1. Minimal Spanning Tree
陳鵬宇 (float)
<float.tw@gmail.com>

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3. Spanning Tree
● 生成樹
● 從圖中分離出一顆樹包含圖中所有點

4. Spanning Tree
● 生成樹
● 從圖中分離出一顆樹包含圖中所有點

5. Minimal Spanning Tree
● 最小生成樹
● 邊的權重和最小的生成樹
5 10
8

6. Minimal Spanning Tree
● 最小生成樹
● 邊的權重和最小的生成樹
5 10
8

7. Algorithm
● Prim's Algorithm
● Kruskal's Algorithm

8. Prim Algorithm
● 每次擴張選擇與樹連接的最小權重邊
3 B
A
5 6
9
8
C
7
D

9. Prim Algorithm
● 每次擴張選擇與樹連接的最小權重邊
3 B
A
5 6
9
8
C
7
D

10. Prim Algorithm
● 每次擴張選擇與樹連接的最小權重邊
3 B
A
5 6
9
8
C
7
D

11. Prim Algorithm
● 每次擴張選擇與樹連接的最小權重邊
3 B
A
5 6
9
8
C
7
D

12. Prim Algorithm
● 每次擴張選擇與樹連接的最小權重邊
3 B
A
5 6
9
8
C
7
D

13. Prim Algorithm
● 每次擴張選擇與樹連接的最小權重邊
3 B
A
5 6
9
8
C
7
D

14. Prim Algorithm
● 每次擴張選擇與樹連接的最小權重邊
3 B
A
5 6
9
8
C
7 Cost 15
D

15. Kruskal's Algorithm
● 兩顆 MST( 把圖切割 ) 要合併時挑選之間最小權
重邊總是最好的
● 單獨的點可以視為一個 MST

16. Kruskal's Algorithm
3 B
A
5 6
9
8
C
7
D

17. Kruskal's Algorithm
● 所有邊
3 B
A
– AB – 3
– AC – 5
5 6
– AD – 8 9
– BC – 6 8
– BD – 9 C
7
– CD – 7 D

18. Kruskal's Algorithm
● sort
3 B
A
– AB – 3
– AC – 5
5 6
– BC – 6 9
– CD – 7 8
– AD – 8 C
7
– BD – 9 D

19. Kruskal's Algorithm
● sort
3 B
A
– AB – 3
– AC – 5
5 6
– BC – 6 9
– CD – 7 8
– AD – 8 C
7
– BD – 9 D

20. Kruskal's Algorithm
● sort
3 B
A
– AB – 3
– AC – 5
5 6
– BC – 6 9
– CD – 7 8
– AD – 8 C
7
– BD – 9 D

21. Kruskal's Algorithm
● sort
3 B
A
– AB – 3
– AC – 5
5 6
– BC – 6 9
– CD – 7 8
– AD – 8 C
7
– BD – 9 D

22. Kruskal's Algorithm
● sort
3 B
A
– AB – 3
– AC – 5
5 6
– BC – 6 9
– CD – 7 8
– AD – 8 C
7
– BD – 9 D

23. Kruskal's Algorithm
● sort
3 B
A
– AB – 3
– AC – 5
5 6
– BC – 6 9
– CD – 7 8
– AD – 8 C
7
– BD – 9 D

24. Note
● MST 並不唯一

25. Practice
UVa - 10034

26. Thank You for Your
Listening.
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