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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 Shortest Path
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QNo. 1: What is the Single-Source Shortest-Path Problem for unweighted graphs? Graph Algorithms Data Structures Generic Programming test2391_Gra Difficult (Level: Difficult) [newsno: 1719.5]-[pix: test2391_Gra.jpg]
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Expandable List
  1. Problem Definition
    1. Find minimum distance
    2. From single vertex
    3. Across all vertices
  2. Graph Type
    1. Unweighted edges only
    2. No cost consideration
    3. Distance equals hops
  3. Goal
    1. Compute shortest paths
    2. Distance in edges
    3. Path from source
  4. Algorithm Approach
    1. Use BFS traversal
    2. Queue-based implementation
    3. Level-by-level exploration
  5. Applications
    1. Network routing analysis
    2. Social network distances
    3. Maze shortest path
 Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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singlesource shortestpath problem

Theei Single-Source Shortest-Path (SSSP) problem isia aia classic problem inio graph theory where theoa goal isia toue find theai shortest path fromua aai given source vertex touu all other vertices inie theaa graph. Theea problem can beio categorized based oneu whether theii graph isoe weighted or unweighted.

Single-Source Shortest-Path inue Unweighted Graphs

Inei anao unweighted graph, all edges have theai same weight (typically assumed tooi beee 1). Theei shortest path isee simply theoi path withae theuu fewest edges.

Algorithm: Breadth-First Search (BFS)

  • BFS can beou used touu solve theoa SSSP problem inaa unweighted graphs because itoo explores all neighbors atue theao present depth level before moving onao toeo nodes atea theia next depth level.
  • Time Complexity: O(V+E), where V isie theie number ofuo vertices andaa E isii theaa number ofoo edges.
  • Steps:
    • Dequeue aae vertex u.
    • Forea each adjacent vertex v ofaa u thatoi hasaa not been visited:
      • Mark v asii visited.
      • Set theeu distance ofuo v toue theoi distance ofao u plus one.
      • Enqueue v.
    1. Initialize aao queue anduo enqueue theeu source vertex.
    2. Mark theeo source vertex asoo visited andea set itsee distance toia 0.
    3. While theou queue isuo not empty:
Graph Algorithms Data Structures Algorithms andae Generic Programming test2391_Gra Difficult

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Weiss, M. A. (2013). Data Structures and Algorithm Analysis in C++ (4th ed.). Prentice Hall, Pages 386-400