SHORTEST PATHS STUDY GUIDE


Graph Representation

Shortest path representation

Edge relaxation

Manually performing Dijkstra's algorithm, Acyclic Shortest Paths algorithm, and Bellman-Ford algorithm. These should be very easy to manully execute.

Dijkstra's algorithm

Acyclic shortest paths

Bellman-Ford algorithm

Recommended Problems

C level

  1. Fall 2009 Final, #4
  2. Fall 2010 Final, #5
  3. Textbook 4.3.1 and 4.4.1

B level

  1. Spring 2008 Final, #11 (this should be very easy if you've done Seam Carving!)
  2. Fall 2011 Final, #4
  3. Spring 2012 Final, #5
  4. Fall 2012 Final, #5
  5. Think about how to solve the undirected version of the shortest paths problem. Why is it easy for graphs with positive edge weights? Why is it hard if we include negative edge weights?
  6. Textbook 4.4.25
  7. Since Prim's algorithm and Dijkstra's algorithm are so similar, why do we need to check for cycles in Prim's, but not in Dijkstra's?
  8. Textbook 4.4.42 and 4.4.44

A level

  1. Fall 2008 Final, #11 (I remember getting asked this at a career fair as a freshman!)
  2. Textbook 4.4.34
  3. Textbook 4.4.37