Data Structure
  • 資料結構自學筆記
  • 1 - Stack & Queue
    • 1.1 - Stack
    • 1.2 - Queue
    • 1.3 - Stack and Queue
  • 2 - Tree & Binary Tree
    • 2.1 - Tree
    • 2.2 - Binary Tree
    • 2.3 - Binary Tree Traversal
    • 2.4 - Binary Search Tree
    • 2.5 - Heap
    • 2.6 - Thread Binary Tree
    • 2.7 - Tree and Binary Tree Conversion
    • 2.8 Advanced Trees
      • 2.8.1 - Min-Max Heap
      • 2.8.2 - Deap
      • 2.8.3 - Symmetric Min-Max Heap
      • 2.8.4 - Extended Binary Tree
      • 2.8.5 - AVL Tree
      • 2.8.6 - M-Way Search Tree
      • 2.8.7 - B Tree
      • 2.8.8 - Red-Black Tree
      • 2.8.9 - Optimal Binary Search Tree
      • 2.8.10 - Splay Tree
      • 2.8.11 - Leftest Heap
      • 2.8.12 - Binomial Heap
  • 3 - Search & Sort
    • 3.1 - Searching
    • 3.2 - Elementary Sorting
      • 3.2.1 - Insertion Sort
      • 3.2.2 - Selection Sort
      • 3.2.3 - Bubble Sort
      • 3.2.4 - Shell Sort
    • 3.3 - Sophisticated Sorting
      • 3.3.1 - Quick Sort
      • 3.3.2 - Merge Sort
      • 3.3.3 - Heap Sort
      • 3.3.4 - Radix Sort
      • 3.3.5 - Bucket Sort
      • 3.3.6 - Counting Sort
    • 3.4 - Summary
  • 4 - Graph
    • 4.1 - Intro
    • 4.2 - Graph Traversal
    • 4.3 - Spanning Tree
      • 4.3.1 - Kruskal's algorithm
      • 4.3.2 - Prim's algorithm
      • 4.3.3 - Sollin's algorithm
    • 4.4 - Shortest Path Length
      • 4.4.1 - Dijkstra's algorithm
      • 4.4.2 - Bellman-Ford algorithm
      • 4.4.3 - Floyd-Warshall algorithm
    • 4.5 - AOV Network
    • 4.6 - AOE Network
    • 4.7 - Others
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  1. 4 - Graph

4.5 - AOV Network

Activity-on-Vertex Network

Previous4.4.3 - Floyd-Warshall algorithmNext4.6 - AOE Network

Last updated 6 years ago

AOV Network中， G=<V,E>G=<V,E>G=<V,E>為有向圖:

  • V(vertex): 代表工作(Activity)

  • E(edge): 代表工作之間的執行順序

    e.g. i→j:i→j:i→j: 代表 iii 必須先於 jjj 執行

Topological Sort

給定一個不具cycle的AOV Network，則至少可以找出≥1組頂點拜訪順序，此順序滿足:

若iii有path到jjj，則在此順序中，iii必定出現在jjj前。

若有cycles，則沒有topological sort。

  • 求法:

  1. 先找出in-degree = 0的頂點

  2. 輸出此頂點，並將此頂點與其out-edge刪除

  3. 重複以上步驟，直到沒有頂點，或找不到in-degree = 0的頂點

  4. 若仍有剩餘的頂點代表此圖沒有topological sort

e.g.

Topological Sort: 1 (2, 3, 4) (5, 6) 括號中可交換順序。