Algorithms Lecture 1: Introduction to AlgorithmsMohamed Loey
We will discuss the following: Algorithms, Time Complexity & Space Complexity, Algorithm vs Pseudo code, Some Algorithm Types, Programming Languages, Python, Anaconda.
Algorithms Lecture 1: Introduction to AlgorithmsMohamed Loey
We will discuss the following: Algorithms, Time Complexity & Space Complexity, Algorithm vs Pseudo code, Some Algorithm Types, Programming Languages, Python, Anaconda.
Unit 1: Fundamentals of the Analysis of Algorithmic Efficiency, Units for Measuring Running Time, PROPERTIES OF AN ALGORITHM, Growth of Functions, Algorithm - Analysis, Asymptotic Notations, Recurrence Relation and problems
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
2. Analysis of Algorithms 2
Running Time (§3.1)
Most algorithms transform
input objects into output
objects.
The running time of an
algorithm typically grows
with the input size.
Average case time is often
difficult to determine.
We focus on the worst case
running time.
Easier to analyze
Crucial to applications such as
games, finance and robotics
0
20
40
60
80
100
120
Running
Time
1000 2000 3000 4000
Input Size
best case
average case
worst case
3. Analysis of Algorithms 3
Experimental Studies (§ 3.1.1)
Write a program
implementing the
algorithm
Run the program with
inputs of varying size and
composition
Use a function, like the
built-in clock() function, to
get an accurate measure
of the actual running time
Plot the results
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 50 100
Input Size
Time
(ms)
4. Analysis of Algorithms 4
Limitations of Experiments
It is necessary to implement the
algorithm, which may be difficult
Results may not be indicative of the
running time on other inputs not included
in the experiment.
In order to compare two algorithms, the
same hardware and software
environments must be used
5. Analysis of Algorithms 5
Theoretical Analysis
Uses a high-level description of the
algorithm instead of an implementation
Characterizes running time as a
function of the input size, n.
Takes into account all possible inputs
Allows us to evaluate the speed of an
algorithm independent of the
hardware/software environment
6. Analysis of Algorithms 6
Pseudocode (§3.1.2)
High-level description
of an algorithm
More structured than
English prose
Less detailed than a
program
Preferred notation for
describing algorithms
Hides program design
issues
Algorithm arrayMax(A, n)
Input array A of n integers
Output maximum element of A
currentMax A[0]
for i 1 to n 1 do
if A[i] currentMax then
currentMax A[i]
return currentMax
Example: find max
element of an array
7. Analysis of Algorithms 7
Pseudocode Details
Control flow
if … then … [else …]
while … do …
repeat … until …
for … do …
Indentation replaces braces
Method declaration
Algorithm method (arg [, arg…])
Input …
Output …
Method/Function call
var.method (arg [, arg…])
Return value
return expression
Expressions
Assignment
(like in C++)
Equality testing
(like in C++)
n2 Superscripts and other
mathematical
formatting allowed
8. Analysis of Algorithms 8
The Random Access Machine
(RAM) Model
A CPU
An potentially unbounded
bank of memory cells,
each of which can hold an
arbitrary number or
character
0
1
2
Memory cells are numbered and accessing
any cell in memory takes unit time.
9. Analysis of Algorithms 9
Primitive Operations
Basic computations
performed by an algorithm
Identifiable in pseudocode
Largely independent from the
programming language
Exact definition not important
(we will see why later)
Assumed to take a constant
amount of time in the RAM
model
Examples:
Evaluating an
expression
Assigning a value
to a variable
Indexing into an
array
Calling a method
Returning from a
method
10. Analysis of Algorithms 10
Counting Primitive
Operations (§3.4.1)
By inspecting the pseudocode, we can determine the
maximum number of primitive operations executed by
an algorithm, as a function of the input size
Algorithm arrayMax(A, n) # operations
currentMax A[0] 2
for i 1 to n 1 do 2 + n
if A[i] currentMax then 2(n 1)
currentMax A[i] 2(n 1)
{ increment counter i } 2(n 1)
return currentMax 1
Total 7n 1
11. Analysis of Algorithms 11
Estimating Running Time
Algorithm arrayMax executes 7n 1 primitive
operations in the worst case. Define:
a = Time taken by the fastest primitive operation
b = Time taken by the slowest primitive operation
Let T(n) be worst-case time of arrayMax. Then
a (7n 1) T(n) b(7n 1)
Hence, the running time T(n) is bounded by two
linear functions
12. Analysis of Algorithms 12
Growth Rate of Running Time
Changing the hardware/ software
environment
Affects T(n) by a constant factor, but
Does not alter the growth rate of T(n)
The linear growth rate of the running
time T(n) is an intrinsic property of
algorithm arrayMax
13. Analysis of Algorithms 13
Growth Rates
Growth rates of
functions:
Linear n
Quadratic n2
Cubic n3
In a log-log chart,
the slope of the line
corresponds to the
growth rate of the
function
1E+0
1E+2
1E+4
1E+6
1E+8
1E+10
1E+12
1E+14
1E+16
1E+18
1E+20
1E+22
1E+24
1E+26
1E+28
1E+30
1E+0 1E+2 1E+4 1E+6 1E+8 1E+10
n
T
(n
)
Cubic
Quadratic
Linear
14. Analysis of Algorithms 14
Constant Factors
The growth rate is
not affected by
constant factors or
lower-order terms
Examples
102n + 105 is a linear
function
105n2 + 108n is a
quadratic function
1E+0
1E+2
1E+4
1E+6
1E+8
1E+10
1E+12
1E+14
1E+16
1E+18
1E+20
1E+22
1E+24
1E+26
1E+0 1E+2 1E+4 1E+6 1E+8 1E+10
n
T
(n
)
Quadratic
Quadratic
Linear
Linear
15. Analysis of Algorithms 15
Big-Oh Notation (§3.5)
Given functions f(n) and
g(n), we say that f(n) is
O(g(n)) if there are
positive constants
c and n0 such that
f(n) cg(n) for n n0
Example: 2n + 10 is O(n)
2n + 10 cn
(c 2) n 10
n 10/(c 2)
Pick c 3 and n0 10
1
10
100
1,000
10,000
1 10 100 1,000
n
3n
2n+10
n
16. Analysis of Algorithms 16
Big-Oh Example
Example: the function
n2 is not O(n)
n2 cn
n c
The above inequality
cannot be satisfied
since c must be a
constant
1
10
100
1,000
10,000
100,000
1,000,000
1 10 100 1,000
n
n^2
100n
10n
n
17. Analysis of Algorithms 17
More Big-Oh Examples
7n-2
7n-2 is O(n)
need c > 0 and n0 1 such that 7n-2 c•n for n n0
this is true for c = 7 and n0 = 1
3n3 + 20n2 + 5
3n3 + 20n2 + 5 is O(n3)
need c > 0 and n0 1 such that 3n3 + 20n2 + 5 c•n3 for n n0
this is true for c = 4 and n0 = 21
3 log n + log log n
3 log n + log log n is O(log n)
need c > 0 and n0 1 such that 3 log n + log log n c•log n for n n0
this is true for c = 4 and n0 = 2
18. Analysis of Algorithms 18
Big-Oh and Growth Rate
The big-Oh notation gives an upper bound on the
growth rate of a function
The statement “f(n) is O(g(n))” means that the growth
rate of f(n) is no more than the growth rate of g(n)
We can use the big-Oh notation to rank functions
according to their growth rate
f(n) is O(g(n)) g(n) is O(f(n))
g(n) grows more Yes No
f(n) grows more No Yes
Same growth Yes Yes
19. Analysis of Algorithms 19
Big-Oh Rules
If is f(n) a polynomial of degree d, then f(n) is
O(nd), i.e.,
1. Drop lower-order terms
2. Drop constant factors
Use the smallest possible class of functions
Say “2n is O(n)” instead of “2n is O(n2)”
Use the simplest expression of the class
Say “3n + 5 is O(n)” instead of “3n + 5 is O(3n)”
20. Analysis of Algorithms 20
Asymptotic Algorithm Analysis
The asymptotic analysis of an algorithm determines
the running time in big-Oh notation
To perform the asymptotic analysis
We find the worst-case number of primitive operations
executed as a function of the input size
We express this function with big-Oh notation
Example:
We determine that algorithm arrayMax executes at most
7n 1 primitive operations
We say that algorithm arrayMax “runs in O(n) time”
Since constant factors and lower-order terms are
eventually dropped anyhow, we can disregard them
when counting primitive operations
21. Analysis of Algorithms 21
Computing Prefix Averages
We further illustrate
asymptotic analysis with
two algorithms for prefix
averages
The i-th prefix average of
an array X is average of the
first (i + 1) elements of X:
A[i] (X[0] + X[1] + … + X[i])/(i+1)
Computing the array A of
prefix averages of another
array X has applications to
financial analysis
0
5
10
15
20
25
30
35
1 2 3 4 5 6 7
X
A
22. Analysis of Algorithms 22
Prefix Averages (Quadratic)
The following algorithm computes prefix averages in
quadratic time by applying the definition
Algorithm prefixAverages1(X, n)
Input array X of n integers
Output array A of prefix averages of X #operations
A new array of n integers n
for i 0 to n 1 do n
s X[0] n
for j 1 to i do 1 + 2 + …+ (n 1)
s s + X[j] 1 + 2 + …+ (n 1)
A[i] s / (i + 1) n
return A 1
23. Analysis of Algorithms 23
Arithmetic Progression
The running time of
prefixAverages1 is
O(1 + 2 + …+ n)
The sum of the first n
integers is n(n + 1) / 2
There is a simple visual
proof of this fact
Thus, algorithm
prefixAverages1 runs in
O(n2) time
0
1
2
3
4
5
6
7
1 2 3 4 5 6
24. Analysis of Algorithms 24
Prefix Averages (Linear)
The following algorithm computes prefix averages in
linear time by keeping a running sum
Algorithm prefixAverages2(X, n)
Input array X of n integers
Output array A of prefix averages of X #operations
A new array of n integers n
s 0 1
for i 0 to n 1 do n
s s + X[i] n
A[i] s / (i + 1) n
return A 1
Algorithm prefixAverages2 runs in O(n) time
25. Analysis of Algorithms 25
properties of logarithms:
logb(xy) = logbx + logby
logb (x/y) = logbx - logby
logbxa = alogbx
logba = logxa/logxb
properties of exponentials:
a(b+c) = aba c
abc = (ab)c
ab /ac = a(b-c)
b = a log
a
b
bc = a c*log
a
b
Summations (Sec. 1.3.1)
Logarithms and Exponents (Sec. 1.3.2)
Proof techniques (Sec. 1.3.3)
Basic probability (Sec. 1.3.4)
Math you need to Review
26. Analysis of Algorithms 26
Relatives of Big-Oh
big-Omega
f(n) is (g(n)) if there is a constant c > 0
and an integer constant n0 1 such that
f(n) c•g(n) for n n0
big-Theta
f(n) is (g(n)) if there are constants c’ > 0 and c’’ > 0 and an
integer constant n0 1 such that c’•g(n) f(n) c’’•g(n) for n n0
little-oh
f(n) is o(g(n)) if, for any constant c > 0, there is an integer
constant n0 0 such that f(n) c•g(n) for n n0
little-omega
f(n) is (g(n)) if, for any constant c > 0, there is an integer
constant n0 0 such that f(n) c•g(n) for n n0
27. Analysis of Algorithms 27
Intuition for Asymptotic
Notation
Big-Oh
f(n) is O(g(n)) if f(n) is asymptotically less than or equal to g(n)
big-Omega
f(n) is (g(n)) if f(n) is asymptotically greater than or equal to g(n)
big-Theta
f(n) is (g(n)) if f(n) is asymptotically equal to g(n)
little-oh
f(n) is o(g(n)) if f(n) is asymptotically strictly less than g(n)
little-omega
f(n) is (g(n)) if is asymptotically strictly greater than g(n)
28. Analysis of Algorithms 28
Example Uses of the
Relatives of Big-Oh
f(n) is (g(n)) if, for any constant c > 0, there is an integer constant n0
0 such that f(n) c•g(n) for n n0
need 5n0
2 c•n0 given c, the n0 that satisfies this is n0 c/5 0
5n2 is (n)
f(n) is (g(n)) if there is a constant c > 0 and an integer constant n0 1
such that f(n) c•g(n) for n n0
let c = 1 and n0 = 1
5n2 is (n)
f(n) is (g(n)) if there is a constant c > 0 and an integer constant n0 1
such that f(n) c•g(n) for n n0
let c = 5 and n0 = 1
5n2 is (n2)