OVERVIEW

1
OVERVIEW

• Sorting
• Quicksort
• Data structures
• binary heaps
• BST
• Greedy algorithm
• Prims algorithm
• Dynamic Programming
• Longest Common subsequence
• shortest triangulation
• Shortest Paths
• Dijkstra
• Bellman-ford
• Matrix Multiplication/Floyd/Johnson
• Computational Geometry
• Convex hull
• Closest Pair
• Voronoi triangulation/graph
• NP-completeness

1-st Midterm 3 problems
2-nd Midterm 3 problems
Only in Finals 4 problems
2
NP-Completeness

• P, NP, NPC
• Yes/no for problems in the book
• Is Max Independent set is NPC?
• If Yes then to which NPC problem we reduce it in
  class?
• prove that the problem is NP
• given a problem,
• YES can be verified in poly-time with the
  certificate
• Example 1
• find diameter of the graph (maximum distance)
• In P since we can use all shortest path
• Since P is in NP, the problem is in NP
• Example 2
• is there proper k-coloring of graph?
• Given coloring we can check in poly-time if it is
  proper

3
FINALS

• Be very careful and concentrated
• Do NOT let yourself stuck with one problem
• CHECK each answer (leave 15min at the end)