1 / 23

Recurrences /

Recurrences /. Divide&Conquer. 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

anise
Download Presentation

Recurrences /

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recurrences / Divide&Conquer 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 R2)

  2. Basics Quiz: 1.1, 1.2, 13.1 Midterm: 7 group a bunch of function by their asymptotic growth loga b a = b c (ab ) = abc ab+c = (ab)(ac)

  3. 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, ...)

  4. 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

  5. Dynamic programming

  6. Dynamic programming

  7. Dynamic programming

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

  9. 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

  10. 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)

  11. Linear programming

  12. 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

  13. NP-completeness

  14. 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

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

  16. 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

  17. Reductions

  18. Reductions

  19. Reductions

  20. Reductions

  21. 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

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

More Related