CSCE 750, Fall 2011, Assignment 13
November 18, 2011
NOTE: We will assume that the HAMILTONIAN CIRCUIT problem (a.k.a. the HAMILTONIAN CYCLE
problem) is for directed graphs:
HAMILTONIAN CIRCUIT (HC)
Instance: A directed graph G
Question: Is there a simple
CSCE750 Analysis of Algorithms
Fall 2016 Test 2 Solutions
Edsger
name
Problem
Value
Your Score
1
25
25
2
25
25
X A single 3 5 note card in your own handwriting is
permitted.
3
25
25
X No calculators nor other reference material are
permitted.
4
25
25
X Sh
CSCE750 Analysis of Algorithms
Fall 2016 Test 1 Solutions
Edsger
name
Problem
Value
Your Score
1
25
25
2
25
25
X A single 3 5 note card in your own handwriting is
permitted.
3
25
25
X No calculators nor other reference material are
permitted.
4
25
25
X Sh
Here are all the quizzes for CSCE 750, Fall 2011.
CSCE 750, Fall 2011, Quiz 1
Show by grouping the sum into blocks that
1
<.
n(lg n)2
n=2
Do not use an integral approximation.
Note: You may assume without proof that
1
<.
k2
k=1
CSCE 750, Fall 2011, Quiz 2
CSCE 750, Fall 2009 Quizzes with Answers
Stephen A. Fenner
September 24, 2011
1. Give an exact closed form for
k=1
2k
.
3k+1
Simplify your answer as much as possible.
Answer: We reduce the expression to a form weve already seen in class:
k=1
2
2k
=
k+1
3
An analysis of randomized Quicksort
CSCE 750, Fall 2011
Stephen A. Fenner
September 29, 2011
We showed in class that the expected run time E (n) of randomized Quicksort run on a list of
n items asymptotically satises the recurrence
2
E (n) = n +
n
n1
E (k
CSCE 750, Fall 2011, Assignment 12
November 10, 2011
Pages 592593 Exercises 22.1-1, 22.1-3, 22.1-6
Pages 601602 Exercises 22.2-1, 22.2-7 (this is just a test for graph bipartiteness)
Pages 629630 Exercises 23.1-1, 23.1-3, 23.1-5, 23.1-7
(not in text) Run
CSCE 750, Fall 2011, Assignment 11
November 6, 2011
I recommend the Wikipedia article on Fibonacci heaps. It is less nely detailed, but more
succinct than the CLRS description.
Page 518 Exercise 19.2-1
Page 526 Exercises 19.4-1, 19.4-2
Not in text Give th
CSCE 750, Fall 2009, Assignment 10
November 3, 2011
Page 456 Exercises 17.1-2, 17.1-3
Pages 462463 Exercises 17.3-2, 17.3-6 (and describe an appropriate potential function for the
analysis), 17.3-7 (and describe an appropriate potential function for the a
CSCE 750, Fall 2011, Assignment 9
October 21, 2011
Page 422 Exercise 16.1-4 (this can be solved without reading Section 16.1, but it would help)
Pages 427428 Exercises 16.2-2 (this is similar, but not identical, to an exercise on the previous
assignment),
CSCE 750, Fall 2011, Assignment 3
September 13, 2011
These are all textbook exercises.
Pages 7475 Exercises 4.1-1, 4.1-2, 4.1-3, 4.1-4, 4.1-5 (Note: I will not derive any quiz question
from these exercises, but there may be such a question on the nal exam
CSCE 750, Fall 2011, Assignment 1
August 19, 2011
Let x R be any real number. Recall that x (the oor of x) is the greatest integer not
exceeding x and that x (the ceiling of x) is the least integer not less than x. Thus x and x
are the only integers satis
Lecture 1
Introduction to Algorithms Analysis
Im assuming youve all had CSCE 350 or the equivalent. Ill assume some basic things from
there, and sometimes quickly review the more important/subtle points.
Well start with Appendix A in CLRS Summations. Why?