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Algorithm Design: Mastering Computational Problem Solving · LearnSpace
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Algorithm Design: Mastering Computational Problem Solving

Курс от Birla Institute of Technology & Science, Pilani
Начальный≈ 33.7 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

Dive into the world of algorithm design, a fundamental aspect of computer science. This course provides a comprehensive understanding of various algorithmic design paradigms such as divide and conquer, greedy methods, dynamic programming, backtracking, and branch and bound. You will explore fundamental graph algorithms, gain practical experience in solving complex graph-related problems, and delve into randomized algorithms and complexity classes. Designed to equip you with the knowledge and skills to tackle a wide range of computational challenges, the course covers the theoretical underpinnings and practical applications of algorithm design principles. By the end of the course, you will be able to design efficient algorithms to solve diverse computational problems, preparing you for advanced studies and professional careers in software development, data analysis, and other IT fields.

Навыки, которые вы освоите

Problem SolvingSolution DesignComputer ProgrammingMathematical Theory & AnalysisComputer Science

Программа курса

9 модулей · 269 учебных материалов

01Foundations of Algorithm Design41 материалов

Let's Get Started

Introducing Algorithm DesignВидеоCourse OverviewЧтениеMeet your Instructor: Prof. Febin VahabВидеоMeet your Instructor: Prof. Rakesh PrasannaВидео

Algorithm Analysis

Учитесь у экспертов

BITS Pilani Instructors Group

Преподаватель курса

Algorithm Design: Mastering Computational Problem Solving
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Обучение на Coursera

≈ 33.7 ч

9 модулей

Язык: Английский

Часть программы вашего университета
Notion of AlgorithmsВидео
Practice Quiz: Notion of AlgorithmsЗадание
Methodologies for Analyzing AlgorithmsВидео
Practice Quiz: Methodologies for Analyzing AlgorithmsЗадание
Notion of Best Case, Average Case, and Worst CaseВидео
Practice Quiz: Notion of Best Case, Average Case, and Worst CaseЗадание
Basic Operation MethodВидео
Practice Quiz: Basic Operation MethodЗадание
Order of Growth of AlgorithmsВидео
Recommended Reading: Methodologies for Analyzing Algorithms Чтение
Practice Quiz: Order of Growth of AlgorithmsЗадание
Asymptotic Notations: Part IВидео
Practice Quiz: Asymptotic Notations: Part IЗадание
Asymptotic Notations: Part IIВидео
Practice Quiz: Asymptotic Notations: Part IIЗадание
Algorithm Analysis: Insertion SortВидео
Recommended Reading: Asymptotic NotationЧтение
Essential Reading: Notion and Analysis of AlgorithmsЧтение
Practice Quiz: Introduction: Algorithm AnalysisЗадание

Analyzing Recursive Algorithms and Solving Recurrences

Analysis of Recursive AlgorithmsВидеоPractice Quiz: Analysis of Recursive AlgorithmsЗаданиеSolving Recurrences: Backward SubstitutionВидеоRecommended Reading: The Iterative Substitution MethodЧтениеPractice Quiz: Solving Recurrences: Backward SubstitutionЗаданиеSolving Recurrences: Recursion Tree—Part IВидеоPractice Quiz: Solving Recurrences: Recursion Tree—Part IЗаданиеSolving Recurrences: Recursion Tree—Part IIВидеоEssential Reading: The Recursion Tree MethodЧтениеRecommended Reading: The Recursion Tree Method for Solving RecurrencesЧтениеPractice Quiz: Solving Recurrences: Recursion Tree—Part IIЗаданиеSolving Recurrences: Master MethodВидеоEssential Reading: The Master MethodЧтениеRecommended Reading: The Master Method for Solving RecurrencesЧтениеRecommended Reading: Recursive Algorithm AnalysisЧтениеPractice Quiz: Solving Recurrences: Master MethodЗадание

Discussion

Analyzing Real-World Algorithms: From Theory to PracticeDIALOGUETest Yourself: Analysis of AlgorithmsЗадание
02Divide and Conquer Strategies31 материалов

Divide and Conquer Paradigm

Design Principles and StrategyВидеоPractice Quiz: Design Principles and StrategyЗаданиеAnalysis of Divide and Conquer Algorithms: MergesortВидеоPractice Quiz: Analysis of Divide and Conquer Algorithms: MergesortЗаданиеDivide and Conquer Algorithm: Quicksort—Part IВидеоPractice Quiz: Divide and Conquer Algorithm: Quicksort—Part IЗаданиеDivide and Conquer Algorithm: Quicksort—Part IIВидеоPractice Quiz: Divide and Conquer Algorithm: Quicksort—Part IIЗаданиеDivide and Conquer Algorithm: Binary SearchВидеоRecommended Reading: Divide-and-Conquer Recurrence Equations ЧтениеPractice Quiz: Divide and Conquer Algorithm: Binary SearchЗадание

Integer Multiplication Problem and Maximum Subarray Problem

Problem 1: Integer Multiplication ProblemВидеоRecommended Reading: Integer MultiplicationЧтениеPractice Quiz: Problem 1: Integer Multiplication ProblemЗаданиеProblem 2: Maximum Subarray Problem—Part IВидеоPractice Quiz: Problem 2: Maximum Subarray Problem—Part IЗаданиеProblem 2: Maximum Subarray Problem—Part IIВидео

Strassen’s Matrix Multiplication Problem

Strassen’s Matrix Multiplication ProblemВидеоPractice Quiz: Strassen’s Matrix Multiplication ProblemЗаданиеMatrix Multiplication: A Simple Divide and Conquer AlgorithmВидеоPractice Quiz: Matrix Multiplication: A Simple Divide and Conquer AlgorithmЗаданиеStrassen’s AlgorithmВидеоPractice Quiz: Strassen’s AlgorithmЗадание

Assessment

Test Yourself: Algorithm Design TechniqueЗадание
03Greedy Algorithm Methodology23 материалов

Greedy Strategy

Change Making ProblemВидеоPractice Quiz: Change Making ProblemЗаданиеGreedy Strategy: Design Principle and Key ElementsВидеоRecommended Reading: Greedy Strategy: Principles and ElementsЧтениеPractice Quiz: Greedy Strategy: Design Principle and Key ElementsЗадание

Knapsack Problem

Introduction to Knapsack Problem ВидеоPractice Quiz: Introduction to Knapsack Problem ЗаданиеFractional Knapsack Algorithm and AnalysisВидеоPractice Quiz: Fractional Knapsack Algorithm and AnalysisЗаданиеFractional Knapsack: Numerical ExampleВидеоRecommended Reading: The Fractional Knapsack Problem ЧтениеPractice Quiz: Fractional Knapsack: Numerical ExampleЗадание

Activity Selection Problem and Job sequencing with Deadlines

Task Scheduling ProblemВидеоPractice Quiz: Task Scheduling ProblemЗаданиеTask Scheduling: Algorithm and AnalysisВидеоRecommended Reading: Task SchedulingЧтениеPractice Quiz: Task Scheduling: Algorithm and AnalysisЗаданиеJob Sequencing with Deadlines: Algorithm and Analysis Видео

Discussion

Greedy Decisions in the Real World: Strategy, Applications, and OptimizationDIALOGUE
04Dynamic Programming 20 материалов

Dynamic Programming

Dynamic Programming Paradigm: The General TechniqueВидеоPractice Quiz: Dynamic Programming Paradigm: The General TechniqueЗаданиеFibonacci Numbers: Top-Down and Bottom-Up Approaches—Part IВидеоPractice Quiz: Fibonacci Numbers: Top-Down and Bottom-Up Approaches—Part IЗаданиеFibonacci Numbers: Top-Down and Bottom-Up Approaches—Part IIВидеоPractice Quiz: Fibonacci Numbers: Top-Down and Bottom-Up Approaches—Part IIЗаданиеRecommended Reading: Dynamic Programming: The General Technique Чтение

Matrix Chain Product

Matrix Chain Product (MCP)ВидеоPractice Quiz: Matrix Chain Product (MCP)ЗаданиеMCP: Applying Dynamic ProgrammingВидеоPractice Quiz: MCP: Applying Dynamic ProgrammingЗаданиеMCP: Numeric ExampleВидеоPractice Quiz: MCP: Numeric ExampleЗадание

Understanding the 0/1 Knapsack Problem

0/1 Knapsack ProblemВидеоRecommended Reading: The 0/1 Knapsack ProblemЧтениеPractice Quiz: 0/1 Knapsack ProblemЗадание

Assessment

Test Yourself: Algorithm Design TechniquesЗадание
05Graph Algorithms - Fundamentals20 материалов

Graph Terminologies and Representations

Review: Graph Properties and TypesВидеоPractice Quiz: Review: Graph Properties and TypesЗаданиеReview: Graph RepresentationsВидеоPractice Quiz: Review: Graph RepresentationsЗаданиеPath, Cycle, Subgraphs, Connectivity, Trees, and ForestsВидеоPractice Quiz: Path, Cycle, Subgraphs, Connectivity, Trees, and ForestsЗаданиеReachability and Strong ConnectivityВидеоRecommended Reading: Graph Terminologies and RepresentationsЧтениеPractice Quiz: Reachability and Strong ConnectivityЗадание

Graph Traversals

Review: Graph Traversal—Breadth First Search (BFS) and AnalysisВидеоPractice Quiz: Review: Graph Traversal—Breadth First Search (BFS) and AnalysisЗаданиеReview: Graph Traversal—Depth First Search (DFS) and AnalysisВидеоPractice Quiz: Review: Graph Traversal—Depth First Search (DFS) and AnalysisЗаданиеBFS and DFS ComparisonВидеоRecommended Reading: Graph TraversalsЧтение

Topological Sorting

Topological Sort: Algorithm and AnalysisВидеоRecommended Reading: Topological SortingЧтениеPractice Quiz: Topological Sort: Algorithm and AnalysisЗадание

Discussion

Graph Algorithms AnalysisОбсуждение
06 Advanced Graph Algorithms20 материалов

Minimum Spanning Trees

Minimum Spanning TreeВидеоPractice Quiz: Minimum Spanning Tree ЗаданиеKruskal’s Design Strategy ВидеоPractice Quiz: Kruskal’s Design Strategy ЗаданиеMST: Prim’s Design Strategy ВидеоPractice Quiz: MST: Prim’s Design Strategy ЗаданиеRecommended Reading: MST, Kruskal’s Design Strategy and Prim’s Design StrategyЧтение

Single Source Shortest Path

Shortest Paths and Properties ВидеоPractice Quiz: Shortest Paths and Properties ЗаданиеThe Bellman-Ford Algorithm ВидеоPractice Quiz: The Bellman-Ford Algorithm ЗаданиеDijkstra’s Algorithm ВидеоRecommended Reading: Single Source Shortest PathЧтение

Transitive Closure and All Pair Shortest Path

Transitive Closure: Design Strategy ВидеоPractice Quiz: Transitive Closure: Design Strategy ЗаданиеAll Pair Shortest Path: Floyd’s Design StrategyВидеоRecommended Readings: Transitive Closure and All Pair Shortest PathЧтениеPractice Quiz: All Pair Shortest Path: Floyd’s Design StrategyЗадание

Assessment

Test Yourself: Graph Algorithms Analysis Задание
07Design Technique: Backtracking and Branch & Bound75 материалов

Introduction to State Space 

Definition of a State in a State Space ВидеоPractice Quiz: Definition of a State in a State Space ЗаданиеFinite and Infinite State Space ВидеоPractice Quiz: Finite and Infinite State Space ЗаданиеTraversing Through State Space ВидеоPractice Quiz: Traversing Through State Space ЗаданиеState Space Tree ВидеоPractice Quiz: State Space Tree ЗаданиеIntroduction to Backtracking ВидеоPractice Quiz: Introduction to Backtracking ЗаданиеDFS as an Example of Backtracking with State Space Tree ВидеоRecommended Reading: Introduction to State Space ЧтениеPractice Quiz: DFS as an Example of Backtracking with State Space Tree Задание

N-queen Problem (4 Queen Problem)

Definition of the State in the N-Queen ProblemВидеоPractice Quiz: Definition of the State in the N-Queen ProblemЗаданиеTraversing Through All State Spaces Using RecursionВидеоPractice Quiz: Traversing Through all State Spaces Using RecursionЗаданиеBacktracking Strategy ExplanationВидеоPractice Quiz: Backtracking Strategy ExplanationЗадание

Graph Coloring Problem

Graph Coloring Problem: Definitions and ApplicationsВидеоPractice Quiz: Graph Coloring Problem: Definitions and ApplicationsЗаданиеNaive Approach to Color with All Possible Colors ВидеоPractice Quiz: Naive Approach to Color with All Possible Colors ЗаданиеBacktracking Strategy with VisualizationВидеоRecommended Reading: Graph Coloring Problem Чтение

Sum of Subset

Problem and State Definition ВидеоPractice Quiz: Problem and State Definition ЗаданиеNaïve Approach to Find Through all Possible SubsetsВидеоPractice Quiz: Naïve Approach to Find Through all Possible SubsetsЗаданиеBacktracking Code and State Space TreeВидеоPractice Quiz: Backtracking Code and State Space TreeЗадание

Least Cost Search 

Introduction to Least Cost SearchВидеоPractice Quiz: Introduction to Least Cost SearchЗаданиеApplication Examples of Least Cost SearchВидеоPractice Quiz: Application Examples of Least Cost SearchЗаданиеPractical Implementation of Least Cost SearchВидеоPractice Quiz: Practical Implementation of Least Cost SearchЗадание

First-In-First-Out (FIFO) Branch and Bound

FIFO Data Structures, Branching, and Bounding FrameworkВидеоPractice Quiz: FIFO Data Structures, Branching, and Bounding FrameworkЗаданиеAnalysis and Implementation of FIFO ApproachВидео0/1 Knapsack Problem Using FIFO Branch and BoundsВидеоPractice Quiz: Analysis and Implementation of FIFO ApproachЗаданиеComparison with Other Branch and Bound Strategies: Challenges and LimitationsВидео

LC Branch and Bound

Bounding Strategies and LC Branching TechniqueВидеоPractice Quiz: Bounding Strategies and LC: Branching TechniqueЗадание0/1 Knapsack Problem Using LC Branch and BoundsВидеоComparison with Other Branch and Bound Strategies, Challenges and LimitationsВидеоPractice Quiz: Comparison with Other Branch and Bound Strategies, Challenges and LimitationsЗаданиеOptimization Techniques with Examples: Project Scheduling and Resource AllocationВидео

Job Sequencing with Timebound (Deadlines) 

Introduction to Job Sequencing with TimeboundВидеоPractice Quiz: Introduction to Job Sequencing with TimeboundЗаданиеImplementation and Analysis with Optimization StrategyВидеоPractice Quiz: Implementation and Analysis with Optimization StrategyЗаданиеJob Sequencing with DeadlineВидео

Discussion and Assessment

Learning from Case Studies: Bridging Theory and Practice in Branch and BoundDIALOGUETest Yourself: Backtracking and Branch & Bound Design TechniquesЗадание
08Randomized Algorithms21 материалов

Randomized Quicksort 

Randomized AlgorithmВидеоPractice Quiz: Randomized AlgorithmЗаданиеClassical QuicksortВидеоRandom Selection of PivotВидеоRandom Selection of PivotЗаданиеRandomized Quicksort AlgorithmВидеоPractice Quiz: Randomized Quicksort AlgorithmЗаданиеAverage Time Complexity ComparisonВидеоRecommended Reading: Randomized Version of Quicksort ЧтениеPractice Quiz: Average Time Complexity ComparisonЗадание

Min Cut Algorithm

Min-Cut Problem DefinitionВидеоPractice Quiz: Min-Cut Problem DefinitionЗаданиеContracting EdgesВидеоPractice Quiz: Contracting EdgesЗаданиеClassical AlgorithmВидеоKarger’s Algorithm for Finding the Min-CutВидео

Discussion

Randomized AlgorithmsОбсуждение
09P, NP, NP-Complete, and NP-Hard Problems18 материалов

Understanding P, NP, NP-Complete, and NP-Hard Problems

Introduction to Complexity Classes ВидеоPractice Quiz: Introduction to Complexity Classes ЗаданиеDefinition of P and NP Classes and Examples ВидеоNP-Completeness: Importance ВидеоUnderstanding NP-Completeness ВидеоPractice Quiz: Understanding NP-Completeness ЗаданиеReductions in Complexity TheoryВидеоPractice Quiz: Reductions in Complexity TheoryЗаданиеNP-Hardness and NP-Hard versus NP-CompleteВидеоSatisfiability Problem (SAT) as an NP-Complete ProblemВидеоPolynomial Time Reducibility: Definition and Examples ВидеоNP-Complete Problems: Introduction ВидеоNP-Complete Problems: Clique and Set-Cover Problems and Hamiltonian Cycle Problem—Part IВидеоNP-Complete Problems: Clique and Set-Cover Problems and Hamiltonian Cycle Problem—Part IIВидеоNP-Complete Problems: Clique and Set-Cover Problems and Hamiltonian Cycle Problem—Part IIIВидеоRecommended Reading: Understanding P, NP, NP-Complete, and NP-Hard ProblemsЧтениеPractice Quiz: NP-Complete Problems: Clique and Set-Cover Problems and Hamiltonian Cycle Problem Задание

Assessment 

Test Yourself: Randomized Algorithms and Computational ProblemsЗадание
Practice Quiz: Problem 2: Maximum Subarray Problem—Part IIЗадание
Maximum Subarray Problem: AnalysisВидео
Recommended Reading: Maximum Subarray ProblemЧтение
Practice Quiz: Maximum Subarray Problem: AnalysisЗадание
Strassen’s Algorithm: AnalysisВидео
Recommended Reading: Strassen’s Algorithm for Matrix Multiplication Чтение
Practice Quiz: Strassen’s Algorithm: AnalysisЗадание
Practice Quiz: Job Sequencing with Deadlines: Algorithm and Analysis Задание
Job Sequencing with Deadlines: Numerical ExampleВидео
Recommended Reading: Job Sequencing with DeadlinesЧтение
Practice Quiz: Job Sequencing with Deadlines: Numerical ExampleЗадание
MCP: Bottom-Up ApproachВидео
Practice Quiz: MCP: Bottom-Up ApproachЗадание
Recommended Reading: Matrix Chain ProductЧтение
Practice Quiz: BFS and DFS ComparisonЗадание
Practice Quiz: Dijkstra’s Algorithm Задание
Backtracking Solution versus Solution Without BacktrackingВидео
Practice Quiz: Backtracking Solution, Optimization Over Without BacktrackingЗадание
Time Complexity ComparisonВидео
Recommende Reading: N-queen Problem (4 Queen Problem)Чтение
Practice Quiz: Time Complexity ComparisonЗадание
Practice Quiz: Backtracking Strategy with VisualizationЗадание
Time Complexity AnalysisВидео
Recommended Reading: Sum of SubsetЧтение
Practice Quiz: Time Complexity AnalysisЗадание
Design Techniques: BacktrackingОбсуждение
Recommended Reading: Graph Terminologies and RepresentationsЧтение
Recommended Reading: The Principles of LC Branch and Bound Чтение
Practice Quiz: Comparison with Other Branch and Bound Strategies: Challenges and LimitationsЗадание
Optimization Techniques with Examples: Network Routing in Telecommunications and Vehicle Routing for DeliveriesВидео
Practice Quiz: Optimization Techniques with Examples: Network Routing in Telecommunications and Vehicle Routing for DeliveriesЗадание
Recommended Reading: First-In-First-Out (FIFO) Branch and BoundЧтение
Practice Quiz: Optimization Techniques with Examples: Project Scheduling and Resource AllocationЗадание
Recommended Reading: LC Branch and BoundЧтение
Essential Reading: Recent Advances in Searching, Branching, and Pruning Within the Realm of Branch-and-Bound AlgorithmsЧтение
Practice Quiz: Karger’s Algorithm for Finding the Min-CutЗадание
Time Complexity ComparisonВидео
Recommended Reading: Min Cut Algorithm Чтение
Practice Quiz: Time Complexity ComparisonЗадание