1. OVERVIEW 1-st Midterm: 3 problems 2-nd Midterm 3 problems
Sorting
Quicksort
Data structures
binary heaps
BST
Greedy algorithm
Prim’s 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
P, NP, NPC
prove that the problem is NP
Approximation Algorithms
Vertex Cover
TSP
Steiner tree problem
1-st Midterm: 3 problems
2-nd Midterm 3 problems
Only in Finals: 4 problems

2. NP-Completeness P, NP, NPC Example 1: Example 2:
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)