Gain insights into essential algorithms for effective problem-solving in Java. Delve into recursion, dynamic programming, and graph algorithms to enhance your coding and tackle complex problems confidently.

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 Java.

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 Java. 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 Java

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

In the $n$ queens problem, why do we keep an array $Q[1….n]$?

In the <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 queens problem, why do we keep 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 $n$ queens problem having $n$ = 4, i.e., the chess board looks like this: 


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


Then 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 queens problem having <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 = 4, i.e., the chess board looks like this:
<img src="/api/collection/10370001/6282863386558464/page/5590964185071616/image/4610111615270912?page_type=collection_lesson" alt="" />
Then how many valid solutions will there be at the end? (Hint: Recall the use of game trees.)

Consider an $n × n$ fake-sugar-packet game, where $n$ = 4, i.e., the game looks like this:

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

How many possibilities are there for the first player to make a move?



Consider an <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">n × n</annotation></semantics></math>n×n fake-sugar-packet game, where <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 = 4, i.e., the game looks like this:
<img src="/api/collection/10370001/6282863386558464/page/5590964185071616/image/6155041181532160?page_type=collection_lesson" alt="" />
How many possibilities are there for the first player to make a move?

How many possible states are there for an $n × n$ 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><mo>×</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">n × n</annotation></semantics></math>n×n sugar-packet game if <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 = 4 and the game tree is at the 3rd level?

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

How many exact decisions are required to be made in each recursive call in a 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