As a developer, mastering the concepts of algorithms and being proficient in implementing them is essential to improving problem-solving skills. This course aims to equip you with an in-depth understanding of algorithms and how they can be utilized for problem-solving in Python.

Starting with the basics, you'll gain a foundational understanding of what algorithms are, with topics ranging from simple multiplication algorithms to analyzing algorithms. Then, you’ll delve into more advanced topics like recursion, backtracking, dynamic programming, and greedy algorithms. You'll also learn about basic graph algorithms, depth-first search, shortest paths, minimum spanning trees, and all-pairs shortest paths. 

By the end of this course, you'll have acquired a wide range of skills that will significantly enhance your ability to solve problems efficiently in Python. Through this course, not only will you improve your coding skills, but you will also gain confidence in tackling complex problems.

Mastering Algorithms for Problem Solving in Python

The minimum spanning tree of $G$ includes the maximum-weight edge in any cycle.

The cycle property of minimum spanning trees does not apply to connected graphs with weighted edges.

The minimum spanning tree of $G$ excludes the minimum-weight edge in any cycle.

The minimum spanning tree of $G$ excludes the maximum-weight edge in any cycle.

What is the cycle property of minimum spanning trees for a connected graph $G$ with weighted edges?

What is the cycle property of minimum spanning trees for a connected graph <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi></mrow><annotation encoding="application/x-tex">G</annotation></semantics></math>G with weighted edges?

Which is a correct algorithm to find the second smallest spanning tree of a given graph $G$?

Which is a correct algorithm to find the second smallest spanning tree of a given graph <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi></mrow><annotation encoding="application/x-tex">G</annotation></semantics></math>G?

What is the time complexity of the subroutine `AddAllSafeEdges`?

What is the time complexity of the subroutine <code>AddAllSafeEdges</code>?

What is the worst-case running time of Borůvka’s algorithm?

What is the worst-case running time of Borůvka’s algorithm?

It computes the minimum-weight edge  in $G$.

It computes an array of safe edges in $G$.

What does the subroutine <code>CAL</code> do?

Reinforce your knowledge of minimum spanning trees and their applications in problem-solving.

Getting Started

Introduction to Algorithm

Recursion

Backtracking

Dynamic Programming

Greedy Algorithms

Prove Your Skills: A Five-Chapter Assessment

Basic Graph Algorithms

Depth-First Search

Minimum Spanning Trees

Shortest Paths

All-Pairs Shortest Paths

Pushing Your Limits: A Comprehensive Assessment

Wrapping up

Quiz: Minimum Spanning Trees