Algorithm and Data Structures Assignment 1
Dr. Andreas Nchter u Fall 2009
Exercise 1.1 Let
n
S(m, n, a, d) := a sum for positive numbers n, m, a, d where m < n. 1. Find a simple formula for S(m, n, a, d).
(a + d k)
k=m+1
2. Write a C/C+/Java function Arit
Lecture 9
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Announcements (1)
Midterm
October 15 14:15-15:30 Remember grading policy:
Assignmen
Course Outline
1. 2. 3. 4. 5. 6. Introduction to Algorithms Sorting Data Structures Advanced Design and Analysis Techniques Graph Algorithms Selected Topics and Outlook
Algorithms and Data Structures Dr. Andreas Nchter September 29, 2009
283
Data Structur
Lecture 8
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Announcements
Midterm
October 15 9.45-11.00 in class Remember grading policy:
Assig
Lecture 7
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Announcements
Oct 15. midterm (here in class)
Algorithms and Data Structures Dr. Andr
Lecture 6
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Last Lecture Introduction To Sorting
The sorting problem: Given: keys Wanted: Find a p
Lecture 5
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Last Lecture
Proof that the program for computing the greatest common divisor (gcd) i
Lecture 4
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Last Lectures
First attempt to define the central word "algorithm" An algorithm is an
Lecture 3
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Last Lecture
Introduction of math symbols used in this lecture Specification of a com
Lecture 2
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Last Lecture
Examples of Algorithms
Summation according to C.F. Gauss
Binary Search
Lecture 1
Computer Science Algorithms and Data Structures
Prof. Dr. Andreas Nchter Research I, Room 105 Jacobs University Bremen
http:/www.nuechti.de [email protected]
Welcome to the Algorithms class
Times:
Tu 11.15 - 12.30 and Th 9.45 - 11.00
Instruct
Algorithms and Data Structures Assignment 7 - Solution
Flavia Grosan, Vladislav Perelman, Dr. Andreas Nchter u Fall 2009
Exercise 7.1 In exercise 6.4 you had to show, that three sets have the same cardinality. Show that the cardinality is 2n n - 2n n-1
Hi
Fundamental Computer Science I Solutions to Assignment 6
Exercise 6.1 Let n be the number of keys sorted by the quicksort algorithm. 1. Show that quicksort needs at least (n) additional memory on the stack for saving return addresses. 2. Show that a small
Algorithm and Data Structures Assignment 5
Dr. Andreas Nchter u Fall 2009
Exercise 5.1 Program sorter Write a sorting program using C/C+ with the name sorter, that 1. accepts up to 32 integers as command line parameter. 2. displays a help message, in case
Algorithm and Data Structures Assignment 4
Dr. Andreas Nchter u Fall 2009
Exercise 4.1 Improve the algorithm insertion sort. Use binary search to identify the position where the element has to be inserted. Show that in this case holds: Cmax (N ) = (N log
Algorithm and Data Structures Assignment 3
Dr. Andreas Nchter u Fall 2009
Exercise 3.1 Compare the following function pairs. State for every pair f, g, if f O(g), g O(f ) and/or f g is true and formally prove your statements! f (n) (a) (b) (c) (d) (e) (f)
Algorithms and Data Structures Assignment 2 - Solution
Flavia Grosan, Vladislav Perelman, Dr. Andreas N chter u Fall 2009
Exercise 2.1 Using the algorithm presented in the slides, it can be inferred: gcd(27, 3) gcd(252, 105) gcd(147, 105) A := 27 A := 252
Algorithm and Data Structures Assignment 2
Dr. Andreas Nchter u Fall 2009
Exercise 2.1 Execute Euclid's algorithms on the numbers 27 and 3 252 and 105 147 and 105 Exercise 2.2 A series A is defined as follows: A1 = 1, An = n - An-1
2
(1) for n > 1.
n(n+1)
Algorithm and Data Structures Assignment 1 - Solution
Dr. Andreas Nchter u Fall 2009
Exercise 1.1 1.
n
S(m, n, a, d) =
k=m+1 n
(a + d k)
n
(1) (d k) (2)
n
=
k=m+1
a+
k=m+1
= (n - (m + 1) + 1) a + d
n k=m+1 m
k k)
k=1
(3) (4) (5)
= (n - m) a + d (
k=1
k-
=
