CSCI-B 503 Syllabus
Prof. Funda Ergun
Fall2014
1. What is an algorithm, analyzing algorithms.
2. Growth of functions, asymptotic complexity.
a. Asymptotic complexity.
b. Analyzing functions, comparing them.
c. Big-Oh, Theta, Omega, little-oh and theta alo
Solving Recurrence
Relations
So what does
T(n) = T(n-1) +n
look like anyway?
Recurrence Relations
Can easily describe the runtime of
recursive algorithms
Can then be expressed in a closed form
(not defined in terms of itself)
Consider the linear search
CSCI 503B:
HOMEWORK 2
Each question has equal weight. Solve the recurrences. Show your work
clearly and explicitly. You can use any of the techniques that we saw in
class. If you need to deal with any arithmetic/geometric series, properties
of exponents,
SOLUTIONS FOR HOMEWORK 3
Question 1
Claim 0.1. No, this greedy strategy can not always give a optimal solution.
Proof. It suces to show a counterexample. Consider the room is available between 1. pm to 12. pm, and we have three activities [1, 6), [6, 12),
Homework Assignment 3
Each question has equal weight.
1. Consider the following variant of the activity selection problem: rather than
scheduling the highest number of activities, we would like to schedule them (without
overlaps) so that we maximize the t
CSCI 503B:
HOMEWORK 2
Each question has equal weight.
1. Consider the following variant of the activity selection problem: rather
than scheduling the highest number of activities, we would like to
schedule them (without overlaps) so that we maximize the t
SOLUTIONS FOR HOMEWORK 2
Preliminaries
Master Theorem. Use the denition from our textbook. Another more generic
form of Master theorem can be found at http:/en.wikipedia.org/wiki/Master_
theorem.
n vs log n.
Claim 0.1. For any
> 0, we have log n = o(n ) =
Homework Assignment 2
Each question has equal weight. Solve the recurrences. Show your work clearly and explicitly.
You can use any of the techniques that we saw in class. If you need to deal with any
arithmetic/geometric series, properties of exponents,
SOLUTIONS FOR HOMEWORK 1
JIECAO CHEN
Definitions from the Textbook
We suggest to use O, o, , as dened in our textbook Introduction to Algorithms, 3Ed.
Denition 0.1 (). (g(n) = cfw_f (n)| positive constants c1 , c2 , and n0 such that 0
c1 g(n) f (n) c2 g(
Homework Assignment 1
1. Let f (n) = n and g (n) = n1+sin (n). Is f (n) = O (g (n)? Is g (n) = O (f (n)? Prove your
answers.
Given: f (n) = n
G (n) = n 1+ sin (n)
Proof:
f (n) = n
g (n) = n1+ sin(n)
Also draw a graph.
Assume f (n) = O (g (n)
Then by defin
CSCI 503B:
HOMEWORK 1
Each question is worth 20 points. Show your work.
1. Let f (n) = n and g(n) = n1+sin(n) . Is f (n) = O(g(n)? Is g(n) =
O(f (n)? Prove your answers.
2. Give an example of a function which is o(1). Just use the denition
(or think intui
COMS 4705 Natural Language Processing Spring 2017
Assignment 1
Language Modeling and Part of Speech Tagging
Due: February 17th, 2017, 11:59:59 PM
Introduction
In this
1.
2.
3.
assignment, we will:
Go through the basics of NLTK, the most popular NLP librar