Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL
Here are my slides for my preparation class for possible students for the Master in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible students in the Master in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible Master students in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL
Here are my slides for my preparation class for possible students for the Master in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
Here are my slides for my preparation class for possible students in the Master in Electrical Engineering and Computer Science (Specialization in Computer Science)... for the entrance examination here at Cinvestav GDL.
In this chapter we will discuss tree data structures, like trees and graphs. The abilities of these data structures are really important for the modern programming. Each of this data structures is used for building a model of real life problems, which are efficiently solved using this model. We will explain what tree data structures are and will review their main advantages and disadvantages. We will present example implementations and problems showing their practical usage. We will focus on binary trees, binary search trees and self-balancing binary search tree. We will explain what graph is, the types of graphs, how to represent a graph in the memory (graph implementation) and where graphs are used in our life and in the computer technologies. We will see where in .NET Framework self-balancing binary search trees are implemented and how to use them.
This is a presentation on Arrays, one of the most important topics on Data Structures and algorithms. Anyone who is new to DSA or wants to have a theoretical understanding of the same can refer to it :D
Insert works in constant time for either end of a linked list. Remove works in constant time only. Seems best that head of the linked list be the front of the queue so that all removes will be from the front. Inserts will be at the end of the list
Array Basics
Copying Arrays
Passing Arrays to Methods
Returning an Array from a Method
(Optional) Variable-Length Argument Lists
The Arrays Class
Two-Dimensional Arrays
(Optional) Multidimensional Arrays
Arrays In Python | Python Array Operations | EdurekaEdureka!
** Python Certification Training: https://www.edureka.co/python **
This Edureka PPT on 'Arrays in Python' will help you establish a strong hold on all the fundamentals in the Python programming language. Below are the topics covered in this PPT:
What is an array?
Is python list same as an array?
How to create arrays in python?
Accessing array elements
Basic array operations
- Finding the length of an array
- Adding Elements
- Removing elements
- Array concatenation
- Slicing
- Looping
Python Tutorial Playlist: https://goo.gl/WsBpKe
Blog Series: http://bit.ly/2sqmP4s
Follow us to never miss an update in the future.
YouTube: https://www.youtube.com/user/edurekaIN
Instagram: https://www.instagram.com/edureka_learning/
Facebook: https://www.facebook.com/edurekaIN/
Twitter: https://twitter.com/edurekain
LinkedIn: https://www.linkedin.com/company/edureka
In this chapter we will discuss tree data structures, like trees and graphs. The abilities of these data structures are really important for the modern programming. Each of this data structures is used for building a model of real life problems, which are efficiently solved using this model. We will explain what tree data structures are and will review their main advantages and disadvantages. We will present example implementations and problems showing their practical usage. We will focus on binary trees, binary search trees and self-balancing binary search tree. We will explain what graph is, the types of graphs, how to represent a graph in the memory (graph implementation) and where graphs are used in our life and in the computer technologies. We will see where in .NET Framework self-balancing binary search trees are implemented and how to use them.
This is a presentation on Arrays, one of the most important topics on Data Structures and algorithms. Anyone who is new to DSA or wants to have a theoretical understanding of the same can refer to it :D
Insert works in constant time for either end of a linked list. Remove works in constant time only. Seems best that head of the linked list be the front of the queue so that all removes will be from the front. Inserts will be at the end of the list
Array Basics
Copying Arrays
Passing Arrays to Methods
Returning an Array from a Method
(Optional) Variable-Length Argument Lists
The Arrays Class
Two-Dimensional Arrays
(Optional) Multidimensional Arrays
Arrays In Python | Python Array Operations | EdurekaEdureka!
** Python Certification Training: https://www.edureka.co/python **
This Edureka PPT on 'Arrays in Python' will help you establish a strong hold on all the fundamentals in the Python programming language. Below are the topics covered in this PPT:
What is an array?
Is python list same as an array?
How to create arrays in python?
Accessing array elements
Basic array operations
- Finding the length of an array
- Adding Elements
- Removing elements
- Array concatenation
- Slicing
- Looping
Python Tutorial Playlist: https://goo.gl/WsBpKe
Blog Series: http://bit.ly/2sqmP4s
Follow us to never miss an update in the future.
YouTube: https://www.youtube.com/user/edurekaIN
Instagram: https://www.instagram.com/edureka_learning/
Facebook: https://www.facebook.com/edurekaIN/
Twitter: https://twitter.com/edurekain
LinkedIn: https://www.linkedin.com/company/edureka
Question In C Programming In mathematics, a set is a colle...Sav.pdfarihantcomp1008
Question: In C Programming: In mathematics, a set is a colle...
Save
In C Programming:
In mathematics, a set is a collection of distinct elements (say integer numbers). For example,
A={2, 5, 7} and B={3, 5, 8, 10} are two different sets. There are several basic operations for
constructing new sets from given two sets, but let\'s just consider three basic ones:
C = union(A,B); ---> C = A B={2, 5, 7, 8, 10} C = intersection(A,B); ---> C = A B={5}
C = difference(A,B); ---> C = A-B = A \\ B ={2, 7} also aka. complement
You are asked to develop a set library (using two different representations: array and link list)
and then implement a driver program that gets two sets and one of the above operation as a
command to apply, then it prints the resulting set...
Developing set library: For interface, create an interface file set.h which contains boiler plate and
the followings:
typedef int setElementT;
typedef struct setCDT *setADT;
setADT setNew(); /* create a new empty set */
void setFree(setADT S); /* free the space allocated for the set S */
int setInsertElementSorted(setADT S, setElementT E);
/* if not successful, return 0; otherwise, return the num of elements after the insertion. Also note
that the elements might be given in different orders, but your function should always keep the set
in a sorted manner after each insertion */
setADT setUnion(setADT A, setADT B);
/* returns a new set containing A B */
setADT setIntersection(setADT A, setADT B);
/* returns a new set containing A B */
setADT setDifference(setADT A, setADT B);
/* returns a new set containing A \\ B */
int setCardinality(setADT S);
/* return the number of elements in S */
void setPrint(setADT S, char *name);
/* print elements of S, A = {2, 5, 7} */
For implementation, you will be asked to have two different implementations:
(40pt) First implement set library as setArrayImp.c which uses a constant size array to store set
elements (suppose max set size is 100). [hint: see ch2 slides 72-78 ]
(40pt) Second implement this library as setLinkedListImp.c which uses a dynamic single linked
list to store set elements.
Develop a driver.c program and compile it with two different imp of set library (20 pt)
1. Create two sets called A and B.
2. Ask user to enter positive integers for set A (end input when user enters -1)
3. Ask user to enter positive integers for set B (end input when user enters -1)
4. In a loop 4.1. Ask user to enter a command:
4.2 If Q is entered, quit from this loop.
4.3 If U, I, or D is entered, compute set C as union, intersection, or difference. setPrint(A, \"A\");
setPrint(A, \"B\"); setPrint(C, \"C\"); print the number of elements in C setFree(C);
5. free A and B
Compile/execute driver.c with setArrayImp.c as well as setListImp.c
//no include files needed
Solution
Create set.h first with the following
typedef int setElementT;
typedef struct setCDT *setADT;
setADT setNew(); /* Creates a new empty set */
void setFree(setADT S); /* Frees the space allocated for the set .
Senior data scientist and founder of the company Intelligentia Data I+D SA de CV. We are offering consultancy services, development of projects and products in Machine Learning, Big Data, Data Sciences and Artificial Intelligence.
My first set of slides (The NN and DL class I am preparing for the fall)... I included the problem of Vanishing Gradient and the need to have ReLu (Mentioning btw the saturation problem inherited from Hebbian Learning)
It has been almost 62 years since the invention of the term Artificial Intelligence by Samuel and Minsky et al. at the Dartmouth workshop College in 1956 (“Dartmouth Summer Research Project on Artificial Intelligence”) where this new area of Computer Science was invented. However, the history of Artificial Intelligence goes back to previous millennia, when the Greeks in their Myths spoke about golden robots at Hephaestus, and the Galatea of Pygmalion. They were the first automatons known at the dawn of history, and although these first attempts were only myths, automatons were invented and built through multiple civilizations in history. Nevertheless, these automatons resembled in quite limited way their final objectives, representing animals and humans. In spite of that, the greatest illusion of an automaton, the Turk by Wolfgang von Kempelen, inspired many people, trough its exhibitions, as Alexander Graham Bell and Charles Babbage to develop inventions that would change forever human history. Thus, the importance of the concept “Artificial Intelligence” as a driver of our technological dreams. And although Artificial Intelligence has never been defined in a precise practical way, the amount of research and methods that have been developed to tackle some of its basics tasks have been and are quite humongous. Thus, the importance of having an introduction to the concepts of Artificial Intelligence, thus the dream can continue.
A review of one of the most popular methods of clustering, a part of what is know as unsupervised learning, K-Means. Here, we go from the basic heuristic used to solve the NP-Hard problem to an approximation algorithm K-Centers. Additionally, we look at variations coming from the Fuzzy Set ideas. In the future, we will add more about On-Line algorithms in the line of Stochastic Gradient Ideas...
Here a Review of the Combination of Machine Learning models from Bayesian Averaging, Committees to Boosting... Specifically An statistical analysis of Boosting is done
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. Images/cinvestav-
Outline
1 Linear List Array Representation
Operations in Array List
2 Dynamic Arrays
How much we need to expand it...
A Strategy for it
Analysis
2 / 24
3. Images/cinvestav-
How do we implement the ADT List?
In our first representation will use an array
Use a one-dimensional array element[]:
a b c d e - - - -
0 1 2 3 4 5 6 7 8
The previous array
A representation of L = (a, b, c, d, e) using position i in element[i].
3 / 24
4. Images/cinvestav-
How do we implement the ADT List?
In our first representation will use an array
Use a one-dimensional array element[]:
a b c d e - - - -
0 1 2 3 4 5 6 7 8
The previous array
A representation of L = (a, b, c, d, e) using position i in element[i].
3 / 24
5. Images/cinvestav-
Where to map in the array
Right To Left Mapping
- - - - e d c b a
Mapping That Skips Every Other Position
a - b - c - d - e - -
Wrap Around Mapping
d e - - - - - - a b c
4 / 24
6. Images/cinvestav-
Where to map in the array
Right To Left Mapping
- - - - e d c b a
Mapping That Skips Every Other Position
a - b - c - d - e - -
Wrap Around Mapping
d e - - - - - - a b c
4 / 24
7. Images/cinvestav-
Where to map in the array
Right To Left Mapping
- - - - e d c b a
Mapping That Skips Every Other Position
a - b - c - d - e - -
Wrap Around Mapping
d e - - - - - - a b c
4 / 24
8. Images/cinvestav-
Representation Used In Text
Something Notable
a b c d e - - - -
0 1 2 3 4 5 6 7 8
Size=5
Thus
1 Put element i of list in element[i].
2 Use a variable size to record current number of elements
5 / 24
9. Images/cinvestav-
Representation Used In Text
Something Notable
a b c d e - - - -
0 1 2 3 4 5 6 7 8
Size=5
Thus
1 Put element i of list in element[i].
2 Use a variable size to record current number of elements
5 / 24
10. Images/cinvestav-
Code
Our Implementation
p u b l i c c l a s s S i m p l e A r r a y L i s t <Item> implements
L i n e a r L i s t <Item >{
// p r i v a t e elements of implementation
p r o t e c t e d Item element [ ] ;
p r o t e c t e d i n t s i z e ;
p r o t e c t e d f i n a l s t a t i c i n t DEFAULT_SIZE = 10;
// C o n s t r u c t o r s
p u b l i c S i m p l e A r r a y L i s t (){
t h i s . s i z e = 0;
t h i s . element = ( Item [ ] ) new Object [ t h i s . DEFAULT_SIZE ] ;
}
p u b l i c S i m p l e A r r a y L i s t ( i n t NewSize ){
t h i s . s i z e = 0;
t h i s . element = ( Item [ ] ) new Object [ NewSize ] ;
}
6 / 24
11. Images/cinvestav-
Data Type Of Array element[]
First than anything
Data type of list elements is unknown.
Thus, we used the genericity of Object
1 Then, we use element[] to be of data type Object.
2 Then, we cast to the new “Item.”
However
You cannot put elements of primitive data types (int, float, double, char,
etc.) into our linear lists.
7 / 24
12. Images/cinvestav-
Data Type Of Array element[]
First than anything
Data type of list elements is unknown.
Thus, we used the genericity of Object
1 Then, we use element[] to be of data type Object.
2 Then, we cast to the new “Item.”
However
You cannot put elements of primitive data types (int, float, double, char,
etc.) into our linear lists.
7 / 24
13. Images/cinvestav-
Data Type Of Array element[]
First than anything
Data type of list elements is unknown.
Thus, we used the genericity of Object
1 Then, we use element[] to be of data type Object.
2 Then, we cast to the new “Item.”
However
You cannot put elements of primitive data types (int, float, double, char,
etc.) into our linear lists.
7 / 24
14. Images/cinvestav-
Data Type Of Array element[]
First than anything
Data type of list elements is unknown.
Thus, we used the genericity of Object
1 Then, we use element[] to be of data type Object.
2 Then, we cast to the new “Item.”
However
You cannot put elements of primitive data types (int, float, double, char,
etc.) into our linear lists.
7 / 24
15. Images/cinvestav-
Outline
1 Linear List Array Representation
Operations in Array List
2 Dynamic Arrays
How much we need to expand it...
A Strategy for it
Analysis
8 / 24
18. Images/cinvestav-
Code
Our Implementation
p u b l i c void add ( i n t index , Item myobject ){
// I n i t i a l V a r i a b l e s
i n t i ;
// Always check f o r p o s s i b l e e r r o r s
i f ( t h i s . s i z e == element . len ght ){
System . out . p r i n t l n ( " L i s t ␣ does ␣ not ␣ have ␣ space " ) ;
System . e x i t ( 0 ) ;
}
i f ( index <0 | | index >t h i s . s i z e ){
System . out . p r i n t l n ( " Index ␣ out ␣ of ␣bound " ) ;
System . e x i t ( 0 ) ;
}
// S h i f t p o s t i i o n s as n e c e s s a r y
f o r ( i = t h i s . s i z e ; i >index ; i −−)
element [ i +1]=element [ i ] ;
// copy element i n t o c o n t a i n e r
element [ i +1]=myobject ;
}
10 / 24
21. Images/cinvestav-
Operations: Get
Here
We have
a b c d e - - - -
0 1 2 3 4 5 6 7 8
Size=5
get(3)
It will return “d”.
The code is simple
p u b l i c Item get ( i n t index ){
// Check always
i f ( t h i s . s i z e == 0) r e t u r n n u l l ;
i f ( index <0 | | index >t h i s . s i z e −1){
System . out . p r i n t l n ( " Index ␣ out ␣ of ␣bound " ) ;
System . e x i t ( 0 ) ;
}
r e t u r n element [ index ]
}
11 / 24
23. Images/cinvestav-
Now, we have a common problem
Because
We do not know how many elements will be stored at the list.
We use
An initial length and dynamically increase the size as needed.
13 / 24
24. Images/cinvestav-
Now, we have a common problem
Because
We do not know how many elements will be stored at the list.
We use
An initial length and dynamically increase the size as needed.
13 / 24
25. Images/cinvestav-
Example
Example
Length of array element[] is 6:
a b c d e f
First create a new and larger array
NewArray = (Item[]) new Object[12]
- - - - - - - - - - - -
Now copy the new elements into the new array!!!
System.arraycopy(element, 0, newArray, 0, element.length);
a b c d e f - - - - - -
14 / 24
26. Images/cinvestav-
Example
Example
Length of array element[] is 6:
a b c d e f
First create a new and larger array
NewArray = (Item[]) new Object[12]
- - - - - - - - - - - -
Now copy the new elements into the new array!!!
System.arraycopy(element, 0, newArray, 0, element.length);
a b c d e f - - - - - -
14 / 24
27. Images/cinvestav-
Example
Example
Length of array element[] is 6:
a b c d e f
First create a new and larger array
NewArray = (Item[]) new Object[12]
- - - - - - - - - - - -
Now copy the new elements into the new array!!!
System.arraycopy(element, 0, newArray, 0, element.length);
a b c d e f - - - - - -
14 / 24
29. Images/cinvestav-
Outline
1 Linear List Array Representation
Operations in Array List
2 Dynamic Arrays
How much we need to expand it...
A Strategy for it
Analysis
16 / 24
30. Images/cinvestav-
First Attempt
What if you use the following policy?
At least 1 more than current array length.
Thus
What would be the cost of all operations?
Generate a new array.
Copy all the items to it.
insert the new element at the end.
17 / 24
31. Images/cinvestav-
First Attempt
What if you use the following policy?
At least 1 more than current array length.
Thus
What would be the cost of all operations?
Generate a new array.
Copy all the items to it.
insert the new element at the end.
17 / 24
32. Images/cinvestav-
First Attempt
What if you use the following policy?
At least 1 more than current array length.
Thus
What would be the cost of all operations?
Generate a new array.
Copy all the items to it.
insert the new element at the end.
17 / 24
33. Images/cinvestav-
First Attempt
What if you use the following policy?
At least 1 more than current array length.
Thus
What would be the cost of all operations?
Generate a new array.
Copy all the items to it.
insert the new element at the end.
17 / 24
34. Images/cinvestav-
First Attempt
What if you use the following policy?
At least 1 more than current array length.
Thus
What would be the cost of all operations?
Generate a new array.
Copy all the items to it.
insert the new element at the end.
17 / 24
35. Images/cinvestav-
What if we do n insertions?
We finish with something like this
1 First Insertion: Creation of the List ⇒ Cost = 1.
2 Second Insertion Cost = 2.
3 Third Insertion Cost = 3
4 etc!!!
Thus, we have
Ok
Not a good idea!!!
18 / 24
36. Images/cinvestav-
What if we do n insertions?
We finish with something like this
1 First Insertion: Creation of the List ⇒ Cost = 1.
2 Second Insertion Cost = 2.
3 Third Insertion Cost = 3
4 etc!!!
Thus, we have
Ok
Not a good idea!!!
18 / 24
37. Images/cinvestav-
What if we do n insertions?
We finish with something like this
1 First Insertion: Creation of the List ⇒ Cost = 1.
2 Second Insertion Cost = 2.
3 Third Insertion Cost = 3
4 etc!!!
Thus, we have
Ok
Not a good idea!!!
18 / 24
38. Images/cinvestav-
What if we do n insertions?
We finish with something like this
1 First Insertion: Creation of the List ⇒ Cost = 1.
2 Second Insertion Cost = 2.
3 Third Insertion Cost = 3
4 etc!!!
Thus, we have
Ok
Not a good idea!!!
18 / 24
39. Images/cinvestav-
What if we do n insertions?
We finish with something like this
1 First Insertion: Creation of the List ⇒ Cost = 1.
2 Second Insertion Cost = 2.
3 Third Insertion Cost = 3
4 etc!!!
Thus, we have
1 + 2 + 3 + · · · + n =
n (n + 1)
2
= O n2
(1)
Ok
Not a good idea!!!
18 / 24
40. Images/cinvestav-
What if we do n insertions?
We finish with something like this
1 First Insertion: Creation of the List ⇒ Cost = 1.
2 Second Insertion Cost = 2.
3 Third Insertion Cost = 3
4 etc!!!
Thus, we have
1 + 2 + 3 + · · · + n =
n (n + 1)
2
= O n2
(1)
Ok
Not a good idea!!!
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Outline
1 Linear List Array Representation
Operations in Array List
2 Dynamic Arrays
How much we need to expand it...
A Strategy for it
Analysis
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A better strategy
Dynamic Array
To avoid incurring the cost of resizing many times, dynamic arrays resize
by an amount a.
In our example we double the size, a = 2
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A better strategy
Dynamic Array
To avoid incurring the cost of resizing many times, dynamic arrays resize
by an amount a.
In our example we double the size, a = 2
Item NewArray [ ] ;
i f ( t h i s . s i z e == element . len ght ){
// Resize the c a p a c i t y
NewArray = ( Item [ ] ) new Object [ 2*this.size ]
f o r ( i n t i =0; i < s i z e ; i ++){
NewArray [ i ]= element [ i ] ;
}
element = NewArray ;
}
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Space Complexity
Every time an insertion triggers a doubling of the array
Thus, space wasted in the new array:
Space Wasted = Old Lenght − 1 (2)
Remember: We double the array and insert!!!
Thus, the average space wasted is
Θ (n) (3)
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Space Complexity
Every time an insertion triggers a doubling of the array
Thus, space wasted in the new array:
Space Wasted = Old Lenght − 1 (2)
Remember: We double the array and insert!!!
Thus, the average space wasted is
Θ (n) (3)
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For example, we have the following
A trade-off between time and space
You have and average time for insertion is 2
2−1 .
In addition, an upper bound for the wasted cells in the array is
(2 − 1) n − 1 = n − 1.
Actually a more general term of expansion, a
Thus, we have:
Average time for insertion is a
a−1 .
An upper bound for the wasted cells in the array is
(a − 1) n − 1 = an − n − 1.
Different languages use different values
Java, a = 3
2 .
Python, a = 9
8
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47. Images/cinvestav-
For example, we have the following
A trade-off between time and space
You have and average time for insertion is 2
2−1 .
In addition, an upper bound for the wasted cells in the array is
(2 − 1) n − 1 = n − 1.
Actually a more general term of expansion, a
Thus, we have:
Average time for insertion is a
a−1 .
An upper bound for the wasted cells in the array is
(a − 1) n − 1 = an − n − 1.
Different languages use different values
Java, a = 3
2 .
Python, a = 9
8
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48. Images/cinvestav-
For example, we have the following
A trade-off between time and space
You have and average time for insertion is 2
2−1 .
In addition, an upper bound for the wasted cells in the array is
(2 − 1) n − 1 = n − 1.
Actually a more general term of expansion, a
Thus, we have:
Average time for insertion is a
a−1 .
An upper bound for the wasted cells in the array is
(a − 1) n − 1 = an − n − 1.
Different languages use different values
Java, a = 3
2 .
Python, a = 9
8
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49. Images/cinvestav-
Outline
1 Linear List Array Representation
Operations in Array List
2 Dynamic Arrays
How much we need to expand it...
A Strategy for it
Analysis
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We have the following final analysis
Amortized Analysis Vs. Classic
Array Classic Analysis Dynamic Array
Amortized Analysis
Indexing O (1) O (1)
Search O (n) O (n)
Add/Remove O (n) O (n)
Space Complexity O (n) O (n)
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