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Some graphs you may have met under different circumstances.

This course explores essential concepts such as topological sort for class order, DFS for maze navigation, avoiding loops using set ADT, analyzing electronic circuits, compiler analysis, common subexpression elimination, and sorting algorithms. Understand connected components, Java class hierarchy, minimum spanning tree, maximal matching, and the Six Degrees of Kevin Bacon.

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Some graphs you may have met under different circumstances.

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  1. Some graphs you may have met under different circumstances.

  2. Course prerequisites • Topological sort gives order to take classes

  3. Maze

  4. Depth first search – Web as graph • Avoid loops: don’t repeat nodes. • Use some kind of Set ADT

  5. Electronic circuits • Edges labelled (resistors, switch, etc) • Analyze Zasha’s incompetence in EE

  6. Profiler call frequency info

  7. Compiler analysis – Common Subexpression Elimination

  8. Proofs – best case correct sorting by comparison • List is x1,…,x8 • Edge is comparison • <7 edges graph not connected • Connected componentscould be on either side.How would the algorithmknow?

  9. (small part of) Java class hierarchy

  10. Cheapest Computer Network – Minimum Spanning Tree

  11. Capacity of highways – max flow

  12. TA assignments • Bipartite graph – 2 node types (TAs and Courses) • Maximal matching (assign as many TAs to as many courses as possible)

  13. Six degrees of Kevin Bacon

  14. Six degrees of Kevin Bacon

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