# Design and Analysis of Algorithms Notes & Study Material by Udit Agarwal | Design and Analysis of Algorithms Handwritten Notes PDF

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## Introduction to Design and Analysis of Algorithms

An Algorithm is defined as a set of operation or computational steps or instructions 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 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.

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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 Reference Books

• Alfred V. Aho, John E. Hopcroft and Jeffrey D. Ullman, “Data Structures and Algorithms”, Pearson Education, Reprint 2006.
• Thomas H. Cormen, Charles E.Leiserson, Ronald L. Rivest and Clifford Stein, “Introduction to Algorithms”, Third Edition, PHI Learning Private Limited, 2012.
• Anany Levitin, “Introduction to the Design and Analysis of Algorithms”, Third Edition, Pearson Education, 2012.
• Donald E. Knuth, “The Art of Computer Programming”, Volumes 1& 3 Pearson Education, 2009. 4. Steven S. Skiena, “The Algorithm Design Manual”, Second Edition, Springer, 2008.
• Design and Analysis of Computer Algorithms by AHO
• Fundamentals of Computer Algorithms(second edition) by Sahni Horowitz
• Introduction to the Design and Analysis of Algorithms by Anany Levitin
• Algorithm Design: Foundations, Analysis and Internet Examples” by Michael T Goodrich and Roberto Tamassia
• Design and Analysis of Algorithms by Dave ### Design and Analysis of Algorithms Syllabus

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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 the 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 examinations.

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?

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?

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