Design and Analysis of Algorithms PDF by Udit Agarwal Study Material and Notes

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Introduction to Design and Analysis of Algorithms

An Algorithm is defined as a set of operation or computational steps or instruction designed to solve problems performing data processing, organise structures, calculation, and automated reasoning tasks. It is an efficient method that expresses a finite amount of space and time and represents a solution in a particular manner. An algorithm is independent of any programming language through the remembrance of the past results to obtain new results.

The important aspect of an algorithm design is the creation of an efficient algorithm to resolve specific or general problems through the use of minimum space and time in an efficient manner.

The primary characteristics of an algorithm are- Finiteness, Input, Output, Definiteness, and Effectiveness.

However, an algorithm is different from a Pseudocode as it defines a well-defined series of steps and resolves a specific problem. Algorithms are generally written in Plain English or simple languages.

CS-Design and Analysis of Algorithms PDF by Udit Agarwal Free Download

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  • Design And Analysis Of Algorithms Pdf By Udit Agarwal
  • Design And Analysis Of Algorithms Pdf By Udit Agarwal Chapter-Wise Division

Design and Analysis of Algorithms Content

The Design And Analysis Of Algorithms Pdf By Udit Agarwal Content gives an initial idea and a basic outline of the important topics or concepts in the book to enhance and effectual is student’s preparation or revision process.

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The updated chapter-wise breakup of the Design And Analysis Of Algorithms Pdf By Udit Agarwal Content is as follows-

Chapter I- Introduction to Algorithm Chapter II- Growth of Functions
  • Introduction
  • Why Study Algorithms
  • Definitions
  • Algorithms Versus Programmes
  • Algorithms Design Techniques
  • Algorithms Classification
  • Algorithms Analysis
  • Formal and Informal Algorithms Analysis
  • How to Calculate the Running Time of an Algorithm
  • Loop Invariants
  • Complexity of Algorithms
  • RAM Machine
  • Best, Worst, and Average- Case Complexity
  • Growth Rate of Functions
  • Asymptotic Analysis
  • Analysing Algorithm Control Structure
  • Logarithms and Exponents 
Chapter III- Recorrances Chapter IV- Analysis of Simple Sorting Algorithms
  • Introduction
  • The Substitution Method
  • The Iteration method
  • Master Method
  • Bubble Sort
  • Selection Sort
  • Insertion Sort
Chapter V- Merge Sort Chapter VI- Heap Sort
  • Introduction
  • Analysis of Merge Sort
  • Insertion Sort and Merge Sort
  • Binary Heap
  • Heap Property
  • Height of a Heap
  • Heapify
  • Building a Heap
  • Heap Sort Algorithm
  • Heap-Insert
  • Heap-Delete
  • Heap-Extract-Max
Chapter VII- Quick Sort Chapter VIII- Sorting in 

Linear Time

  • Introduction
  • Partitioning in Array
  • Performance of Quick Sort
  • Versions of Quick Sort
  • Stability
  • Counting Sort
  • Radix Sort
  • Bucket Sort
Chapter IX- Medians and Order Statistics Chapter X-Dictionaries and Hash Tables
  • Selection problem
  • Finding Minimum (or Maximum)
  • Finding Minimum and Maximum Simultaneously
  • Selection of ith Order- Statistic in Linear Time
  • Worst-Case Linear-Time Statistics
  • Choosing The Pivot
  • Dictionaries
  • Log Files
  • Hash Tables
  • Hashing
  • Hash Functions
  • Universal Hashing
  • Hashing With Open Addressing
  • Rehashing
Chapter XI-Elementary Data Structures Chapter XII- Binary Search Tree
  • Introduction
  • Abstract Data Type
  • Stack Queue
  • Linked List
  • Binary-Trees
  • Binary-Search-Tree-Property
  • Binary-Search-Tree-Property Versus Heap Property
  • Querying a Binary Search Tree
Chapter XIII- AVL Tree Chapter XIV- Spray Trees
  • Introduction
  • Balance Factor
  • Insertion in an AVL Search Tree
  • The efficiency of AVL Trees
  • Introduction
  • Splaying
  • Splay versus Move-to-Root
Chapter XV- Red-Black Trees Chapter XVI- Augmenting Data Structures
  • Introduction
  • Operations on RB Trees
  • Elementary Properties of Red-Black Trees
  • Augmenting a Red-Black Tree
  • Retrieving an element with a given rank
  • Determining the rank of an element
  • Data Structure Maintenance
  • An Augmentation Strategy
  • Interval Trees
Chapter XVII- B-Trees Chapter XVIII- Binomial Heaps
  • Introduction
  • Definition of B-Tree
  • Searching for a Key k in B-Tree
  • Creating an Empty B-Tree
  • How do we Search for a Predecessor?
  • Inserting a Key into a B-Tree
  • Mergeable heaps
  • Binomial Trees and Binomial Heaps
  • Binomial Heaps
Chapter XIX- Fibonacci Heaps Chapter XX- Data Structures for Disjoint Sets
  • Introduction
  • Structure of Fibonacci Heaps
  • Potential Functions
  • Operations
  • Bounding the Maximum Degree
  • Introduction
  • Disjoint-Set Operations
  • UNION-FIND Algorithm
  • Applications of Disjoint-Set Data Structures
  • Linked-List Representation of Disjoint-Set 
  • Disjoint-Set Forests
  • Properties of Ranks
Chapter XXI- Dynamic Programming Chapter XXII- Greedy Algorithms
  • Introduction
  • Common Characteristics 
  • Matrix Multiplication
  • Memoization
  • Longest Common Subsequence (LCS)
  • Introduction
  • An Activity-Selection Problem
  • Knapsack Problems
  • Huffman Codes
  • Prefix Codes
  • Greedy Algorithms for constructing a Huffman Code
  • Activity or Task-Scheduling problem
  • Travelling Salesperson Problem
  • Matroids
  • Minimum Spanning Tree
Chapter XXIII- Backtracking Chapter XXIV- Branch and Bound
  • Introduction
  • Recursive Maze Algorithm
  • Hamiltonian Circuit problem
  • Subset- Sum Problem
  • N-Queens Problem
  • Introduction
  • Live Node, Dead Node, and Bounding Functions
  • FIFO Branch-and-Bound Algorithm
  • Least Cost (LC) Search
  • The 15 Puzzle: An Example
  • Branch-and-Bound Algorithm for TSI
  • Knapsack Problem
  • Assignment Problem
Chapter XXV-Amortized Analysis Chapter XXVI- Elementary Graphs Algorithms
  • Introduction
  • Aggregate analysis
  • Accounting method or Taxation Method
  • Potential Method
  • Introduction
  • How is the Graph Represented?
  • Breadth-First Search
  • Depth First Search
  • Topological Sorts
  • Strongly connected components
Chapter XXVII- Minimum Spanning Tree Chapter XXVIII- Single Source Shortest Paths
  • Spanning Tree
  • Kruskal’s Algorithm
  • Prim’s Algorithm
  • Introduction
  • Shortest Path: Existence
  • Representing Shortest Paths
  • Shortest Path: Properties
  • Dijkstra’s Algorithm
  • The Bellman-Ford’s Algorithm
  • Single Source shortest Paths in directed acyclic graphs
Chapter XXIX- All-Pairs Shortest Paths Chapter XXX- Maximum Flow
  • Introduction
  • Matrix Multiplication
  • The Floyd-Warshall Algorithm
  • Transitive Closure
  • Johnson’s Algorithm
  • Flow Networks and Flows
  • Network Flow Problem
  • Residual Networks, Augmenting Paths, and Cuts
  • Max-Flow, Min-Cut Theorem
  • Ford-Fulkerson Algorithm
Chapter XXXI- Sorting Networks Chapter XXXII- Algorithms for Parallel Computers 
  • Comparison Networks
  • Bitonic Sorting Networks
  • Merging Networks
  • Parallel Computing
  • Why use Parallel Computing?
  • von Neumann Algorithm
  • Flynn’s Classical taxonomy
  • Parallel Algorithms
  • Concurrent Versus Exclusive Memory Access
  • List Ranking by Pointer Jumping
  • The Euler-Tour Technique
  • CRCW Algorithms Versus EREW Algorithms
  • Brent’s Theorem
Chapter XXXIII-Matrix Operations Chapter XXXIV- Number-Theorthic Algorithms 
  • Introduction
  • Operations on Matrices
  • Strassen’s Algorithm for Matrix Multiplication
  • Solving Systems for Linear Equations
  • Computing an LU Decomposition 
  • Computing an LUP Decomposition 
  • Some Facts from Elementary Number Theory
  • Euclid’s GCD Algorithms
  • The Chinese Remainder Theorem
  • The RSA Public-key Cryptosystem
Chapter XXXV- Polynomials and the FFT  Chapter XXXVI- String Matching
  • Polynomials
  • Representation of Polynomials
  • Evaluating Polynomial Functions
  • Complex Roots of Unity
  • Discrete Fourier Transform
  • Fast Fourier Transform (FFT)
  • Introduction
  • The Naive String-matching Algorithm
  • The Rabin-Karp Algorithm
  • String Matching with Finite Automata
  • The Knutt-Morris-Pratt (KMP) Algorithm
  • The Boyer-Moore Algorithm
Chapter XXXVII- Computational Geometry Chapter XXXVIII- NP-Completeness
  • Introduction
  • Strengths and limitations of Computational Geometry
  • Polygons
  • Convex Polygons
  • Convex Hulls
  • Graham’s Scan Algorithms
  • Jarvis’s March Algorithm
    • Classes of Problems
    • The Class NP (Non-Deterministic Polynomial)
  • NP-Completeness
  • The Class co-NP
  • Satisfiability (SAT)
  • Circuit Satisfiability 
  • Proving NP-Completeness
  • Problems for NP-complete Problem
  • (formula) Satisfiability 
  • 3-CNF Satisfiability 
  • The Clique Problem
  • The Vertex-Cover Problem
  • The Subset-Sum Problem
  • The Hamiltonian-Cycle Problem
  • The traveling-Salesman Problem
Chapter XXXIX- Approximate Algorithms Chapter XXXX- Randomized Algorithm
  • Introduction
  • Performance Ratios
  • Examples of Approximate Algorithms
  • Introduction
  • Applications
  • Advantages and Disadvantages

List of Design and Analysis of Algorithms PDF by Udit Agarwal Important Questions

Candidates pursuing Computer Science or Electrical Engineering course programme can access the article Design And Analysis Of Algorithms Pdf By Udit Agarwal and read through the list of all the essential questions mentioned below for the course programme. All the provided review questions aim to help candidates excel in their examination.

  1. Explain the primary characteristics of an Algorithm briefly.
  2. Discuss the method to calculate the running time of an Algorithm.
  3. Discuss the INSERTION SORT on an array A-(41,31,69,16,38,62) with a neat-labelled diagram.
  4. Analyse the working procedure of Insertion Sort in the worst case.
  5. With the application of Merge Sort, Sort the following list- 70, 80, 40, 50, 60, 12, 35, 95, 10
  6. Define Merge Sort, and briefly explain the working procedure of Merge Sort during its best case, worst case, and average-case complexity.
  7. Discuss the heap-Sort Algorithm of the following input with a neat-labelled diagram (2, 5, 16,4, 10,23,39, 18,26,15)
  8. Consider that the running time of all the elements of array A having the same value, elucidate on the running time of the QUICK SORT.
  9. Considering that the key of each record has a value of either 0 or 1, modify the bucket key algorithm.
  10. Devise an algorithm that can record and search in a chained method.
  11. Write a C program that can break a single circularly-linked list into two circularly linked lists.0
  12. 25Describe the outlook of a splay tree if the keys are accessed in increasing order.
  13. Illustrate how an AVL tree can be designed as a Red-Black Tree.
    Illustrate with a neat-labelled diagram of a Red-Black Tree disconnected to an AVL tree.
  14. Explain briefly about the non-recursive version of OS-SELECT.

FAQ’s on Design and Analysis of Algorithms PDF by Udit Agarwal

Question 1.
Explain the definition of Algorithms briefly.

Answer:
An Algorithm is a sequence or a set of computational rules that transform input into output or carries the calculation either on a machine or by hand. Through algorithms and abstraction can be extracted on a physical machine.

Question 2.
Derive the classification of Algorithms

Answer:
Algorithms, when grouped, adopt a similar structure like a problem-solving technique. A few Algorithm types to consider are-

  • Greedy Algorithms
  • Randomized Algorithms
  • Divide and Conquer Algorithms
  • Recursive Algorithms
  • Branch and Bound Algorithms
  • Backtracking Algorithms
  • Brute Force Algorithms
  • Dynamic Programming Algorithms

Question 3.
How is Design And Analysis Of Algorithms Pdf By Udit Agarwal useful?

Answer:
The Design And Analysis Of Algorithms Pdf By Udit Agarwal Book provide a comprehensive understanding of all the important concepts. The pdf even presents mock exercises to simply and better a student’s preparation or revision process. The book gives a detailed view of all aspects of Design And Analysis Of Algorithms.

Question 4.
Name a few important questions from Design And Analysis Of Algorithms Pdf By Udit Agarwal Book.

Answer:

  • Explain the primary characteristics of an Algorithm briefly.
  • Discuss the method to calculate the running time of an Algorithm.
  • Consider that the running time of all the elements of array A having the same value, elucidate on the running time of the QUICK SORT.
  • Considering that the key of each record has a value of either 0 or 1, modify the bucket key algorithm.
  • Devise an algorithm that can record and search in a chained method.

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