Day 1 Chapter 1 Unit 1
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This document introduces algorithms and their design. It defines an algorithm as a sequence of unambiguous instructions to solve a problem within a finite time. It discusses algorithm notation, features, and examples for finding the greatest common divisor and prime numbers. The document outlines the algorithm design process of understanding the problem, deciding on a representation, designing a model, proving correctness, analyzing efficiency, coding it, and classifying algorithms. It also covers important problem types like sorting, searching, and graphs, and fundamental data structures like arrays, linked lists, stacks, queues, trees, and graphs.
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1) Initialize the largest variable to the first element of the array
2) Iterate through the rest of the array using a while loop
3) Compare each element to the largest and update largest if a larger number is found
4) After iterating through the entire array, largest will hold the largest element
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1. An algorithm is a sequence of unambiguous instructions to solve a problem within a finite amount of time. It takes an input, processes it, and produces an output.
2. Designing an algorithm involves understanding the problem, choosing a computational model and problem-solving approach, designing and proving the algorithm's correctness, analyzing its efficiency, coding it, and testing it.
3. Important algorithm design techniques include brute force, divide and conquer, decrease and conquer, transform and conquer, dynamic programming, and greedy algorithms.
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Design & Analysis of Algorithms Lecture Notes
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Unit 1 chapter 1 Design and Analysis of Algorithms
Unit 1 chapter 1 Design and Analysis of AlgorithmsP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
Anna University Regulation 2017
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Text : Introduction to Design and Analysis of Algorithms by Anany Levitinl01-intro (3).ppt
This document discusses algorithms and their design. It defines an algorithm as a sequence of unambiguous instructions to solve a problem within a finite time. The key steps in designing algorithms are: understanding the problem, choosing appropriate data structures and computational means, designing and proving the algorithm, analyzing its efficiency, and coding it. Important problem types include sorting, searching, graphs, and numerical problems. Fundamental data structures include arrays, linked lists, stacks, queues, trees, graphs, sets, bags and dictionaries.
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1) The definition of an algorithm and its key characteristics like being unambiguous, finite, and efficient.
2) The fundamental steps of algorithmic problem solving like understanding the problem, designing a solution, and analyzing efficiency.
3) Methods for specifying algorithms using pseudocode, flowcharts, or natural language.
4) Analyzing an algorithm's time and space efficiency using asymptotic analysis and orders of growth like best-case, worst-case, and average-case scenarios.
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This document provides an overview of algorithms and algorithm analysis. It discusses key concepts like what an algorithm is, different types of algorithms, and the algorithm design and analysis process. Some important problem types covered include sorting, searching, string processing, graph problems, combinatorial problems, geometric problems, and numerical problems. Examples of specific algorithms are given for some of these problem types, like various sorting algorithms, search algorithms, graph traversal algorithms, and algorithms for solving the closest pair and convex hull problems.
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The document provides an introduction to algorithms presented by Sachin Sharma Bhandari. It defines algorithms, discusses analyzing time and space efficiency, and provides examples of sorting and other problems solved by algorithms. It also reviews data structures like stacks, queues, linked lists, and binary trees that are important for algorithm design.
Model and Design
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This slides contains assymptotic notations, recurrence relation like subtitution method, iteration method, master method and recursion tree method and sorting algorithms like merge sort, quick sort, heap sort, counting sort, radix sort and bucket sort.
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This document discusses deep learning and inductive programming. It begins by defining deep learning as a stateless function that can take in high-dimensional or categorical variables as input and provide low-dimensional outputs for classification or high-dimensional outputs for generation. The document then provides an example of converting Celsius to Fahrenheit using a simple formula. It contrasts this with an inductive, data-driven approach requiring no prior knowledge of the model or algorithm. The document suggests neural networks can approximate any high-dimensional function, acting as a universal computing mechanism. It speculates that by 2020, over half of newly developed software will have inductively trained components, representing a large paradigm shift. Finally, it discusses how new engineering disciplines are needed as new
ADA complete notes
1. An algorithm is a sequence of unambiguous instructions to solve a problem within a finite amount of time. It takes an input, processes it, and produces an output.
2. Designing an algorithm involves understanding the problem, choosing a computational model and problem-solving approach, designing and proving the algorithm's correctness, analyzing its efficiency, coding it, and testing it.
3. Important algorithm design techniques include brute force, divide and conquer, decrease and conquer, transform and conquer, dynamic programming, and greedy algorithms.
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This document summarizes a presentation on introducing algorithms and analyzing their performance. It defines an algorithm as a step-by-step procedure to solve a problem and transform inputs to outputs. There are two ways to analyze performance: space complexity and time complexity. Time complexity depends on the input size and running time of the algorithm. An example compares two algorithms for finding the maximum number in an array: one sorts the array in O(n^2) time while the other compares each element to the first in O(n) time. The conclusion states that analyzing an algorithm's resource usage is more important than just designing it.
Design & Analysis of Algorithms Lecture Notes
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
Amortized analysis
Amortized analysis gives the average performance of algorithms over many operations, rather than analyzing each operation individually. There are three main methods: aggregate analysis assigns costs to operations to find an upper bound cost; accounting assigns costs but allows "credits" from low-cost operations to pay for high-cost ones; potential assigns costs and uses potential energy differences rather than credits. Examples discussed include binary and binomial heaps, randomized quicksort, and approximation algorithms for NP-complete problems that provide fast, near-optimal solutions.
Notion of an algorithm
The document discusses the importance of algorithms and their role in problem solving. It defines what an algorithm is and explains that they are sets of instructions to solve problems efficiently. The document outlines different algorithm design techniques and how algorithms shape applications like search engines, recommendations, and maps. It also discusses qualities of good algorithms like correctness, termination, and performance and analyzing algorithms through pseudocode and empirical testing.
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Euclid's algorithm is an efficient method for computing the greatest common divisor (GCD) of two numbers. It works by repeatedly finding the remainder of dividing the larger number by the smaller number, and then setting the larger number equal to the smaller number and the smaller number equal to the remainder, until the smaller number is zero. The last non-zero remainder is the GCD. The time complexity of Euclid's algorithm is O(log n) where n is the smaller of the two input numbers. Algorithm analysis techniques such as worst-case, best-case, average-case analysis and asymptotic notations can be used to formally analyze the efficiency of algorithms.
CP4151 Advanced data structures and algorithms
The document introduces algorithms and their role in computing. It defines algorithms as tools for solving well-specified computational problems. Algorithms must be correct, producing the appropriate output for each input, and efficient, using as little resources as possible. Examples of algorithms provided include sorting a list alphabetically and determining if a number is prime. Pseudo-code is used to describe algorithms in a language-independent way.
Data Structures and Algorithm Analysis
Definition of Data Structure,
What is Data Structure?
Types of data structure
Algorithm Analysis
Asymptotic Notation
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TestFile
Tissues are groups of cells that work together to perform specific functions. They are made up of clusters of cells known as tissues. There are different types of tissues in plants and animals since they have different structures and functions. Plants contain three main tissue types - dermal, permanent and meristematic tissues. The four primary animal tissue types are epithelial, connective, muscle and nervous tissues which carry out specialized roles.
3.1 Trees ( Introduction, Binary Trees & Binary Search Trees)
3.1 Trees ( Introduction, Binary Trees & Binary Search Trees)P. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
This document provides information and resources about trees as a data structure for an online class on data structures. It includes links to YouTube videos that explain trees in an animated way and binary trees. It also includes a link to a quiz on Nearpod and discusses binary search trees. The document is from Dr. P. Subathra, a professor in the Department of Information Technology at KAMARAJ College of Engineering & Technology in Madurai, Tamil Nadu, India.2.1 STACK & QUEUE ADTS
This document discusses data structures stacks and queues. It provides definitions and examples of stacks and queues. Stacks follow LIFO (last in first out) and are useful for undo sequences and function calls. Queues follow FIFO (first in first out) and are useful for things like printer queues. The document discusses implementations of stacks and queues using arrays and linked lists. It provides pseudocode for common stack and queue operations like push, pop, enqueue, dequeue.
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2.2 stack applications Infix to Postfix & Evaluation of Post FixP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
This document discusses applications of stacks, including converting between infix, prefix, and postfix notation. It provides examples of evaluating arithmetic expressions in postfix notation. Key points include:
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This document discusses doubly linked lists. It begins by explaining some of the limitations of circular singly linked lists, such as the inability to easily traverse backwards. Doubly linked lists are then introduced as a solution, with each node containing pointers to both the next and previous nodes. The key operations on doubly linked lists like insertion at the beginning, end, and middle as well as deletion at the beginning, end, and middle are described algorithmically. Traversal in both the forward and backward directions is also covered. Code examples are provided to demonstrate creating and manipulating doubly linked lists.
1. 5 Circular singly linked list
1. 5 Circular singly linked listP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document discusses circular singly linked lists. It begins by explaining the issue with singly linked lists, which is that nodes cannot be revisited. It then introduces circular singly linked lists as a solution. It describes the memory representation of a circular linked list using node pointers. It lists common operations on circular linked lists like insertion, deletion, searching and display. It provides examples of creating a new list, inserting nodes at the beginning and end, and deleting nodes from the beginning and end. It notes that a tail pointer should be used instead of the head pointer for certain operations.1. 4 Singly linked list deletion
1. 4 Singly linked list deletionP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document discusses various deletion operations on singly linked lists. It provides algorithms and code snippets for deleting the first element, last element, a given element, and an element at a given position in a singly linked list. The algorithms handle both empty lists and non-empty lists with single and multiple nodes. Key steps include checking for empty lists, traversing the list to find the required element or position while tracking the previous node, and updating pointers after deleting the node.1. 3 singly linked list insertion 2
1. 3 singly linked list insertion 2P. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
This document discusses algorithms for inserting nodes into singly linked lists at different positions. It provides pseudocode and illustrations for inserting a node after a given element, before a given element, and at a specified position.
For each insertion operation, it outlines the steps: 1) create a new node, 2) get the data, 3) check for empty list or specified position and traverse the list to find the insertion point. It then shows how to insert the new node by adjusting the next pointers of the preceding and current nodes. Examples are given with initial and final list illustrations for each insertion type.1. 2 Singly Linked List
The document discusses singly linked lists and their advantages over arrays. It describes a lecture on data structures covering singly linked lists. The lecture explains what is wrong with static memory allocation in arrays and how linked lists provide a dynamic structure using nodes and pointers. It shows examples of creating linked list nodes, inserting nodes at the beginning and end of a list, and traversals through a non-empty list. The key operations on singly linked lists like creation, insertion, deletion and traversal are also summarized.
1. C Basics for Data Structures Bridge Course
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Approximation Algorithms TSPP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
This document discusses approximation algorithms for solving NP-hard problems like the traveling salesman problem (TSP) and knapsack problem. It provides an overview of approximation algorithms, defining them as polynomial-time algorithms that provide good but not necessarily optimal solutions. The document then focuses on approximation algorithms for the TSP, describing greedy algorithms like nearest neighbor, minimum spanning tree based algorithms like Christofides, and local search heuristics like 2-opt and Lin-Kernighan. It concludes by noting some applications of approximating the TSP.Optimal binary search tree dynamic programming
Optimal binary search tree dynamic programmingP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document discusses optimal binary search trees (OBST) and describes the process of creating one. It begins by introducing OBST and noting that the method can minimize average number of comparisons in a successful search. It then shows the step-by-step process of calculating the costs for different partitions to arrive at the optimal binary search tree for a given sample dataset with keys and frequencies. The process involves calculating Catalan numbers for each partition and choosing the minimum cost at each step as the optimal is determined.The stable marriage problem iterative improvement method
The stable marriage problem iterative improvement methodP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document discusses the stable marriage problem and its iterative improvement method. It describes a stable marriage as a pairing between two disjoint sets where each member of one set is paired with exactly one member of the other set. It states that the stable marriage algorithm terminates with a stable marriage output after no more than n^2 iterations. Some applications of stable marriage problems mentioned include assigning students to universities and doctors to hospitals.Maximum matching in bipartite graphs iterative improvement method
Maximum matching in bipartite graphs iterative improvement methodP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document discusses two approaches for finding the maximum matching in bipartite graphs - Ford Fulkerson's augmenting path method and the shortest augmenting path method using breadth-first search (BFS). It provides examples of applying both methods to a sample graph, finding augmenting paths and increasing the number of matching pairs at each step until reaching the maximum matching.Knapsack dynamic programming formula top down (1)
Knapsack dynamic programming formula top down (1)P. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document describes the dynamic programming approach to solving the 0/1 knapsack problem. It provides the recursive formula for calculating F(i,Cj), which represents the maximum profit for a knapsack of capacity Cj using items 1 to i. It works through an example calculation of F(i,Cj) by recursively applying the formula and breaking it down into sub-problems.Knapsack dynamic programming formula bottom up
Knapsack dynamic programming formula bottom upP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document describes the 0/1 knapsack problem and its dynamic programming solution. It presents the bottom-up dynamic programming approach, showing a table that is populated with the maximum profits possible given item weights and the knapsack capacity. The table is populated row-by-row, considering all possible item combinations. Finally, it traces back through the table to find the optimal set of items to include in the knapsack.Huffman tree coding greedy approach
Huffman tree coding greedy approachP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
The document discusses Huffman tree coding, which is a variable-length encoding technique used for lossless data compression. It assigns variable-length codewords to input characters based on their frequency of occurrence, with more common characters represented by shorter codewords. The document provides an example of constructing a Huffman tree for an alphabet and encoding and decoding sample text strings using the generated Huffman codes.Simplex method
The document describes the simplex method for solving linear programming problems. It provides an example problem in standard form and walks through two iterations of the simplex method to find the optimal solution. The key steps of the simplex method include identifying the entering and departing variables, calculating the pivot element, pivoting the rows, and checking for convergence. After two iterations, the example problem converges to an optimal objective value of 14 when x=3 and y=1.
Simplex method
The document describes the simplex method for solving linear programming problems. It involves iteratively improving the solution by moving from one vertex of the feasible region to an adjacent vertex with a better objective value. The method works by representing the problem in standard form and then performing pivoting steps. It begins with an initial basic feasible solution and moves to adjacent basic feasible solutions until reaching the optimal solution.
Multiplication of integers & strassens matrix multiplication subi notes
Multiplication of integers & strassens matrix multiplication subi notesP. Subathra Kishore, KAMARAJ College of Engineering and Technology, Madurai
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Day 1 Chapter 1 Unit 1
- 1. The Design and Analysis of Algorithms by Anany Levitin
- 2. 2 CHAPTER 1: INTRODUCTIONCHAPTER 1: INTRODUCTION What is an Algorithm ? Steps in Designing and Implementing an Algorithm Important Problem Types Fundamental Data Structures
- 3. 3 ALGORITHM A sequence of unambiguous instructions for solving a problem, i.e. for obtaining the required output for any legitimate input in a finite amount of time
- 4. Notation of the Algorithm 4
- 5. 5 Special Features of Algorithms Non-ambiguity Range of inputs The same algorithm can be represented in different ways Several algorithms for solving the same problem Different algorithms with different speeds
- 6. Find the GCD(m,n) Method 1: Descriptive Algorithm 6
- 7. GCD using Euclid’s Method gcd(m,n)=gcd(n,m nod n) Find: 1. GCD(124,12) 2. GCD(160,15) 3. GCD(338,22) 4. GCD(150,8) 7
- 8. Find the GCD(m,n) Method 2: Descriptive Algorithm 8
- 9. Find the GCD(m,n) Method 2: Pseudocode Representation 9
- 10. Find the set of all Prime numbers Method 1: Middle School Level Find Set of ALL Prime Numbers within 25 10
- 11. Find the set of all Prime numbers Method 2: Sieve of Erathosthenes Find Set of ALL Prime Numbers within 25 11
- 12. 12 CHAPTER 1: INTRODUCTIONCHAPTER 1: INTRODUCTION What is an Algorithm? Steps in Designing and Implementing an Algorithm Important Problem Types Fundamental Data Structures
- 13. Fundamentals of Algorithmic Problem Solving / Algorithm Design & Analysis Process 13
- 14. 14 What does it mean to understand the problem? What are the problem objects? What are the operations applied to the objects? Deciding on computational means How the objects would be represented? How the operations would be implemented?
- 15. 15 Design an algorithm • Build a computational model of the solving process Prove correctness • Correct output for every legitimate input in finite time • Based on correct math formula • By induction
- 16. 16 Analyze the algorithm Efficiency: time and space Simplicity: Generality: range of inputs, special cases Optimality: no other algorithm can do better Coding How the objects and operations in the algorithm are represented in the chosen programming language?
- 17. 17 Important problem types Sorting Searching String processing Graph problems Combinatorial problems Geometric problems Numerical problems
- 18. 18 Fundamental data structures Linear data structures Array Linked list Stack Queue Operations: search, delete, insert Implementation: static, dynamic
- 19. 19 Non-linear data structures Graphs Trees : connected graph without cycles Rooted trees Ordered trees Binary trees Graph representation: adjacency lists, adjacency matrix Tree representation: as graphs; binary nodes Fundamental data structures
- 20. 20 Fundamental data structures Sets, Bags, Dictionaries Set: unordered collection of distinct elements Operations: membership, union, intersection Representation: bit string; linear structure Bag: unordered collection, elements may be repeated Dictionary: a bag with operations search, add, delete
- 21. 21 Conclusion Algorithm classification By types of problems By design technique Design techniques a general approach to solving problems
- 22. Check if you are Clear with: Definition of Algorithm Notation of Algorithm Examples: GCD and Prime Fundamentals of Algorithms / Process of Design & Analysis of Algorithms Types of Problems Fundamental Data Structures 22
- 23. Have a GREAT Day..!!! 23