Lecture Notes For All: Algorithms and Data Structures Notes

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Wednesday, February 24, 2010

Algorithms and Data Structures Notes

Algorithms










Description: This lectures will provide a rigorous introduction to the design and
analysis of algorithms. Here we discuss classic problems (e.g., sorting,
traveling salesman problem), classic algorithm design strategies (e.g.,
divide-and-conquer, greedy approaches), and classic algorithms and data
structures (e.g., hash tables, Dijkstra's algorithm). We will also analyze
algorithm complexity throughout, and touch on issues of tractibility such
as "NP-Completeness".
Texts:
Required:
Introduction to Algorithms (Second Edition) by Cormen, Leiserson,
Rivest, and Stein, McGraw-Hill (2001).

This book is similar to the first edition, so you could probably get by with
only the first edition. However, all homework problems assigned from the
book will be referenced from the second edition; it is your responsibility to
find a way to look them up. I strongly recommend that you buy the text
rather than borrow it; this is one of only two text books that I still use on a
regular basis. It is an indispensable reference.


Lectures: A tentative schedule of lecture topics is given below. The "CULTURE" topics
represent interesting but non-essential material from fields such as computational geometry and
computer graphics; they add some variety to the schedule but also give us some
slack if we get behind schedule. If we cover a "culture" topic
in class, you will be tested on it.


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Number Date Topic
Source
Text
1 1/16 Introduction, administration, time and space complexity

PPT

--
2 1/18 Basics: asymptotic notation PPT 3.1-3.2
3 1/21 Basics: recurrences (mergesort) PPT 4.1
4 1/23 Basics: recurrences
continued, master theorem
PPT 4.3, 6.1-6.2
5 1/25 Sorting: intro to heapsort PPT 6, 7.1-7.3
6 1/28 Sorting: heapsort, priority
queues
PPT 7.4
7 1/30 Sorting: quicksort PPT 5.1-5.3
8 2/1 Sorting: quicksort average
case analysis
PPT 5.4 last section
9 2/4 Sorting: linear time sorting algorithms PPT 8.1-8.2
10 2/6 Sorting: linear time algorithms continued;

Order statistics: selection in expected linear time
PPT 8.3-8.4

9.1-9.2
11 2/8 Order statistics: selection in worst-case linear time PPT 9.3
12 2/11 Review for exam PPT

2/13 Basics, Sorting, Order Statistics
--
13 2/15 Structures: binary search trees PPT 12.1-12.3
14 2/18 Structures: red-black trees PPT 13.1-13.2
15 2/20 Structures: red-black trees
(insertion)
PPT 13.3-13.4
16 2/22 Structures: skip lists PPT --
17 2/25 Structures: skip lists, hash tables PPT 11.1-11.2
18 2/27 Structures: hash tables
(hash functions)
PPT 11.3-11.4
19 3/1 Structures: hash tables (universal hashing) PPT 11.3-11.4
20 3/4 Augmenting structures: dynamic order statistics PPT 14.1-14.2
21 3/6 Augmenting structures:
interval trees
PPT 14.3
22 3/8 Graph algorithms: the basics PPT 22.1-22.3
-- --

--
23 3/18 Graph algorithms: BFS PPT 22.3
24 3/20 Graph algorithms: DFS PPT 23.1
EXAM 3/22 Data structures
--





25 3/27 Minimum spanning trees PPT 23.2
26 3/29 Shortest paths: Bellman-Ford PPT 24.1-24.3
27 4/1 Shortest paths: DAG,
Dijkstra's algorithm
PPT
28 4/3 Finish Dijkstra's. Kruskals
algorithm; disjoint sets
PPT 21.1-21.3, 23.2
29 4/5 Disjoint sets; amortized analysis PPT 17.1-17.2
30 4/8 Amortized analysis continued PPT 17.3-17.4
31 4/10 Dynamic programming PPT 15.1, 15.3
32 4/12 Dynamic programming (longest common subsequence) PPT 15.4
33 4/15 Dynamic programming (knapsack problem) PPT
34 4/17 Greedy algorithms PPT 16.1-16.2
35 4/19 NP-Completeness PPT 34.1-34.2
36 4/22 NP-Completeness continued PPT 34.1-34.2
37 4/24 NP-Completeness: reductions PPT 34.3-4
38 4/26 NP-Completeness: reductions PPT 34.3-4
39 4/29 Review for final PPT --




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