Exact Analysis is Hard!
We have agreed that the best, worst, and average case
complexity of an algorithm is a numerical function of
the size of the instances.
1
2
3
4
.
However, it is dicult to work with exactly because it
is typically very complicated!
T

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Matlab/Freemat/Octave/Scilab: Arithmetic Operators
The mathematical symbols that can be used in Matlab/FreeMat/Octave/Scilab and the
corresponding mathematical symbol is given in the following table.
operation
addition
subtraction
multipli

ALGORITHM
On
NUMRICAL METHODS
By
T K RAJAN
SELN GRADE LECTURER IN MATHEMATICS
GOVT VICTORIA COLLEGE PALAKKAD
ASCENDING ORDER OF A SET OF NUMBERS
Arrange the following set of numbers in ascending order
385, 994, -234, -56, 0.
ALGORITHM
Step 1: Read the num

Khaled A. Al-Utaibi
alutaibi@uoh.edu.sa
Definition of Divide & Conquer Technique
Examples:
Binary Search
Merge Sort
Quick Sort
The main idea of the divide & conquer
technique is to take a problem of large input
size, then divide it into many sub-problems

Khaled A. Al-Utaibi
alutaibi@uoh.edu.sa
Algorithm Design Techniques
Definition of Brute Force Method
Examples:
Linear Search
Selection Sort
Merging Problem
Brute force
Greedy
Divide-and-conquer
Decrease-and-conquer
Transform-and-conquer
Dynamic programmin

Outline
Complexity
Basic tools
Big-Oh
Big Omega
Big Theta
Examples
Lecture 3: Analysing Complexity of Algorithms
Big Oh, Big Omega, and Big Theta Notation
Georgy Gimelfarb
COMPSCI 220 Algorithms and Data Structures
1 / 15
Outline
Complexity
1
Complexity
2

Khaled A. Al-Utaibi
alutaibi@uoh.edu.sa
Running Time
Order of Growth
Asymptotic Notations:
The O-Notation
The -Notation
The -Notation
Estimating the Running Time
Time is a critical resource to be investigated in the
analysis of algorithms.
The running tim

CS2210
Data Structures and Algorithms
Lecture 2:
Analysis of Algorithms
Asymptotic notation
Instructor: Olga Veksler
2004 Goodrich, Tamassia
Outline
Comparing algorithms
Pseudocode
Theoretical Analysis of Running time
Primitive Operations
Counting primit

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Matlab : Numerical Solution of Ordinary Differential Equations
Matlab has facilities for the numerical solution of ordinary differential equations 1
(ODEs) of any order. In this document we first consider the solution of a first
order ODE.