Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
Algorithm and its Properties
Computational Complexity
TIME COMPLEXITY
SPACE COMPLEXITY
Complexity Analysis and Asymptotic notations.
Big-oh-notation (O)
Omega-notation (Ω)
Theta-notation (Θ)
The Best, Average, and Worst Case Analyses.
COMPLEXITY Analyses EXAMPLES.
Comparing GROWTH RATES
Algorithm and its Properties
Computational Complexity
TIME COMPLEXITY
SPACE COMPLEXITY
Complexity Analysis and Asymptotic notations.
Big-oh-notation (O)
Omega-notation (Ω)
Theta-notation (Θ)
The Best, Average, and Worst Case Analyses.
COMPLEXITY Analyses EXAMPLES.
Comparing GROWTH RATES
Growth of Functions
CMSC 56 | Discrete Mathematical Structure for Computer Science
October 6, 2018
Instructor: Allyn Joy D. Calcaben
College of Arts & Sciences
University of the Philippines Visayas
Basic Computer Engineering Unit II as per RGPV SyllabusNANDINI SHARMA
Algorithm, Flowchart, Categories of Programming Languages, OOPs vs POP, concepts of OOPs, Inheritance, C++ Programming, How to write C++ program as a beginner, Array, Structure, etc
AVL Tree in Data Structures- It is height balanced tree with balance factor 1, -1 or 0. The different type of rotations used in this tree are: RR, LL, RL, LR
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
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.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
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/
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
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About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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.
2. Analysis of Algorithms
An algorithm is a finite set of precise instructions for
performing a computation or for solving a problem.
What is the goal of analysis of algorithms?
To compare algorithms mainly in terms of running time
but also in terms of other factors (e.g., memory
requirements, programmer's effort etc.)
What do we mean by running time analysis?
Determine how running time increases as the size
of the problem increases.
2
3. Input Size
Input size (number of elements in the input)
size of an array
# of elements in a matrix
# of bits in the binary representation of the input
vertices and edges in a graph
3
4. Types of Analysis
Worst case
Provides an upper bound on running time
An absolute guarantee that the algorithm would not run longer, no
matter what the inputs are
Best case
Provides a lower bound on running time
Input is the one for which the algorithm runs the fastest
Average case
Provides a prediction about the running time
Assumes that the input is random
4
Lower Bound RunningTime Upper Bound≤ ≤
5. Types of Analysis: Example
Example: Linear Search Complexity
Best Case : Item found at the beginning: One comparison
Worst Case : Item found at the end: n comparisons
Average Case :Item may be found at index 0, or 1, or 2, . . . or n - 1
Average number of comparisons is: (1 + 2 + . . . + n) / n = (n+1) / 2
Worst and Average complexities of common sorting algorithms
5
Method Worst Case Average Case Best Case
Selection Sort n2
n2
n2
Insertion Sort n2
n2
n
Merge Sort nlogn nlogn nlogn
Quick Sort n2
nlogn nlogn
6. How do we compare algorithms?
We need to define a number of objective
measures.
(1) Compare execution times?
Not good: times are specific to a particular
computer !!
(2) Count the number of statements executed?
Not good: number of statements vary with the
programming language as well as the style of the
individual programmer.
6
7. Ideal Solution
Express running time as a function of the
input size n (i.e., f(n)).
Compare different functions corresponding
to running times.
Such an analysis is independent of
machine time, programming style, etc.
7
8. Example
Associate a "cost" with each statement.
Find the "total cost” by finding the total number of times
each statement is executed.
Algorithm 1 Algorithm 2
Cost Cost
arr[0] = 0; c1 for(i=0; i<N; i++) c2
arr[1] = 0; c1 arr[i] = 0; c1
arr[2] = 0; c1
... ...
arr[N-1] = 0; c1
----------- -------------
c1+c1+...+c1 = c1 x N (N+1) x c2 + N x c1 =
(c2 + c1) x N + c2
8
9. Another Example
Algorithm 3 Cost
sum = 0; c1
for(i=0; i<N; i++) c2
for(j=0; j<N; j++) c2
sum += arr[i][j]; c3
------------
c1 + c2 x (N+1) + c2 x N x (N+1) + c3 x N2
9
10. Asymptotic Analysis
To compare two algorithms with running
times f(n) and g(n), we need a rough
measure that characterizes how fast each
function grows.
Hint: use rate of growth
Compare functions in the limit, that is,
asymptotically!
(i.e., for large values of n)
10
11. Rate of Growth
Consider the example of buying elephants and
goldfish:
Cost: cost_of_elephants + cost_of_goldfish
Cost ~ cost_of_elephants (approximation)
The low order terms in a function are relatively
insignificant for large n
n4
+ 100n2
+ 10n + 50 ~ n4
i.e., we say that n4
+ 100n2
+ 10n + 50 and n4
have the
same rate of growth
11
17. Big-O Notation
We say fA(n)=30n+8 is order n, or O (n)
It is, at most, roughly proportional to n.
fB(n)=n2
+1 is order n2
, or O(n2
). It is, at most,
roughly proportional to n2
.
In general, any O(n2
) function is faster- growing
than any O(n) function.
17
18. Visualizing Orders of Growth
On a graph, as
you go to the
right, a faster
growing
function
eventually
becomes
larger...
18
fA(n)=30n+8
Increasing n →
fB(n)=n2
+1
Valueoffunction→
19. More Examples …
n4
+ 100n2
+ 10n + 50 is O(n4
)
10n3
+ 2n2
is O(n3
)
n3
- n2
is O(n3
)
constants
10 is O(1)
1273 is O(1)
19
20. Back to Our Example
Algorithm 1 Algorithm 2
Cost Cost
arr[0] = 0; c1 for(i=0; i<N; i++) c2
arr[1] = 0; c1 arr[i] = 0; c1
arr[2] = 0; c1
...
arr[N-1] = 0; c1
----------- -------------
c1+c1+...+c1 = c1 x N (N+1) x c2 + N x c1 =
(c2 + c1) x N + c2
Both algorithms are of the same order: O(N)
20
21. Example (cont’d)
Algorithm 3 Cost
sum = 0; c1
for(i=0; i<N; i++) c2
for(j=0; j<N; j++) c2
sum += arr[i][j]; c3
------------
c1 + c2 x (N+1) + c2 x N x (N+1) + c3 x N2
= O(N2
)
21
24. Examples
2n2
= O(n3
):
n2
= O(n2
):
1000n2
+1000n = O(n2
):
n = O(n2
):
24
2n2
≤ cn3
⇒ 2 ≤ cn ⇒ c = 1 and n0= 2
n2
≤ cn2
⇒ c ≥ 1 ⇒ c = 1 and n0= 1
1000n2
+1000n ≤ 1000n2
+ n2
=1001n2
⇒ c=1001 and n0 = 1000
n ≤ cn2
⇒ cn ≥ 1 ⇒ c = 1 and n0= 1
25. More Examples
Show that 30n+8 is O(n).
Show ∃c,n0: 30n+8 ≤ cn, ∀n>n0 .
Let c=31, n0=8. Assume n>n0=8. Then
cn = 31n = 30n + n > 30n+8, so 30n+8 < cn.
25
26. Big-O example, graphically
Note 30n+8 isn’t
less than n
anywhere (n>0).
It isn’t even
less than 31n
everywhere.
But it is less than
31n everywhere to
the right of n=8.
26
n>n0=8 →
Increasing n →
Valueoffunction→
n
30n+8
cn =
31n
30n+8
∈O(n)
27. No Uniqueness
There is no unique set of values for n0 and c in proving the
asymptotic bounds
Prove that 100n + 5 = O(n2
)
100n + 5 ≤ 100n + n = 101n ≤ 101n2
for all n ≥ 5
n0 = 5 and c = 101 is a solution
100n + 5 ≤ 100n + 5n = 105n ≤ 105n2
for all n ≥ 1
n0 = 1 and c = 105 is also a solution
Must find SOME constants c and n0 that satisfy the asymptotic notation relation
27
31. Examples
n2
/2 –n/2 = Θ(n2
)
½ n2
- ½ n ≤ ½ n2
∀n ≥ 0 ⇒ c2= ½
½ n2
- ½ n ≥ ½ n2
- ½ n * ½ n ( ∀n ≥ 2 ) = ¼ n2
⇒ c1=
¼
n ≠ Θ(n2
): c1 n2
≤ n ≤ c2 n2
⇒ only holds for: n ≤ 1/c1
31
33. Relations Between Different Sets
Subset relations between order-of-growth sets.
33
R→R
Ω( f )O( f )
Θ( f )
• f
34. Logarithms and properties
In algorithm analysis we often use the notation “log n”
without specifying the base
nn
nn
elogln
loglg 2
=
= =y
xlog
34
Binary logarithm
Natural logarithm
)lg(lglglg
)(lglg
nn
nn kk
=
=
xy log
=xylog yx loglog +
=
y
x
log yx loglog −
logb x =
ab
xlog
=xb
alog
log
log
a
a
x
b
35. More Examples
For each of the following pairs of functions, either f(n) is
O(g(n)), f(n) is Ω(g(n)), or f(n) = Θ(g(n)). Determine
which relationship is correct.
f(n) = log n2
; g(n) = log n + 5
f(n) = n; g(n) = log n2
f(n) = log log n; g(n) = log n
f(n) = n; g(n) = log2
n
f(n) = n log n + n; g(n) = log n
f(n) = 10; g(n) = log 10
f(n) = 2n
; g(n) = 10n2
f(n) = 2n
; g(n) = 3n
35
f(n) = Θ (g(n))
f(n) = Ω(g(n))
f(n) = O(g(n))
f(n) = Ω(g(n))
f(n) = Ω(g(n))
f(n) = Θ(g(n))
f(n) = Ω(g(n))
f(n) = O(g(n))
36. Properties
Theorem:
f(n) = Θ(g(n)) ⇔ f = O(g(n)) and f = Ω(g(n))
Transitivity:
f(n) = Θ(g(n)) and g(n) = Θ(h(n)) ⇒ f(n) = Θ(h(n))
Same for O and Ω
Reflexivity:
f(n) = Θ(f(n))
Same for O and Ω
Symmetry:
f(n) = Θ(g(n)) if and only if g(n) = Θ(f(n))
Transpose symmetry:
f(n) = O(g(n)) if and only if g(n) = Ω(f(n))
36