CSCI 2300 Spring 2010

Rensselaer Polytechnic Institute
Department of Computer Science

CSCI 2300: Introduction to Algorithms

Spring 2010

ANNOUNCEMENTS

Solutions to HW6 can be picked up from Aseem's mailbox in AE 119.

Office hours for questions regarding the finals: Apirak: Mon 2-4PM, Aseem: Tuesday 10:30AM-12:30PM (Lally 09A), Sanmay: Tue 1:30-3:30PM.

All grades through HW6 are up on LMS. Please let us know if you see any problems with your grades on there.

For HW 7, Question 8.4(d), you only need to give a polynomial time algorithm, not an O(|V|) algorithm.

Midterms have been graded. You can check your grades on LMS. For this test only, the grade ranges are approximately as follows: 33+ is an A-range grade. 25-33 is a B-range grade. 20-25 is a C-range grade. Below 20 is a D or F range grade. Don't take these individual numbers too seriously because the midterm is only one component and it is not that hard to improve your grade over the rest of the semester. However, if you were not doing well on your homeworks and you got less than 20, you may want to consider dropping if that is an option.

You should now be able to see your grades for individual assignments on RPILMS. Let us know if you see any problems with your grades.

If only various programmers at Microsoft had taken this class, they wouldn't have made this mistake (hopefully!). Now who thinks all this analysis of algorithms isn't useful?!

The lab schedule has been tweaked. The 3rd lab will be after spring break instead of before, and there are some changes further down the line.

Welcome to DSA! We will meet on Mondays and Thursdays at noon in Amos Eaton 214. The first meeting will be on the 25th of January. Please note that there are several changes from last year's version of the course.

OVERVIEW

This is a foundational course in the design and analysis of algorithms and the data structures they are coupled with. While we will concentrate on the theoretical design and analysis of algorithms and data structures, we will reinforce the theory with examples, laboratories, and applied homework questions.

The goal of this course is to provide a strong foundation in algorithms and data structures in preparation for jobs in industry or for more advanced courses. Algorithms are the basic language of computer science. After taking this course, you should be able to prove the correctness of and analyze the running times of different algorithms. You should also be able to use different algorithm-design techniques to solve particular problems. Data structures and algorithms also form a major component of any software system. After taking this course you should be able to make intelligent decisions about alternative techniques in the context of practical problems, choosing from existing data structures and algorithms or designing your own when necessary.

STAFF

Instructor: Sanmay Das
Office: Lally 302
Phone: x2782
Office hours: Mondays from 1:30-3:00 PM, and by appointment.

TA: Aseem Brahma (email: brahma at rpi)
Labs: W 10-12 in Lally 104 with UTA Eric Rozell (rozele)
and W 2-4 in Sage 2715 with UTA Elsa Gonsiorowski (gonsie)

TA: Apirak Hoonlor (email: hoonla at cs dot rpi)
Labs: W 12-2 in Lally 104 with UTAs Nick Glickenhouse (glickn), Elsa Gonsiorowski (gonsie), and Eric Rozell (rozele)
and W 4-6 in Lally 104 with UTAs Eric Rozell (rozele) and Varun Madiath (vamega at gmail)

POLICIES

TEXTBOOKS

There are two textbooks for this class

DPV: Algorithms by Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani, McGraw-Hill, ISBN 0073523408.
CLRS: Introduction to Algorithms (2nd or 3rd Ed is fine) by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein, MIT Press/McGraw-Hill, ISBN 0070131511 (for the 2nd Ed).

PROGRAMMING

This is not a programming class. The labs involve programming, but you are expected to be a competent C++ programmer coming in -- the lectures will not discuss any code. The TAs and UTAs can provide some help on programming issues in lab. Neither of the textbooks deals with programming issues at all. You may want to consult your textbooks from CS2, or Stroustrup's The C++ Programming Language.

LECTURES

Lectures will be on Mondays and Thursdays from 12pm to approximately 1:30pm in Amos Eaton 214. The "Mathematical Background" appendix of CLRS is background reading for the whole class. In the readings, chapter numbers for CLRS are for the 3rd edition.The table of contents for the 3rd edition is here, if you want to compare to another edition.

Date	Topics	Readings	Extras
Jan 25	Introduction. Course policies. Course overview. Some interesting problems.	DPV Chapter 0
Jan 28	Generating random permutations. Fibonacci numbers.	CLRS Section 5.3 (Randomized Algorithms), DPV Chapter 0.
Feb 1	Arithmetic. Modular arithmetic.	DPV 1.1, 1.2.
Feb 4	More modular arithmetic. Euclid's Algorithm. Modular division.	DPV 1.2.
Feb 8	Running times. Divide-and-conquer and recurrence relations. Integer multiplication and mergesort.	DPV 0.3, 2.1, 2.2, 2.3. CLRS 4.3, 4.4, 4.5.
Feb 11	More divide-and-conquer: sorting lower bound, selection.	DPV 2.4, CLRS 8.1.
Feb 15	No class (President's Day)
Feb 18	Quicksort, matrix multiplication	DPV 2.4, 2.5. CLRS 4.2 and Chapter 7.
Feb 22	Intro to graphs. Depth-first search	DPV 3.1, 3.2, 3.3. CLRS 22.1, 22.3, 22.4.
Feb 25	Directed graphs. Topological sort.	DPV 3.3, 3.4. CLRS 22.4.
Mar 1	Strongly connected components. Breadth-first search.	DPV 3.4, 4.1, 4.2. CLRS 22.5, 22.2.
Mar 4	Dijkstra's algorithm. Priority queues.	DPV 4.3, 4.4, 4.5. CLRS 24.3, 6.1, 6.2.
Mar 15	Negative edges. The Bellman-Ford Algorithm. Shortest paths in DAGs.	DPV 4.6, 4.7. CLRS 24.1, 24.2.
Mar 18	Spanning Trees, and Prim's algorithm for MSTs.	DPV 5.1. CLRS 23.1.
Mar 22	Kruskal's algorithm. The disjoint set data structure.	DPV 5.1. CLRS 23.2.
Mar 25	Midterm exam.
Mar 29	Midterm solutions. Disjoint set amortized analysis, contd.	DPV 5.1.
Apr 1	Building a heap. Heapsort. Intro to AVL trees	CLRS 6.1-6.4.
Apr 5	AVL Tree insertion. Hash tables. Chaining.	Wikipedia on AVL trees. CLRS 11.1, 11.2.
Apr 8	Open addressing. Universal hash functions..	CLRS 11.3, 11.4. DPV 1.5.
Apr 12	Cuckoo hashing.	Cuckoo hashing notes from Rasmus Pagh
Apr 15	Cuckoo hashing contd. Bloom Filters. Intro to Huffman coding.	Wikipedia on Bloom Filters, DPV 5.2.
Apr 19	Guest lecture by Prof. Anshelevich. Flow networks. Max-flow = min-cut. The Ford-Fulkerson algorithm.	DPV 7.2. CLRS 26.1, 26.2.
Apr 22	Max-flow contd. Bipartite matching. Huffman coding	DPV 7.3, 5.2.
Apr 26	Dynamic programming: shortest paths in DAGs, longest increasing subsequence, edit distance.	DPV 6.1, 6.2, 6.3.
Apr 29	Dynamic programming: knapsack, chain matrix multiplication.	DPV 6.4, 6.5.
May 3	Dyanmic programming: all pairs shortest paths. The classes P an NP.	DPV 6.6, 8.1
May 6	NP complete problems and reductions (SAT, 3SAT, Independent Set, Vertex Cover, Clique).	DPV 8.2, 8.3
May 10	TSP and the DP approach to TSP. Extras (Circuit-SAT, Halting Problem)	DPV 8.3

LABS

Jan 27: No lab
Feb 3: Lab 1
Feb 10: Recitation/OH
Feb 16 (Tuesday): Lab 2. Files necessary for Lab 2 are here.
Feb 17: Recitation/OH
Feb 24: Recitation/OH
Mar 3: Recitation/OH
Mar 17: Lab 3. Files necessary for Lab 3 are here.
Mar 24: Recitation/OH
Mar 31: Lab 4. Files necessary for Lab 4 are here.
Apr 7: Recitation/OH
Apr 21: Lab 5. Files necessary for Lab 5 are here.
Apr 28: Recitation/OH
May 5: Lab 6. The sequence files are here.

HOMEWORKS

HW1: Due Feb 11
HW2: Due Feb 18
HW3: Due Mar 4
HW4: Due Mar 22
HW5: Due Apr 12
HW6: Due Apr 29
HW7: Due May 10