Partial Solutions for
Introduction to algorithms
second edition
Professor: Song You
TA: Shao Wen
ACKNOWLEDGEMENT
CLASS ONE: JINZI
CLASS TWO: LIUHAO, SONGDINMIN, SUNBOSHAN, SUNYANG
CLASS FOUR:DONGYANHAO, FANSHENGBO, LULU, XIAODONG,
CLASS FIVE:GAOCHEN, WANG
CSci 2033
Fall 2012
Elementary Computational Linear Algebra
General Information
This course is an introduction to linear algebra and matrix theory and computation. It covers the fundamentals of linear algebra (vectors, matrices, determinants, rank, eigenv
Intro to matlab getting started To start type matlab under unix (or click icon under windows).
You will get the matlab logo and then the prompt: > In version 6 a new command window will pop-out, in which you can type commands. You can avoid this [matlab v
LINEAR INDEPENDENCE [1.7]
Linear independence
Denition
The set cfw_v1, ., vp is said to be linearly dependent if
there exist weights c1, ., cp, not all zero, such that
c1v1 + c2v2 + . + cpvp = 0
It is linearly independent otherwise
The above equation i
THE MATRIX EQUATION AX = B
[1.4]
The matrix equation Ax = b
Denition: If A is an mn matrix, with columns a1, ., an,
and if x is in Rn, then the product of A and x, denoted
by Ax is the linear combination of the columns of A using
the corresponding entries
THE ECHELON FORM
[1.2]
The standard echelon form
A rectangular matrix is in echelon form (or row echelon
form) if it has the following three properties:
1. All nonzero rows are above any rows of all zeros.
2. Each leading entry of a row is in a column to
Gauss-Jordan - variants
First: Pivoting can be implemented just like Gaussian
elimination.
Important: Never swap a row with a row above it! (destroys structure) Always swap a row with a row below it
(when interchange is needed).
Common variant: After an
LINEAR EQATIONS
[1.1] + (CONTINUED)
Linear Systems of Equations: Gaussian Elimination
Back to arbitrary linear systems.
Principle of the method: Since triangular systems are easy
to solve, we will transform a linear system into one that
is triangular. Ma
Let us start .
Lecture notes will be posted on the class web-site
usually before the lecture. [if I am late do not hesitate to
send me e-mail!]
Review them and try to get some understanding if
possible before class.
Read the relevant section (s) in the
CSci 2033, F12
Homework # 2
Due Date: 10/01/2012
1. Consider the ane plane consisting of all vectors in R3 that are of the form
2
1
1
1 + 2 + 0
1
0
0
(a) On a geometrical gure (hand-drawn OK) - show how you determine the point
corresponding to the select
CSci 2033, F12
Homework # 1
Due Date: 09/17/2012
1. Exercise 32 from set 1.1 of text 2. First part: Exercise 12. Second part: do the same problem but change the last equation
to 2x1 + x2 + 7x3 = 6
3. A steel company has four dierent types of scrap metal (
Discrete Mathematics Problems
William F. Klostermeyer
Dept. of Computer and Information Sciences
University of North Florida
Jacksonville, FL 32224
E-mail: [email protected]
Contents
0 Preface
1 Logic
1.1 Basics . . . . . .
1.2 Truth Tables and
1.3 Quantie
The
Musa Challenge
November 10, 2012
Minneapolis, MN
Tournament Events:
*Divisions May Change On Day Of Event For Fairest Matches Between All Actual Participating Competitors*
FORMS
F -1
F -2
F -3
F -4
F -5
F -6
F -7
F -8
F -9
F-10
LTB-1
LTB-2
LTB-3
SPARR
Lecture Outline (CS 303, Dong Xu, 4/21/04)
Things to start
Discussion on the quiz Questions?
Dynamic programming
Used for optimization problems 4-step method Plan for this chapter
Assembly-line scheduling
Problem formulation 4-step solution
Matrix-cha
Thomas H. Cormen
Charles E. Leiserson
Ronald L. Rivest
Clifford Stein
Introduction to Algorithms
Second Edition
The MIT Press
Cambridge, Massachusetts London, England
McGraw-Hill Book Company
Boston
Burr Ridge, IL
New York
San Francisco
Dubuque, IA
St. Lo
ICS 311 Spring 2004 Syllabus MW 3:00-4:15pm POST 127 Instructor: Dr. Milica Barjaktarovic Contact: [email protected] Office and phone: POST 314 Office Hours: one hour before and after the class, and by appointment. Class web site: http:/www2.hawaii.e
x = "There are 0 types of people" % 10
binary = "binary"
do_not = "don't"
y = "Those who know and those who ." % (binary, do_not)
print x
print y
print "I said: %r." % x
print "I also said: ''." % y
hilarious = False
joke_evaluation = "Isn't that joke so