graph

11. Elements of a graph (Conclusion)
11
Elements
Node(Vertex) Edge
State
Relationship
∴ All events are on the graph
(It's not necessarily optimal.)

12. The computer handles
the graphs
Write a program to achieve
my goals.
12
2

13. Graph Implementation
13
Conclusion : Adjacency List

14. Graph Implementation
14
Conclusion : Adjacency List
http://vivi.dyndns.org/tech/cpp/list.html
List

15. Graph Implementation
15
Conclusion : Adjacency List
ListArray = List List List List
|V|
, , , ,

16. Graph Implementation
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Conclusion : Adjacency List
When stretching the edge from A to B :
Array[A].add(B)
※Add…Methods to add the right element to the list on the left

17. Graph Implementation
17
Example(C++)
TOO EASY!!!
(for IT student)

18. Speeding up operations
using graphs
Fast operations using segment trees.
18
3

19. What is a Segment-Tree ?
19

20. What is a Segment-Tree ?
20
Parent
ChildChild

21. What is a Segment-Tree ?
21
Parent
ChildChild
A graph in which all of the
formulas 1 and 2 are satisfied!

22. What is a Segment-Tree ?
22
Example
3 48 1
11 5
16
Sum
SumSum

23. What is a Segment-Tree ?
23
Example
3 48 1
11 5
16
intervals
Fast calculation of total intervals.
8 + 3 + 4 = 11 + 4
O(N) -> O(log N)
(N := number of elements)
O(x) ... Bachmann-Landau O-notation
Sum
SumSum

24. Compare - Problem
24https://onlinejudge.u-
aizu.ac.jp/courses/library/3/DSL/all/DSL_2_B

25. Compare - Condition
25
computer performance
CPU 3.1 GHz dual core Intel Core i5
Memory 8 GB 2133 MHz LPDDR3
user function
normal Coding with the stupid way.
segTree Coding with the Segment-Tree.
assertion Checking the output.
measurement program
testcase https://judgedat.u-aizu.ac.jp/testcases/DSL_2_B/20/in

26. Compare - Result
26
The difference is
15
times !!
*1) Average value after 10 measurements.

27. Conclusion
Here are my conclusions so far.
27
4

28. Conclusion
▰ All events are on the graph.
▰ Graphs can be easily handled
on a computer.
▰ It is possible to speed up certain
operations with a graph.
28

29. Conclusion
▰ All events are on the graph.
▰ Graphs can be easily handled
on a computer.
▰ It is possible to speed up certain
operations with a graph.
29

30. Conclusion
▰ All events are on the graph.
▰ Graphs can be easily handled
on a computer.
▰ It is possible to speed up certain
operations with a graph.
30
That's all, Thanks!