In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
Fractional programming (A tool for optimization)VARUN KUMAR
The document discusses fractional programming problems (FPP), which involve optimizing an objective function that is the ratio of two other functions. It outlines three common transforms used to convert FPPs into more tractable forms: 1) Charnes-Cooper transform decouples the numerator and denominator, 2) Dinkelbach's transform iteratively updates an auxiliary variable, and 3) quadratic transform ensures the transformed objective function is concave to allow convex optimization techniques to be applied. The document provides detailed mathematical derivations of the quadratic transform to justify its formulation.
The document discusses recursion through examples such as calculating factorials and multiplying numbers recursively. It defines recursion as solving a problem by solving smaller instances of the same problem. Recursive algorithms break down a problem into smaller sub-problems until reaching a base case, and use the solutions to the sub-problems to solve the original problem.
1. Classes allow the creation of user-defined data types through the grouping of related data members and member functions.
2. Class members can be declared as private, public or protected and determine accessibility outside the class.
3. Methods are defined similarly to regular functions but can access any member of the class without passing them as parameters.
The document discusses defining and using methods in Java. It defines what a method is and its key components like the method signature, return type, parameters, and body. It then demonstrates a sample max method to return the maximum of two numbers and traces the steps of invoking the method from the main method, including passing arguments, executing the method body, and returning the result. The document aims to explain the basics of methods in Java, including how to define reusable methods and invoke them to perform certain tasks.
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
Fractional programming (A tool for optimization)VARUN KUMAR
The document discusses fractional programming problems (FPP), which involve optimizing an objective function that is the ratio of two other functions. It outlines three common transforms used to convert FPPs into more tractable forms: 1) Charnes-Cooper transform decouples the numerator and denominator, 2) Dinkelbach's transform iteratively updates an auxiliary variable, and 3) quadratic transform ensures the transformed objective function is concave to allow convex optimization techniques to be applied. The document provides detailed mathematical derivations of the quadratic transform to justify its formulation.
The document discusses recursion through examples such as calculating factorials and multiplying numbers recursively. It defines recursion as solving a problem by solving smaller instances of the same problem. Recursive algorithms break down a problem into smaller sub-problems until reaching a base case, and use the solutions to the sub-problems to solve the original problem.
1. Classes allow the creation of user-defined data types through the grouping of related data members and member functions.
2. Class members can be declared as private, public or protected and determine accessibility outside the class.
3. Methods are defined similarly to regular functions but can access any member of the class without passing them as parameters.
The document discusses defining and using methods in Java. It defines what a method is and its key components like the method signature, return type, parameters, and body. It then demonstrates a sample max method to return the maximum of two numbers and traces the steps of invoking the method from the main method, including passing arguments, executing the method body, and returning the result. The document aims to explain the basics of methods in Java, including how to define reusable methods and invoke them to perform certain tasks.
Complexity analysis - The Big O NotationJawad Khan
Complexity analysis determines how resource requirements like time and memory scale with problem size. Computation time depends on hardware, while complexity analyzes algorithm scaling. Big O notation describes asymptotic function growth. Common complexities are O(1) constant, O(log n) logarithmic, O(n) linear, O(n^2) quadratic. Statements are O(1), if/else max branch, loops run n times, nested loops run n*m times, functions match calling structure, and when statements have undefined time.
The document discusses arrays and motivates their use. It explains that arrays allow storing a large number of values in a program and accessing them through indices. Arrays solve the problem of having to declare many individual variables to store multiple values. The document then introduces the concept of arrays, how to declare and initialize array variables, and how to access elements within an array using indices. It provides examples of declaring, initializing, and accessing one-dimensional and two-dimensional arrays.
The document discusses three cases for deleting a node from a binary search tree: 1) if the node has no children, simply remove it, 2) if the node has one child, make the parent point to the child, and 3) if the node has two children, find its successor, remove the successor, and replace the node with the successor. It then provides pseudocode for the delete operation and examples of building a BST and performing an in-order traversal.
The document discusses defining and using methods in Java. It defines what a method is and its key components like the method signature, return type, parameters, and body. It then demonstrates a sample max method to return the maximum of two numbers and traces the steps of invoking the method from the main method, including passing arguments, executing the method body, and returning the result. The document aims to explain the basics of methods in Java, including how to define reusable methods and invoke them to perform certain tasks.
1. The document discusses recursion and provides examples of recursively defined problems and their solutions, including factorials, powers, greatest common divisor, Fibonacci series, Towers of Hanoi, and counting cells in a blob.
2. Recursion involves breaking a problem into smaller subproblems of the same type until reaching a base case that can be solved directly. The solutions to subproblems are then combined to solve the original problem.
3. Examples of recursively defined problems include mathematical formulas, searching and sorting algorithms like binary search, and problems like Towers of Hanoi that are naturally broken down recursively.
This document discusses time and space complexity analysis of algorithms. It analyzes the time complexity of bubble sort, which is O(n^2) as each pass through the array requires n-1 comparisons and there are n passes needed. Space complexity is typically a secondary concern to time complexity. Time complexity analysis allows comparison of algorithms to determine efficiency and whether an algorithm will complete in a reasonable time for a given input size. NP-complete problems cannot be solved in polynomial time but can be verified in polynomial time.
Monadic Comprehensions and Functional Composition with Query ExpressionsChris Eargle
Build monads using the C# language with a C# style, then use the appropriate methods to ensure the LINQ query syntax works with this functional design pattern. After describing monads, we will cut the middleman and apply the same techniques directly to objects and functions to achieve better results with a declarative syntax.
An Introduction to ECDSA and it's use in Bitcoin (1)Hakeem Hunte
This document provides an introduction to ECDSA and its use in Bitcoin. It begins by explaining how Bitcoin uses a blockchain to record transactions and ensure their authenticity through digital signatures. ECDSA is the algorithm used to generate these signatures. The document then discusses public key cryptography and how ECDSA works. It introduces concepts like elliptic curves, finite fields, point addition/doubling, and scalar multiplication which are important to understanding how ECDSA generates public/private key pairs to digitally sign transactions on the Bitcoin blockchain.
The document describes experience with partial SIMDization in the Open64 compiler using dynamic programming. It discusses applying partial SIMDization to pack isomorphic instructions into SIMD instructions without fully vectorizing loops. It outlines applying a dynamic programming approach based on the Barik-Zhao-Sarkar algorithm to choose optimal SIMD tile combinations. Initial results show applying this to a hot loop in GROMACS was able to SIMDize over 88% of operations, demonstrating the potential of the technique.
This document discusses backtracking algorithms and provides examples for solving problems using backtracking, including:
1) Generating all subsets and permutations of a set using backtracking.
2) The eight queens problem, which can be solved using a backtracking algorithm that places queens on a chessboard one by one while checking for threats.
3) Key components of backtracking algorithms including candidate construction, checking for solutions, and pruning search spaces for efficiency.
The document discusses algorithm analysis and design. It begins with an introduction to analyzing algorithms including average case analysis and solving recurrences. It then provides definitions of algorithms both informal and formal. Key aspects of algorithm study and specification methods like pseudocode are outlined. Selection sort and tower of Hanoi problems are presented as examples and analyzed for time and space complexity. Average case analysis is discussed assuming all inputs are equally likely.
The document discusses primitive recursive functions and predicates. It defines primitive recursive functions as those that can be constructed from initial functions using only composition and recursion. Some examples of primitive recursive functions given are addition, multiplication, factorial, power, predecessor, absolute value, and bounded quantification. Predicates like equality, less than, negation, conjunction, disjunction, division, and primality are also shown to be primitive recursive. The concept of bounded minimalization is introduced, where a function returns the least value t for which a primitive recursive predicate P(t,x1,...xn) is true.
The document discusses the RSA encryption algorithm and provides a mathematical background on topics related to RSA. It begins with an abstract and index, then covers notation, definitions, big-O notation, binary operations and their time complexities, linear congruences, relatively prime numbers, Euler's totient function, and the Miller-Rabin primality test. It analyzes the RSA algorithm, provides an example, and presents Python code to implement RSA encryption.
This document contains a 30 question mid-semester exam for a data structures and algorithms course. The exam covers topics like asymptotic analysis, sorting algorithms, hashing, binary search trees, and recursion. It provides multiple choice questions to test understanding of algorithm time complexities, worst-case inputs, and recursive functions. Students are instructed to attempt all questions in the 2 hour time limit and notify the proctor if any electronic devices other than calculators are used.
A Primality test is an algorithm for determining whether an input number is Prime. Among other fields of mathematics, it is used for Cryptography. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input).
This document discusses primitive recursive functions, which are a class of computable functions. It describes three initial functions - the zero function, successor function, and identity function. It then explains two building operations: composition and primitive recursion. Composition allows replacing arguments with other functions. Primitive recursion defines new functions from old ones. The document provides an example of defining the factorial function using primitive recursion. It also discusses minimization and defines partial recursive, general recursive, and primitive recursive functions. Finally, it presents Ackermann's function and calculates examples using it.
This document discusses the complexity of primality testing. It begins by explaining what prime and composite numbers are, and why primality testing is important for applications like public-key cryptography that rely on the assumption that factoring large composite numbers is computationally difficult. It then covers algorithms for primality testing like the Monte Carlo algorithm and discusses their runtime complexities. It shows that while testing if a number is composite can be done in polynomial time, general number factoring is believed to require exponential time, making primality testing an important problem.
Big O notation describes how efficiently an algorithm or function grows as the input size increases. It focuses on the worst-case scenario and ignores constant factors. Common time complexities include O(1) for constant time, O(n) for linear time, and O(n^2) for quadratic time. To determine an algorithm's complexity, its operations are analyzed, such as the number of statements, loops, and function calls.
Quicksort is a divide and conquer algorithm that works by partitioning an array around a pivot element and recursively sorting the subarrays. It has average case performance of O(n log n) but worst case of O(n^2). Randomized quicksort improves the algorithm by choosing the pivot randomly, ensuring the worst case is also O(n log n) on average.
The document discusses recursion, including:
1) Recursion is a programming technique where a method calls itself to solve a problem. It involves a base case and recursive calls.
2) Examples of recursive definitions and programs are given, such as computing factorials and sums recursively.
3) Recursion can be direct, where a method calls itself, or indirect through multiple method calls eventually leading back to the original method.
The document discusses analyzing the running time of algorithms using Big-O notation. It begins by introducing Big-O notation and how it is used to generalize the running time of algorithms as input size grows. It then provides examples of calculating the Big-O running time of simple programs and algorithms with loops but no subprogram calls or recursion. Key concepts covered include analyzing worst-case and average-case running times, and rules for analyzing the running time of programs with basic operations and loops.
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
Complexity analysis - The Big O NotationJawad Khan
Complexity analysis determines how resource requirements like time and memory scale with problem size. Computation time depends on hardware, while complexity analyzes algorithm scaling. Big O notation describes asymptotic function growth. Common complexities are O(1) constant, O(log n) logarithmic, O(n) linear, O(n^2) quadratic. Statements are O(1), if/else max branch, loops run n times, nested loops run n*m times, functions match calling structure, and when statements have undefined time.
The document discusses arrays and motivates their use. It explains that arrays allow storing a large number of values in a program and accessing them through indices. Arrays solve the problem of having to declare many individual variables to store multiple values. The document then introduces the concept of arrays, how to declare and initialize array variables, and how to access elements within an array using indices. It provides examples of declaring, initializing, and accessing one-dimensional and two-dimensional arrays.
The document discusses three cases for deleting a node from a binary search tree: 1) if the node has no children, simply remove it, 2) if the node has one child, make the parent point to the child, and 3) if the node has two children, find its successor, remove the successor, and replace the node with the successor. It then provides pseudocode for the delete operation and examples of building a BST and performing an in-order traversal.
The document discusses defining and using methods in Java. It defines what a method is and its key components like the method signature, return type, parameters, and body. It then demonstrates a sample max method to return the maximum of two numbers and traces the steps of invoking the method from the main method, including passing arguments, executing the method body, and returning the result. The document aims to explain the basics of methods in Java, including how to define reusable methods and invoke them to perform certain tasks.
1. The document discusses recursion and provides examples of recursively defined problems and their solutions, including factorials, powers, greatest common divisor, Fibonacci series, Towers of Hanoi, and counting cells in a blob.
2. Recursion involves breaking a problem into smaller subproblems of the same type until reaching a base case that can be solved directly. The solutions to subproblems are then combined to solve the original problem.
3. Examples of recursively defined problems include mathematical formulas, searching and sorting algorithms like binary search, and problems like Towers of Hanoi that are naturally broken down recursively.
This document discusses time and space complexity analysis of algorithms. It analyzes the time complexity of bubble sort, which is O(n^2) as each pass through the array requires n-1 comparisons and there are n passes needed. Space complexity is typically a secondary concern to time complexity. Time complexity analysis allows comparison of algorithms to determine efficiency and whether an algorithm will complete in a reasonable time for a given input size. NP-complete problems cannot be solved in polynomial time but can be verified in polynomial time.
Monadic Comprehensions and Functional Composition with Query ExpressionsChris Eargle
Build monads using the C# language with a C# style, then use the appropriate methods to ensure the LINQ query syntax works with this functional design pattern. After describing monads, we will cut the middleman and apply the same techniques directly to objects and functions to achieve better results with a declarative syntax.
An Introduction to ECDSA and it's use in Bitcoin (1)Hakeem Hunte
This document provides an introduction to ECDSA and its use in Bitcoin. It begins by explaining how Bitcoin uses a blockchain to record transactions and ensure their authenticity through digital signatures. ECDSA is the algorithm used to generate these signatures. The document then discusses public key cryptography and how ECDSA works. It introduces concepts like elliptic curves, finite fields, point addition/doubling, and scalar multiplication which are important to understanding how ECDSA generates public/private key pairs to digitally sign transactions on the Bitcoin blockchain.
The document describes experience with partial SIMDization in the Open64 compiler using dynamic programming. It discusses applying partial SIMDization to pack isomorphic instructions into SIMD instructions without fully vectorizing loops. It outlines applying a dynamic programming approach based on the Barik-Zhao-Sarkar algorithm to choose optimal SIMD tile combinations. Initial results show applying this to a hot loop in GROMACS was able to SIMDize over 88% of operations, demonstrating the potential of the technique.
This document discusses backtracking algorithms and provides examples for solving problems using backtracking, including:
1) Generating all subsets and permutations of a set using backtracking.
2) The eight queens problem, which can be solved using a backtracking algorithm that places queens on a chessboard one by one while checking for threats.
3) Key components of backtracking algorithms including candidate construction, checking for solutions, and pruning search spaces for efficiency.
The document discusses algorithm analysis and design. It begins with an introduction to analyzing algorithms including average case analysis and solving recurrences. It then provides definitions of algorithms both informal and formal. Key aspects of algorithm study and specification methods like pseudocode are outlined. Selection sort and tower of Hanoi problems are presented as examples and analyzed for time and space complexity. Average case analysis is discussed assuming all inputs are equally likely.
The document discusses primitive recursive functions and predicates. It defines primitive recursive functions as those that can be constructed from initial functions using only composition and recursion. Some examples of primitive recursive functions given are addition, multiplication, factorial, power, predecessor, absolute value, and bounded quantification. Predicates like equality, less than, negation, conjunction, disjunction, division, and primality are also shown to be primitive recursive. The concept of bounded minimalization is introduced, where a function returns the least value t for which a primitive recursive predicate P(t,x1,...xn) is true.
The document discusses the RSA encryption algorithm and provides a mathematical background on topics related to RSA. It begins with an abstract and index, then covers notation, definitions, big-O notation, binary operations and their time complexities, linear congruences, relatively prime numbers, Euler's totient function, and the Miller-Rabin primality test. It analyzes the RSA algorithm, provides an example, and presents Python code to implement RSA encryption.
This document contains a 30 question mid-semester exam for a data structures and algorithms course. The exam covers topics like asymptotic analysis, sorting algorithms, hashing, binary search trees, and recursion. It provides multiple choice questions to test understanding of algorithm time complexities, worst-case inputs, and recursive functions. Students are instructed to attempt all questions in the 2 hour time limit and notify the proctor if any electronic devices other than calculators are used.
A Primality test is an algorithm for determining whether an input number is Prime. Among other fields of mathematics, it is used for Cryptography. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input).
This document discusses primitive recursive functions, which are a class of computable functions. It describes three initial functions - the zero function, successor function, and identity function. It then explains two building operations: composition and primitive recursion. Composition allows replacing arguments with other functions. Primitive recursion defines new functions from old ones. The document provides an example of defining the factorial function using primitive recursion. It also discusses minimization and defines partial recursive, general recursive, and primitive recursive functions. Finally, it presents Ackermann's function and calculates examples using it.
This document discusses the complexity of primality testing. It begins by explaining what prime and composite numbers are, and why primality testing is important for applications like public-key cryptography that rely on the assumption that factoring large composite numbers is computationally difficult. It then covers algorithms for primality testing like the Monte Carlo algorithm and discusses their runtime complexities. It shows that while testing if a number is composite can be done in polynomial time, general number factoring is believed to require exponential time, making primality testing an important problem.
Big O notation describes how efficiently an algorithm or function grows as the input size increases. It focuses on the worst-case scenario and ignores constant factors. Common time complexities include O(1) for constant time, O(n) for linear time, and O(n^2) for quadratic time. To determine an algorithm's complexity, its operations are analyzed, such as the number of statements, loops, and function calls.
Quicksort is a divide and conquer algorithm that works by partitioning an array around a pivot element and recursively sorting the subarrays. It has average case performance of O(n log n) but worst case of O(n^2). Randomized quicksort improves the algorithm by choosing the pivot randomly, ensuring the worst case is also O(n log n) on average.
The document discusses recursion, including:
1) Recursion is a programming technique where a method calls itself to solve a problem. It involves a base case and recursive calls.
2) Examples of recursive definitions and programs are given, such as computing factorials and sums recursively.
3) Recursion can be direct, where a method calls itself, or indirect through multiple method calls eventually leading back to the original method.
The document discusses analyzing the running time of algorithms using Big-O notation. It begins by introducing Big-O notation and how it is used to generalize the running time of algorithms as input size grows. It then provides examples of calculating the Big-O running time of simple programs and algorithms with loops but no subprogram calls or recursion. Key concepts covered include analyzing worst-case and average-case running times, and rules for analyzing the running time of programs with basic operations and loops.
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
Algorithms required for data structures(basics like Arrays, Stacks ,Linked Li...DebiPrasadSen
An algorithm is a well-defined computational procedure that takes input values and produces output values. It has several key properties including being well-defined, producing the correct output for any possible input, and terminating after a finite number of steps. When analyzing algorithms, asymptotic complexity is important as it measures how processing requirements grow with increasing input size. Common complexity classes include constant O(1), logarithmic O(log n), linear O(n), quadratic O(n^2), and exponential O(2^n) time. For large inputs, slower asymptotic growth indicates better performance.
This document discusses time complexity and big O notation for analyzing the runtime of algorithms. It provides examples of common algorithms like sorting, searching, and matrix multiplication and their time complexities. For example, matrix-vector multiplication runs in O(N2) time, where N is the size of the matrix. The document also explains that big O notation describes the asymptotic worst-case growth rate of an algorithm's runtime as the problem size increases.
This document discusses algorithms and their analysis. It begins by defining an algorithm and analyzing its time and space complexity. It then discusses different asymptotic notations used to describe an algorithm's runtime such as Big-O, Omega, and Theta notations. Examples are provided to illustrate how to determine the tight asymptotic bound of functions. The document also covers algorithm design techniques like divide-and-conquer and analyzes merge sort as an example. It concludes by defining recurrences used to describe algorithms and provides an example recurrence for merge sort.
The document discusses orders of growth and how they are used to analyze how the resources required to evaluate procedures scale with input size. It introduces the big-O notation O(f) which represents the set of all functions that grow no faster than the input function f. Some examples are provided to illustrate how to determine if one function is in the set O(f) of another. The key is that there must exist positive constants c and n0 such that for all n ≥ n0, g(n) ≤ c*f(n).
This document discusses asymptotic analysis and big-O notation for analyzing the time complexity of algorithms. It begins by defining key concepts like growth rate, asymptotic notations such as O(n), Ω(n) and Θ(n). It then provides examples of analyzing the time efficiency of different algorithms like finding the maximum element in an array and computing prefix averages. The document explains how to determine the asymptotic complexity by counting the total number of operations and expressing it using big-O notation. It also discusses properties of big-O notation like rules for dropping constant factors and lower order terms.
how to calclute time complexity of algortihmSajid Marwat
This document discusses algorithm analysis and complexity. It defines key terms like asymptotic complexity, Big-O notation, and time complexity. It provides examples of analyzing simple algorithms like a sum function to determine their time complexity. Common analyses include looking at loops, nested loops, and sequences of statements. The goal is to classify algorithms according to their complexity, which is important for large inputs and machine-independent. Algorithms are classified based on worst, average, and best case analyses.
This document discusses algorithm analysis and complexity. It defines key terms like algorithm, asymptotic complexity, Big-O notation, and time complexity. It provides examples of analyzing simple algorithms like summing array elements. The running time is expressed as a function of input size n. Common complexities like constant, linear, quadratic, and exponential time are introduced. Nested loops and sequences of statements are analyzed. The goal of analysis is to classify algorithms into complexity classes to understand how input size affects runtime.
- The document discusses asymptotic analysis and Big-O, Big-Omega, and Big-Theta notation for analyzing the runtime complexity of algorithms.
- It provides examples of using these notations to classify functions as upper or lower bounds of other functions, and explains how to determine if a function is O(g(n)), Ω(g(n)), or Θ(g(n)).
- It also introduces little-o and little-omega notations for strict asymptotic bounds, and discusses properties and caveats of asymptotic analysis.
The document discusses Big O notation, which is used to describe the asymptotic upper bound of an algorithm's running time. It defines Big O notation formally as f(n) being O(g(n)) if there exist positive constants c and n0 such that f(n) is less than or equal to c * g(n) for all n greater than or equal to n0. The document provides examples of functions being Big O of other functions, such as 2n + 7 being O(n) and 2(n + 1) being O(2n). It explains that Big O notation characterizes the worst-case growth rate of an algorithm.
1. Algorithm analysis helps determine which algorithm is most efficient in terms of time and space consumed by analyzing the rate of growth of the time and space complexity functions as the input size increases.
2. Big-O notation provides an asymptotic upper bound on the growth rate of an algorithm, while Omega and Theta notations provide asymptotic lower and tight bounds respectively.
3. Recurrence relations can be used to analyze the time complexity of recursive algorithms, where the running time T(n) is expressed as a function of smaller inputs.
The document discusses how computer scientists measure the cost of algorithms using asymptotic analysis. It introduces the big-O, Omega, and Theta notations to classify algorithms based on how their running time grows relative to the size of the input. Big-O represents an upper bound, Omega a lower bound, and Theta a tight bound of an algorithm's growth rate. The analysis allows abstracting away machine-specific details to understand an algorithm's fundamental performance properties.
This document discusses big-O notation and asymptotic analysis of algorithms. It defines big-O notation as describing an upper bound on the running time of an algorithm. The key properties of big-O notation are explained, including that the fastest growing term dominates and that hierarchies of functions exist based on their growth rates. Examples are provided to demonstrate calculating the big-O of expressions and classifying algorithms based on whether their growth is constant, logarithmic, polynomial, exponential, or factorial.
This document discusses analyzing the efficiency and complexity of algorithms. It begins by explaining that running time depends on input size and nature, and is generally measured by the number of steps or operations. Different examples are provided to demonstrate analyzing loops and recursive functions to derive asymptotic complexity bounds. Key points covered include using Big-O notation to classify algorithms according to worst-case running time, analyzing nested loops, sequences of statements, and conditional statements. The document emphasizes that asymptotic complexity focuses on higher-order terms as input size increases.
This document discusses asymptotic notations that are used to characterize an algorithm's efficiency. It introduces Big-Oh, Big-Omega, and Theta notations. Big-Oh gives an upper bound on running time. Big-Omega gives a lower bound. Theta gives both upper and lower bounds, representing an algorithm's exact running time. Examples are provided for each notation. Time complexity is also introduced, which describes how the time to solve a problem changes with problem size. Worst-case time analysis provides an upper bound on runtime.
This document provides an overview of algorithms and asymptotic notation. It discusses that asymptotic notation allows algorithms to be compared based on how their running time grows relative to the input size. The key points covered include:
- Asymptotic notation describes the asymptotic behavior of a function, such as how fast algorithm running time grows relative to the input.
- Big O notation describes the worst case upper bound. If f(n) is O(g(n)), f(n) grows no faster than g(n).
- Common time complexities include O(1), O(log n), O(n), O(n log n), O(n^2).
- The dominating factor determines
This document discusses mathematical notations and asymptotic analysis used to analyze algorithms, including big O, Omega, and Theta notation. It defines common mathematical functions like floor, ceiling, modulo, and factorial. It also covers permutations, exponents, and logarithms. The document explains that big O notation provides an upper bound on running time, Omega provides a lower bound, and Theta provides a tight bound. Finally, it categorizes common algorithm time complexities as constant, linear, logarithmic, polynomial, and exponential time.
The document discusses algorithms, including their definition, properties, analysis of time and space complexity, and examples of recursion and iteration. It defines an algorithm as a finite set of instructions to accomplish a task. Properties include inputs, outputs, finiteness, definiteness, and effectiveness. Time complexity is analyzed using big-O notation, while space complexity considers static and variable parts. Recursion uses function calls to solve sub-problems, while iteration uses loops. Examples include factorial calculation, GCD, and Towers of Hanoi solved recursively.
The document discusses algorithms and algorithm analysis. It provides examples to illustrate key concepts in algorithm analysis including worst-case, average-case, and best-case running times. The document also introduces asymptotic notation such as Big-O, Big-Omega, and Big-Theta to analyze the growth rates of algorithms. Common growth rates like constant, logarithmic, linear, quadratic, and exponential functions are discussed. Rules for analyzing loops and consecutive statements are provided. Finally, algorithms for two problems - selection and maximum subsequence sum - are analyzed to demonstrate algorithm analysis techniques.
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
Linked lists are a dynamic data structure that allows elements to be added or removed without reshifting the other elements. Each element, called a node, contains data and a reference to the next node. The nodes are not stored contiguously in memory. A linked list is accessed through a head pointer that points to the first node. Additional nodes can be traversed using each node's next pointer. This allows efficient insertion and deletion compared to arrays, though direct access to a particular element requires traversing the list sequentially from the head.
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
In this playlist
https://youtube.com/playlist?list=PLT...
I'll illustrate algorithms and data structures course, and implement the data structures using java programming language.
the playlist language is arabic.
The Topics:
--------------------
1- Arrays
2- Linear and Binary search
3- Linked List
4- Recursion
5- Algorithm analysis
6- Stack
7- Queue
8- Binary search tree
9- Selection sort
10- Insertion sort
11- Bubble sort
12- merge sort
13- Quick sort
14- Graphs
15- Hash table
16- Binary Heaps
Reference : Object-Oriented Data Structures Using Java - Third Edition by NELL DALE, DANEIEL T.JOYCE and CHIP WEIMS
Slides is owned by College of Computing & Information Technology
King Abdulaziz University, So thanks alot for these great materials
This document discusses quick sort, one of the most common sorting algorithms. Quick sort uses two main ideas - partitioning and recursion. It works by partitioning an array around a pivot element, and then recursively sorting the subarrays on each side of the pivot. In the best case, where the pivot always partitions the array in half, quick sort runs in O(n log n) time. However, its performance depends on how well it can partition the array on each iteration. The document provides pseudocode for quick sort and discusses strategies for choosing a good pivot element to improve its average runtime.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
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For more information about PECB:
Website: https://pecb.com/
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Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.