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

To keep a record of which square in each row keeps a queen.

In the n-queen’s problem, why do we have an array $Q[1….n]$?

In the n-queen’s problem, why do we have an array <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi><mo stretchy="false">[</mo><mn>1</mn><mo>…</mo><mi mathvariant="normal">.</mi><mi>n</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">Q[1….n]</annotation></semantics></math>Q[1….n]?

Consider an $n$ queen problem with $n = 4$ so that the chess board looks like this: 


![](/api/collection/10370001/6282863386558464/page/5590964185071616/image/4610111615270912?page_type=collection_lesson)


How many valid solutions will there be at the end? (Hint: recall the use of game trees.)


Consider an <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n queen problem with <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">n = 4</annotation></semantics></math>n=4 so that the chess board looks like this:
<img src="/api/collection/10370001/6282863386558464/page/5590964185071616/image/4610111615270912?page_type=collection_lesson" alt="" />
How many valid solutions will there be at the end? (Hint: recall the use of game trees.)

Consider an $n$ x $n$ fake sugar packet game with $n = 4$ so that the game looks like this:

![](/api/collection/10370001/6282863386558464/page/5590964185071616/image/6155041181532160?page_type=collection_lesson)

How many possible moves can the first player make?



Consider an <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n x <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n fake sugar packet game with <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">n = 4</annotation></semantics></math>n=4 so that the game looks like this:
<img src="/api/collection/10370001/6282863386558464/page/5590964185071616/image/6155041181532160?page_type=collection_lesson" alt="" />
How many possible moves can the first player make?

How many possible states are there for an $n$ x $n$ sugar packet game if $n = 4$ and the game tree is at the 3rd level?

How many possible states are there for an <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n x <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math>n sugar packet game if <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>=</mo><mn>4</mn></mrow><annotation encoding="application/x-tex">n = 4</annotation></semantics></math>n=4 and the game tree is at the 3rd level?

How many exact decisions are required to be made in each recursive call in backtracking algorithm?

How many exact decisions are required to be made in each recursive call in backtracking algorithm?

Reinforce your understanding of backtracking algorithms 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: Backtracking