BackTracking Algorithm: Technique and ExamplesFahim Ferdous
This slides gives a strong overview of backtracking algorithm. How it came and general approaches of the techniques. Also some well-known problem and solution of backtracking algorithm.
BackTracking Algorithm: Technique and ExamplesFahim Ferdous
This slides gives a strong overview of backtracking algorithm. How it came and general approaches of the techniques. Also some well-known problem and solution of backtracking algorithm.
In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type until these become simple enough to be solved directly.
This presentation is useful to study about data structure and topic is Binary Tree Traversal. This is also useful to make a presentation about Binary Tree Traversal.
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.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
Do Not just learn computer graphics an close your computer tab and go away..
APPLY them in real business,
Visit Daroko blog for real IT skills applications,androind, Computer graphics,Networking,Programming,IT jobs Types, IT news and applications,blogging,Builing a website, IT companies and how you can form yours, Technology news and very many More IT related subject.
-simply google:Daroko blog(professionalbloggertricks.com)
• Daroko blog (www.professionalbloggertricks.com)
• Presentation by Daroko blog, to see More tutorials more than this one here, Daroko blog has all tutorials related with IT course, simply visit the site by simply Entering the phrase Daroko blog (www.professionalbloggertricks.com) to search engines such as Google or yahoo!, learn some Blogging, affiliate marketing ,and ways of making Money with the computer graphic Applications(it is useless to learn all these tutorials when you can apply them as a student you know),also learn where you can apply all IT skills in a real Business Environment after learning Graphics another computer realate courses.ly
• Be practically real, not just academic reader
In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type until these become simple enough to be solved directly.
This presentation is useful to study about data structure and topic is Binary Tree Traversal. This is also useful to make a presentation about Binary Tree Traversal.
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.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
Do Not just learn computer graphics an close your computer tab and go away..
APPLY them in real business,
Visit Daroko blog for real IT skills applications,androind, Computer graphics,Networking,Programming,IT jobs Types, IT news and applications,blogging,Builing a website, IT companies and how you can form yours, Technology news and very many More IT related subject.
-simply google:Daroko blog(professionalbloggertricks.com)
• Daroko blog (www.professionalbloggertricks.com)
• Presentation by Daroko blog, to see More tutorials more than this one here, Daroko blog has all tutorials related with IT course, simply visit the site by simply Entering the phrase Daroko blog (www.professionalbloggertricks.com) to search engines such as Google or yahoo!, learn some Blogging, affiliate marketing ,and ways of making Money with the computer graphic Applications(it is useless to learn all these tutorials when you can apply them as a student you know),also learn where you can apply all IT skills in a real Business Environment after learning Graphics another computer realate courses.ly
• Be practically real, not just academic reader
Convex Hull - Chan's Algorithm O(n log h) - Presentation by Yitian Huang and ...Amrinder Arora
Chan's Algorithm for Convex Hull Problem. Output Sensitive Algorithm. Takes O(n log h) time. Presentation for the final project in CS 6212/Spring/Arora.
The Gesture Recognition Technology is rapidly growing technology and this PPT describes about the working of gesture recognition technology,the sub fields in it, its applications and the challenges it faces.
My talk about computational geometry in NTU's APEX Club in NTU, Singapore in 2007. The club is for people who are keen on participating in ACM International Collegiate Programming Contests organized by IBM annually.
Trigonometric Function of General Angles LectureFroyd Wess
More: www.PinoyBIX.org
Lesson Objectives
Trigonometric Functions of Angles
Trigonometric Function Values
Could find the Six Trigonometric Functions
Learn the signs of functions in different Quadrants
Could easily determine the signs of each Trigonometric Functions
Solve problems involving Quadrantal Angles
Find Coterminal Angles
Learn to solve using reference angle
Solve problems involving Trigonometric Functions of Common Angles
Solve problems involving Trigonometric Functions of Uncommon Angles
Here are my slides in some basic algorithms in Computational Geometry:
1.- Line Intersection
2.- Sweeping Line
3.- Convex Hull
They are the classic one, but there is still a lot for anybody wanting to get in computer graphics to study. I recomend
Mark de Berg, Otfried Cheong, Marc van Kreveld, and Mark Overmars. 2008. Computational Geometry: Algorithms and Applications (3rd ed. ed.). TELOS, Santa Clara, CA, USA.
CW RADAR, FMCW RADAR, FMCW ALTIMETER, AND THEIR PARAMETERSveerababupersonal22
It consists of cw radar and fmcw radar ,range measurement,if amplifier and fmcw altimeterThe CW radar operates using continuous wave transmission, while the FMCW radar employs frequency-modulated continuous wave technology. Range measurement is a crucial aspect of radar systems, providing information about the distance to a target. The IF amplifier plays a key role in signal processing, amplifying intermediate frequency signals for further analysis. The FMCW altimeter utilizes frequency-modulated continuous wave technology to accurately measure altitude above a reference point.
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.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
3. X ⊆ R² satisfy the following properties
for any two points p,qϵX.
The convex linear combination or the entire
segment p,q ⊂X,where p and q are two vector
points.
4. A polygon P is said to be convex if:
- P is non intersecting;and
- For any two points p and q on the boundary
of P, segment pq lies entirely inside P.
convex
nonconvex
5. Convex hull is defined as a set of given object
Convex hull of a set Q of points, denoted by
CH(Q)is the smallest convex polygon P for which
each points in Q is either on the boundary of P or
in its interior.
6. a) Brute Force Algorithm
b) Quick Hull
c) Divide and Conquer
d) Grahams scan
e) Jarvis march(Gift wrapping)
7. Given a set of points P, test each line segment
to see if it makes up an edge of convex hull.
8. If the rest of the points are on one side of the
segment ,the segment is on the convex hull.
Otherwise the segment is not on the hull.
9. Computation time of convex hull using brute
force algoritm is O(nᶾ) :-
O(n) complexity tests, for each of O(n²)
edges.
In a d-dimensional space, the complexity
is O(nᵈ⁺¹)
10. Quick Hull uses a divide and conquer approach.
For all a,b,c ϵ P, the points contained in ∆abc∩P
cannot be on the convex hull.
11. The initial input to the
algorithm is an
arbitrary set of points.
12. Starting with the given
set of points the first
operation done is the
calculation of the two
maximal points on the
horizontal axis.
13. Next the line formed by
these two points is used
to divide the set into two
different parts.
Everything left from this
line is considered one
part, everything right of
it is considered another
one.
Both of these parts are
processed recursively.
14. To determine the next
point on the convex hull
a search for the point
with the greatest distance
from the dividing line is
done.
This point, together with
the line start and end
point forms a triangle.
15. All points inside this
triangle can not be part
of the convex hull
polygon, as they are
obviously lying in the
convex hull of the three
selected points.
Therefore these points
can be ignored for every
further processing step.
16. Having this in mind the
recursive processing can
take place again.
Everything right of the
triangle is used as one
subset, everything left of
it as another one.
17. • At some point the
recursively processed
point subset does only
contain the start and end
point of the dividing line.
• If this is case this line has
to be a segment of the
searched hull polygon and
the recursion can come to
an end.
18. QuickHull(s)
{
//Find convex hull from the set S of n points.
Convex hull:={}
1. Find left and right most points,say A and B, and add A and B to
convex hull
2. Segment AB divides the remaining (n-2)points into 2 groups S1
and S2.
where S1 are points in S that are on the right side of the oriented
line from A to B
and S2 are points in S that are on the right side of the oriented
line from B to A
3. FindHull (S1,A,B)
4. FindHull (S2,B,A)
19. Findhull (Sk,P,Q)
{
//find points on convex hull from the set of points that are on the right
side of the oriented line from P to Q
If Sk has no points,
then return.
From the given set of points in Sk, find farthest point,say c, from
segment PQ
Add points C to convex hull at the location between P and Q three
points P,Q and C partition the remaining points of Sk into 3 subsets
: S0,S1,S2
Where S0 are points inside triangle PCQ, S1 are points on the right
side of the oriented line from P to C and S2 are points on the right
side of the oriented line from from C to Q.
FindHull (S1,P,C)
FindHull (S2,C,Q)
21. •Preprocessing: sort the points
by x-coordinate
•Divide the set of points into
two sets A and B:
•A contains the left n/2
points,
• B contains the right n/2
points
•Recursively compute the
convex hull of A
•Recursively compute the
convex hull of B
A B
22. •Preprocessing: sort the points by x-
coordinate
•Divide the set of points into two sets
A and B:
•A contains the left n/2 points,
• B contains the right n/2 points
•Recursively compute the convex
hull of A
•Recursively compute the convex
hull of B
•Merge the two convex hulls
O(n log n)
O(1)
T(n/2)
T(n/2)
O(n)
23. In merging hull we find upper and lower tangent of CH1 and
CH2
Find the Upper Tangent:
Start at the rightmost vertex of CH1 and the leftmost vertex of
CH2.
Upper tangent will be a line segment
such that it makes a left turn with
next counter-clockwise vertex of CH1
and makes a right turn with next
clockwise vertex of CH2.
CH1 CH2
24. If the line segment connecting them is not the upper
tangent:
– If the line segment does not make a left turn with
next counter clockwise vertex of CH1, rotate to the
next counter-clockwise vertex in CH1.
– Else if the line segment does not
make a right turn with the next
clockwise vertex of CH2, rotate to
the next clockwise vertex in CH2.
Repeat as necessary.
CH1 CH2
25. Find the Lower Tangent
Start at the rightmost vertex of CH1 and the leftmost
vertex of CH2.
Lower tangent will be a line segment
such that it makes a right turn with
next clockwise vertex of CH1
and makes a left turn with next
counter clockwise vertex of CH2.
CH1 CH2
26. If the line segment connecting them is not the lower
tangent:
– If the line segment does not make a right turn with
next clockwise vertex of CH1, rotate to the next
clockwise vertex in CH1.
– Else if the line segment does not
make a left turn with the next
counter-clockwise vertex of CH2,
rotate to the next counter clockwise
vertex in CH2.
Repeat as necessary.
CH1 CH2
27. Graham scan is a method of computing the
convex hull of a finite set of points in the plane
with time complexity O(n logn).
The algorithm finds all vertices of the convex hull
ordered along its boundary
Graham's scan solves the convex-hull problem by
maintaining a stack S of candidate points. Each
point of the input set Q is pushed once onto the
stack.
28. And the points that are not vertices of CH(Q) are
eventually popped from the stack. When the
algorithm terminates, stack S contains exactly the
vertices of CH(Q), in counterclockwise order of their
appearance on the boundary.
When we traverse the convex hull counter clockwise,
we should make a left turn at each vertex.
Each time the while loop finds a vertex at which we
make a non left turn ,the vertex is popped from the
vertex.
43. Phase 1 takes time O(N logN) points are sorted
by angle around the anchor
Phase 2 takes time O(N) each point is inserted
into the sequence exactly once, and each point
is removed from the sequence at most once
Total time complexity O(N log N)
44. Proposed by R.A. Jarvis in 1973
1.Also known as the “gift wrapping” technique.
2.Start at some extreme point on the hull.
3.In a counterclockwise fashion, each point
within the hull is visited and the point that
undergoes the largest right-hand turn from the
current extreme point is the next point on the hull.
4.Finds the points on the hull in the order in which
they appear.
45. This is perhaps the most simple-minded algorithm for
the convex hull , and yet in some cases it can be very fast.
The basic idea is as follows:
Start at some extreme point, which is guaranteed to be on
the hull.
At each step, test each of the points, and find the one which
makes the largest right-hand turn. That point has to be the
next one on the hull.
Because this process marches around the hull in counter-
clockwise order, like a ribbon wrapping itself around the
points, this algorithm also called the "gift-wrapping"
algorithm
46.
47. The corresponding convex hull algorithm is
called Jarvis’s march. Which builds the hull in
O(nh) time by a process called “gift-wrapping”.
The algorithm operates by considering any one
point that is on the hull say, the lowest point.
We then find the “next” edge on the hull in
counter clockwise order.
48. In order to find the biggest right hand turn, the
last two points added to the hull, p1 and p2, must
be known.
Assuming p1 and p2 are known, the angle these
two points form with the remaining possible hull
points is calculated. The point that minimizes the
angle is the next point in the hull.
Continue to make right turns until the original
point is reached and the hull is complete.
49.
50. The idea of Jarvis’s Algorithm is simple, we start from the
leftmost point (or point with minimum x coordinate value)
and we keep wrapping points in counter clockwise direction.
The big question is, given a point p as current point, how to
find the next point in output?
The idea is to use orientation()here. Next point is selected as
the point that beats all other points at counter clockwise
orientation, and the point which has right hand most turn is
taken as next point.
51. Algorithm
First, a base point po is selected, this is the point
with the minimum y-coordinate
Select leftmost point in case of tie.
The next convex hull vertices p1 has the least polar
angle w.r.t. the positive horizontal ray from po.
Measure in counter clockwise direction.
If tie, choose the farthest such point.
Vertices p2, p3, . . . , pk are picked similarly until yk =
ymax
pi+1 has least polar angle w.r.t. positive ray
from po.
If tie, choose the farthest such point.
52. Implementation technique
The points are stored in a fixed array of size one thousand.
A static sized contiguous array is an appropriate data structure
because of the algorithm’s sequential and repetitious point
checking.
Searching operations would be considerably slower assuming
non-contiguous memory allocation of nodes in a linked list.
Using a static array makes it far more likely the data with be
brought into cache, where operations can happen considerably
faster.
53.
54. Application
Blue lines represent point-to-point comparisons. As
Jarvis’ March progresses around the convex hull,it finds
the point with the most minimal or maximal angle
relative to itself; that is the next point in the convex
hull.
Blue lines radiate from every point in the completed
polygon. This is because the algorithm tests every point
in the set at every node in the convex hull.
Although not visible, blue lines also show tests
between neighbor points. However, because those edges
are part of the perimeter of the convex hull, a green line
covers them.
55. O(nh) complexity, with n being the total number of
points in the set, and h being the number of points
that lie in the convex hull.
This implies that the time complexity for this
algorithm is the number of points in the set
multiplied by the number of points in the hull
The worst case for this algorithm is denoted by
O(n2), which is not optimal.
Favorable conditions in which to use the Jarvis
march include problems with a very low number
of total points, or a low number of points on the
convex hull in relation to the total number of
points.
56. Since the algorithm spends O(n) time for each
convex hull vertex, the worst-case running time is
O(n2).
However, if the convex hull has very few vertices,
Jarvis's march is extremely fast.
A better way to write the running time is O(nh),
where h is the number of convex hull vertices.
In the worst case, h = n, and we get our old O(n2)
time bound, but in the best case h = 3, and the
algorithm only needs O(n) time.
This is a so called output-sensitive algorithm, the
smaller the output, the faster the algorithm.
57. Computer visualization, ray tracing
(e.g. video games, replacement of bounding boxes)
Path finding
(e.g. embedded AI of Mars mission rovers)
Geographical Information Systems (GIS)
(e.g. computing accessibility maps)
Visual pattern matching
(e.g. detecting car license plates)
Verification methods
(e.g. bounding of Number Decision Diagrams)
Geometry
(e.g. diameter computation)
58. Que1. Computation time of convex hull using brute
force algorithm is O(nᶾ):-O(n) complexity tests, for
each of O(n²) edges. Give an O(nlogn) time
complexity for computing the convex hull.
Ques2. Consider 10 points (P₀ to P₉) and then construct
a convex hull using Graham scan method.