2. Recurrences / HW: 2.4 Quiz: 2.1, 4.1, 4.2, 5.2, 7.3, 7.4 Midterm: 8 given a recursive algorithm, state the recurrence solve a recurrence, using Master theorem given a recurrence and its solution, prove that the solution is correct solve a problem using divide&conquer (study: merge sort, closest pair of points in R 2 ) Divide&Conquer

3. Basics Quiz: 1.1, 1.2, 13.1 Midterm: 7 group a bunch of function by their asymptotic growth a = b log a b (a b ) = a bc c a b+c = (a b )(a c )

4. Basics Quiz: 1.1, 1.2, 13.1 Midterm: 7 quicksort, heapsort, mergesort, counting sort, bucket sort, radix sort, sorting lower bound heaps, B-trees union find basic geometry (do two lines intersect, is a point to the left of a line,...)

5. Dynamic programming HW: 5.1, 5.2, 5.3, 5.4, 6.3, 6.4, 7.1, 8.2, 10.1 Midterm: 10, 11, 12 Quiz: 6.1, 6.2, 7.1, 7.2 given a problem and the interpretation of the entries in the dynamic programming table, design the heart of the algorithm

6. Dynamic programming

9. Linear-time median HW: 1.3, 3.1, 3.2, 5.5 employ the linear-time median algorithm

10. Greedy algorithms HW: 4.1, 4.2, 4.3, 4.4, 6.2 Midterm: 6 Quiz: 5.1, 11.1, 11.2 does the greedy algorithm work for a given problem? find counterexample / prove it does

11. Linear programming HW: 12.1, 12.2, 12.3 Midterm: Quiz: 12.1, 12.2, given a linear program, find its dual given a problem, formulate it as a linear program (e.g., HW 12.1)

12. Linear programming

13. NP-completeness HW: Midterm: Quiz: 10.3, 11.1, 11.2 is a given algorithm polynomial-time? basic NP-complete problems: (3-SAT, Independent set, 3-Coloring, Clique, Subset-Sum, Hamilltonian path, Vertex Cover, Integer Linear Programming, Max-Cut) Cook’s Theorem

14. NP-completeness

15. Graph algorithms HW: 6.1 Quiz 9.1, 9.2 Midterm: 1, 2, 3, 5, 9 DFS, BFS, topological sort, connected components, minimum spanning tree (Kruskal, Prim), shortest paths (Dijkstra, Bellman-Ford, Warshall) maximum/maximal/perfect matching, augmenting paths, flows, residual networks, Ford-Fulkerson, maximum-weight matching, Max-Flow=Min-Cut theorem

16. Approximation algorithms vertex cover 2 - approx set cover O(log n) - approx metric TSP 1.5 - approx knapsack (1+  ) - approx

17. Reductions HW: 8.1, 8.3, 9.1, 9.2, 9.3, 11.1 Quiz: 8.2, 8.3, 10.1 solve one problem using a black-box for another problem

18. Reductions

22. Probability theory HW: 2.1, 2.2 Quiz: 3.1, 3.2, 4.3, 5.3 random variable, expectation coupon collector problem linearity of expectation Las Vegas / Monte Carlo

23. Score information HW: total - two-lowest = score 1 rank a-b Quiz: total - two-lowest = score 2 rank a-b max 220 330 score 1 25 220 score 2 20 + max 330 75 midterm 25 +