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The algorithm is the set of rules that are followed by calculations and processes by computers. Learning how to design and analyze algorithms will put you in an advantage for your professional growth and development.

This [course_title] will introduce you the teaching techniques focusing on the design and analysis of efficient algorithm with emphasis on the methods of application. You will be provided with information on dynamic programming, complexity, etc. here.

Assessment

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

Certification

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Course Credit: MIT 

Course Curriculum

TWO MOTIVATING APPLICATIONS
Application: Internet Routing 00:11:00
Application: Sequence Alignment 00:09:00
INTRODUCTION TO GREEDY ALGORITHMS
Introduction to Greedy Algorithms 00:13:00
Application: Optimal Caching 00:11:00
A SCHEDULING APPLICATION
Problem Definition 00:06:00
A Greedy Algorithm 00:13:00
Correctness Proof – Part I 00:07:00
Correctness Proof – Part II 00:05:00
Handling Ties [Advanced – Optional] 00:07:00
PRIM'S MINIMUM SPANNING TREE ALGORITHM
MST Problem Definition 00:11:00
Prim’s MST Algorithm 00:07:00
Correctness Proof 00:16:00
Correctness Proof II 00:08:00
Proof of Cut Property [Advanced – Optional] 00:12:00
Fast Implementation I 00:15:00
Fast Implementation II 00:10:00
KRUSKAL'S MINIMUM SPANNING TREE ALGORITHM
Kruskal’s MST Algorithm 00:08:00
Correctness of Kruskal’s Algorithm 00:10:00
Implementing Kruskal’s Algorithm via Union-Find 00:10:00
Implementing Kruskal’s Algorithm via Union-Find II 00:14:00
MSTs: State-of-the-Art and Open Questions [Advanced – Optional] 00:09:00
CLUSTERING
Application to Clustering 00:11:00
Correctness of Clustering Algorithm 00:10:00
ADVANCED UNION-FIND
Lazy Unions [Advanced – Optional] 00:10:00
Union-by-Rank [Advanced – Optional] 00:12:00
Analysis of Union-by-Rank [Advanced – Optional] 00:15:00
Path Compression [Advanced – Optional] 00:15:00
Path Compression: The Hopcroft-Ullman Analysis I [Advanced – Optional] 00:10:00
Path Compression: The Hopcroft-Ullman Analysis II [Advanced – Optional] 00:12:00
The Ackermann Function [Advanced – Optional] 00:16:00
Path Compression: Tarjan’s Analysis I [Advanced – Optional] 00:14:00
Path Compression: Tarjan’s Analysis II [Advanced – Optional] 00:14:00
HUFFMAN CODES
Introduction and Motivation 00:09:00
Problem Definition 00:10:00
A Greedy Algorithm 00:17:00
A More Complex Example 00:04:00
Correctness Proof I 00:10:00
Correctness Proof II 00:13:00
INTRODUCTION TO DYNAMIC PROGRAMMING
Introduction: Weighted Independent Sets in Path Graphs 00:08:00
WIS in Path Graphs: A Linear-Time Algorithm 00:10:00
WIS in Path Graphs: A Reconstruction Algorithm 00:07:00
Principles of Dynamic Programming 00:08:00
THE KNAPSACK PROBLEM
The Knapsack Problem 00:10:00
A Dynamic Programming Algorithm 00:10:00
Example [Review – Optional] 00:13:00
SEQUENCE ALIGNMENT
Optimal Substructure 00:14:00
A Dynamic Programming Algorithm 00:12:00
OPTIMAL BINARY SEARCH TREES
Problem Definition 00:13:00
Optimal Substructure 00:10:00
Proof of Optimal Substructure 00:07:00
A Dynamic Programming Algorithm 00:10:00
A Dynamic Programming Algorithm II 00:10:00
THE BELLMAN-FORD ALGORITHM
Single-Source Shortest Paths, Revisited 00:11:00
Optimal Substructure 00:11:00
The Basic Algorithm I 00:09:00
The Basic Algorithm II 00:11:00
Detecting Negative Cycles 00:09:00
A Space Optimization 00:13:00
Internet Routing I [Optional] 00:12:00
Internet Routing II 00:07:00
ALL-PAIRS SHORTEST PATHS
Problem Definition 00:07:00
Optimal Substructure 00:12:00
The Floyd-Warshall Algorithm 00:14:00
A Reweighting Technique 00:14:00
Johnson’s Algorithm 00:11:00
Johnson’s Algorithm II 00:12:00
NP-COMPLETE PROBLEMS
Polynomial-Time Solvable Problems 00:15:00
Reductions and Completeness 00:14:00
Definition and Interpretation of NP-Completeness I 00:11:00
Definition and Interpretation of NP-Completeness II 00:08:00
The P vs. NP Question 00:09:00
Algorithmic Approaches to NP-Complete Problems 00:13:00
FASTER EXACT ALGORITHMS FOR NP-COMPLETE PROBLEMS
The Vertex Cover Problem 00:09:00
Smarter Search for Vertex I 00:10:00
Smarter Search for Vertex Cover II 00:08:00
The Traveling Salesman Problem 00:15:00
A Dynamic Programming Algorithm for TSP 00:12:00
APPROXIMATION ALGORITHMS FOR NP-COMPLETE PROBLEMS
A Greedy Knapsack Heuristic 00:14:00
Analysis of a Greedy Knapsack Heuristic I 00:07:00
Analysis of a Greedy Knapsack Heuristic II 00:10:00
A Dynamic Programming Heuristic for Knapsack 00:12:00
Knapsack via Dynamic Programming, Revisited 00:11:00
Analysis of Dynamic Programming Heuristic 00:15:00
LOCAL SEARCH ALGORITHMS
The Maximum Cut Problem I 00:09:00
The Maximum Cut Problem II 00:09:00
Principles of Local Search I 00:09:00
Principles of Local Search II 00:11:00
The 2-SAT Problem 00:15:00
Random Walks on a Line 00:16:00
Analysis of Papadimitriou’s Algorithm 00:15:00
THE WIDER WORLD OF ALGORITHMS
Stable Matching [Optional] 00:15:00
Matchings, Flows, and Braess’s Paradox [Optional] 00:14:00
Linear Programming and Beyond [Optional] 00:12:00
Epilogue 00:01:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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