Homework 3
Alex Roque
COT 6405
Analysis of Algorithms
HW3
20)
a) To show that there will always be a point of maximum overlap in an endpoint of one of these
segments, we can prove by induction:
Proof by induction:
First, we must observe our property of 2
Analysis of Algorithms
CECS 528
Midterm 1. Review and exercises
Framework of the exam
Out of 50 points
Covers four topics:
Asymptotic growths of functions
Analysis of algorithms using the recurrence, Master Method
Multiplication of polynomials using
Analysis of Algorithms
CECS 528
Quiz 1
Quiz 1. 1
What is the meaning of the following statement:
+ = ?
Quiz 1.1
What is the meaning of the following statement:
+ = ?
Answer. Here = + , and = .
The definition of = () is that
()/() = .
+
= .
Quiz 1.2
Ar
1. Use the Master method to solve the following recurrences
#1
Solve the recursive equation
For this equation a = 9, b = 3, and f(n) = n. Intuitively this equation would represent an algorithm
that divides the original inputs into nine groups each consist
CSE 548: Analysis of Algorithms
Lectures 4 & 5
( Divide-and-Conquer Algorithms:
Polynomial Multiplication
& the Fast Fourier Transform )
Rezaul A. Chowdhury
Department of Computer Science
SUNY Stony Brook
Fall 2012
Coefficient Representation of Polynomial
Homework 3. Strassen Algorithm
Put your solution and answers to the following questions on paper. Bring it to the class on week
of October 4.
1. Use the Strassens algorithm to compute the matrix product of two translational matrices:
1
= (0
0
0
0
1
0
0
0
Analysis of Algorithms
CECS 528
HW 1. Selected answers
Let f (n) and g(n) be asymptotically nonnegative functions.
Prove that max (f (n), g(n) = ( f (n) + g(n).
Ordering
Attempt the ordering of the following functions:
(3/2)n , n3 , lg2 n, lg(n!), n1/lgn
Homework 2. Recurrences
Put your analysis and answers to the following questions on paper. Bring it to the class on
Monday-Tuesday, September 21-22.
1. Use the Master method to solve the following recurrences:
1. T(n)= 9T(n/3)+n
2. T(n)= T(2n/3)+1
3. T(n)
Homework 1. Growth of the functions
Put your analysis and answers to the following questions on paper. Bring it to the class next
Wednesday, September 9.
1. Let f (n) and g(n) be asymptotically nonnegative functions. Using the basic definition of
notation