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

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Minimal Spanning Tree● 最小生成樹● 邊的權重和最小的生成樹

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8

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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

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3

7

9

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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

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