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Minimal Spanning Tree
陳鵬宇 (float)<float.tw@gmail.com>
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Spanning Tree● 生成樹● 從圖中分離出一顆樹包含圖中所有點
Spanning Tree● 生成樹● 從圖中分離出一顆樹包含圖中所有點
Minimal Spanning Tree● 最小生成樹● 邊的權重和最小的生成樹
5
8
10
Minimal Spanning Tree● 最小生成樹● 邊的權重和最小的生成樹
5
8
10
Algorithm● Prim's Algorithm● Kruskal's Algorithm
Prim Algorithm● 每次擴張選擇與樹連接的最小權重邊
A
D
B
C
5
3
7
9
6
8
Prim Algorithm● 每次擴張選擇與樹連接的最小權重邊
A
D
B
C
5
3
7
9
6
8
Prim Algorithm● 每次擴張選擇與樹連接的最小權重邊
A
D
B
C
5
3
7
9
6
8
Prim Algorithm● 每次擴張選擇與樹連接的最小權重邊
A
D
B
C
5
3
7
9
6
8
Prim Algorithm● 每次擴張選擇與樹連接的最小權重邊
A
D
B
C
5
3
7
9
6
8
Prim Algorithm● 每次擴張選擇與樹連接的最小權重邊
A
D
B
C
5
3
7
9
6
8
Prim Algorithm● 每次擴張選擇與樹連接的最小權重邊
A
D
B
C
5
3
7
9
6
8
Cost 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
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
● 所有邊– AB – 3– AC – 5– AD – 8– BC – 6– BD – 9– CD – 7
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
● sort– AB – 3– AC – 5– BC – 6– CD – 7– AD – 8– BD – 9
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
● sort– AB – 3– AC – 5– BC – 6– CD – 7– AD – 8– BD – 9
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
● sort– AB – 3– AC – 5– BC – 6– CD – 7– AD – 8– BD – 9
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
● sort– AB – 3– AC – 5– BC – 6– CD – 7– AD – 8– BD – 9
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
● sort– AB – 3– AC – 5– BC – 6– CD – 7– AD – 8– BD – 9
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
● sort– AB – 3– AC – 5– BC – 6– CD – 7– AD – 8– BD – 9
Kruskal's Algorithm
A
D
B
C
5
3
7
9
6
8
Note● MST 並不唯一
Practice
UVa - 10034
102/3/27 26
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