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Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming

Approx. 15 hours to complete

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Course Summary

Learn about the importance of greedy algorithms and how they can be applied to solve real-world problems in this course. From job scheduling to network routing, you'll gain a deep understanding of this powerful algorithmic technique.

Key Learning Points

Understand the basics of greedy algorithms and their applications
Learn how to analyze the correctness and efficiency of greedy algorithms
Apply greedy algorithms to solve a variety of real-world problems

Learning Outcomes

Understand the fundamentals of greedy algorithms and their role in problem solving
Analyze and design efficient greedy algorithms for real-world problems
Apply greedy algorithms to a variety of problems in different domains

Prerequisites or good to have knowledge before taking this course

Basic knowledge of programming and data structures
Familiarity with fundamental algorithms

Course Difficulty Level

Intermediate

Course Format

Self-paced
Online

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Related Education Paths

Notable People in This Field

Donald Knuth
Edsger Dijkstra
Jon Bentley

Related Books

Description

The primary topics in this part of the specialization are: greedy algorithms (scheduling, minimum spanning trees, clustering, Huffman codes) and dynamic programming (knapsack, sequence alignment, optimal search trees).

Outline

Week 1
Application: Internet Routing
Application: Sequence Alignment
Introduction to Greedy Algorithms
Application: Optimal Caching
Problem Definition
A Greedy Algorithm
Correctness Proof - Part I
Correctness Proof - Part II
Handling Ties [Advanced - Optional]
MST Problem Definition
Prim's MST Algorithm
Correctness Proof I
Correctness Proof II
Proof of Cut Property [Advanced - Optional]
Fast Implementation I
Fast Implementation II
Week 1 Overview
Overview, Resources, and Policies
Lecture slides
Optional Theory Problems (Week 1)
Problem Set #1
Programming Assignment #1

Week 2
Kruskal's MST Algorithm
Correctness of Kruskal's Algorithm
Implementing Kruskal's Algorithm via Union-Find I
Implementing Kruskal's Algorithm via Union-Find II
MSTs: State-of-the-Art and Open Questions [Advanced - Optional]
Application to Clustering
Correctness of Clustering Algorithm
Lazy Unions [Advanced - Optional]
Union-by-Rank [Advanced - Optional]
Analysis of Union-by-Rank [Advanced - Optional]
Path Compression [Advanced - Optional]
Path Compression: The Hopcroft-Ullman Analysis I [Advanced - Optional]
Path Compression: The Hopcroft-Ullman Analysis II [Advanced - Optional]
The Ackermann Function [Advanced - Optional]
Path Compression: Tarjan's Analysis I [Advanced - Optional]
Path Compression: Tarjan's Analysis II [Advanced - Optional]
Week 2 Overview
Optional Theory Problems (Week 2)
Problem Set #2
Programming Assignment #2

Week 3
Introduction and Motivation
Problem Definition
A Greedy Algorithm
A More Complex Example
Correctness Proof I
Correctness Proof II
Introduction: Weighted Independent Sets in Path Graphs
WIS in Path Graphs: Optimal Substructure
WIS in Path Graphs: A Linear-Time Algorithm
WIS in Path Graphs: A Reconstruction Algorithm
Principles of Dynamic Programming
Week 3 Overview
Problem Set #3
Programming Assignment #3

Week 4
The Knapsack Problem
A Dynamic Programming Algorithm
Example [Review - Optional]
Optimal Substructure
A Dynamic Programming Algorithm
Problem Definition
Optimal Substructure
Proof of Optimal Substructure
A Dynamic Programming Algorithm I
A Dynamic Programming Algorithm II
Week 4 Overview
Optional Theory Problems (Week 4)
Info and FAQ for final exam
Problem Set #4
Programming Assignment #4
Final Exam

Summary of User Reviews

Discover the algorithms that are used to solve the most common problems in computer science with the Algorithms: Greedy course on Coursera. Users praise the course for its comprehensive coverage and engaging approach to learning.

Key Aspect Users Liked About This Course

The course is praised for its comprehensive coverage and engaging approach to learning.

Pros from User Reviews

Comprehensive coverage of algorithms
Engaging approach to learning
Great explanations and examples
Challenging but rewarding assignments
Great instructor with a deep understanding of the subject

Cons from User Reviews

Can be difficult for beginners
Assignments can be time-consuming
Requires a strong background in mathematics
Could benefit from more interactive elements
Not suited for those looking for a quick overview of algorithms

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