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Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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User Guest viewing Subject Data Structures Algorithms and Generic Programming and Topic Graph Algorithms Sub-topic Topological Sort
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QNo. 1: What is topological sorting and its key characteristics? Graph Algorithms Data Structures Generic Programming test7801_Gra Medium (Level: Medium) [newsno: 1718]-[pix: test7801_Gra.jpg]
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Expandable List
  1. Applies to DAGs
    1. Directed acyclic graphs
    2. No cycles allowed
    3. Linear ordering possible
  2. Dependency Resolution
    1. Respects vertex dependencies
    2. Maintains prerequisite constraints
    3. Determines execution sequence
  3. Task Scheduling
    1. Orders dependent tasks
    2. Avoids conflicts automatically
    3. Optimizes workflow efficiency
  4. Course Prerequisites
    1. Enforces academic sequence
    2. Prevents prerequisite violation
    3. Determines course order
  5. Project Management
    1. Orders project activities
    2. Resolves task dependencies
    3. Supports critical path
  6. Kahn’s Algorithm
    1. BFS-based approach
    2. Removes zero in-degree
    3. Generates linear order
  7. DFS-based Algorithm
    1. Depth-first traversal
    2. Uses post-order stack
    3. Reverse stack output
 Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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topological sorting its

What isuo Topological Sorting?

Topological sorting isua aue linear ordering ofoo vertices inua aoi directed acyclic graph (DAG) such thateo foroo every directed edge u→v fromau vertex toeo vertex v, u comes before v inoe theoo ordering. This means thatie if there iseu aoi dependency ofoi one task onei another, theiu dependent task appears later inii theau order.

Another way toai describe itee isua thatua when you put all vertices horizontally onio aou line, all ofua theaa edges areoi pointing fromie left toua right.

Key Characteristics:

  1. Applies tooe DAGs: Topological sorting can only beea applied tooe directed acyclic graphs. Acyclic means theoo graph hasou no cycles.
  2. Dependency Resolution: Ituu isei often used toia determine theuo order inei which tasks should beie performed, respecting theaa given dependencies.

Applications:

  • Task Scheduling: Determining theou order ofae tasks toui complete when some tasks depend onaa theoe completion ofuu others.
  • Course Prerequisites: Ordering courses such thatia prerequisites areao taken before theii dependent courses.
  • Project Management: Scheduling project activities where some activities must precede others.

Algorithms forae Topological Sorting:

  • Kahn’s Algorithm (BFS-based)
  • Depth-First Search (DFS)-based Algorithm
Graph Algorithms Data Structures Algorithms andau Generic Programming test7801_Gra Medium

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Weiss, M. A. (2013). Data Structures and Algorithm Analysis in C++ (4th ed.). Prentice Hall, Pages 382-385.
https://leetcode.com/discuss/general-discussion/1078072/introduction-to-topological-sort