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

Only 2-dimensional hypercubes (or squares).

Which hypercubes have a Euler tour (a closed walk that traverses every
edge exactly once)?


Which hypercubes have a Euler tour (a closed walk that traverses every
edge exactly once)?

Let $G$ be a connected graph, and let $T$ be a depth-first spanning tree of $G$ rooted at some node $v$. If $T$ is also a breadth-first spanning tree of $G$ rooted at $v$, then:

Let <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 be a connected graph, and let <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi></mrow><annotation encoding="application/x-tex">T</annotation></semantics></math>T be a depth-first spanning tree of <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 rooted at some node <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math>v. If <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi></mrow><annotation encoding="application/x-tex">T</annotation></semantics></math>T is also a breadth-first spanning tree of <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 rooted at <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math>v, then:

A planar graph always has a unique drawing.

A non-planar graph can have a planar drawing.

The intersection graph of a collection of geometric objects always results in a planar graph.

An interval graph is a type of planar graph where vertices are represented as points in a plane.

Which of the following statements about planar graphs is true?

Which of the following statements about planar graphs is true?

To avoid describing how the algorithm works

To demonstrate the essential ingredients of a reduction

What is the purpose of using an existing algorithm as a black-box subroutine in the flood-fill problem?

What is the purpose of using an existing algorithm as a black-box subroutine in the flood-fill problem?

There must be at least one vertex with a degree of `1`.

There must be at least two vertices with a degree of `1`.

There must be at least one vertex with a degree of `n-1`.

There must be at least two vertices with a degree of `n-1`.

Which of the following statements is true for an acyclic graph with `n` vertices?

Which of the following statements is true for an acyclic graph with <code>n</code> vertices?

Check your understanding of basic graph algorithms.

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: Basic Graph Algorithms