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

# Weighted directed graph (two vertices)
Suppose we are given a weighted directed graph $G = (V, E, w)$ with two special vertices, and we want to find the shortest path from a source vertex $s$ to a target vertex $t$. That is, we want to find the directed path $P$ starting at $s$ and ending at $t$ that minimizes the function

$$w(P) := \underset{u\rightarrow v \epsilon P}{\sum} w(u\rightarrow v).$$

The expression above represents the sum of the weights of all edges.

For example, if we want to answer the question, “What’s the fastest way to drive from my old apartment in Champaign, Illinois, to my friend’s old apartment in Columbus, Ohio?” we might use a graph whose vertices are cities, edges are roads, weights are driving times, $s$ is Champaign, and $t$ is Columbus. The graph is directed because driving times along the same road might be different in different directions. (At one time, there was a speed trap on I-70 just east of the Indiana/Ohio border, but only for eastbound traffic.)

# Shortest path trees

Almost every algorithm known for computing shortest paths from one vertex to another actually solves (large portions of) the following more general **single source shortest path** or **SSSP** problem: Find shortest paths from the source vertex $s$ to every other vertex in the graph. This problem is usually solved by finding a shortest path tree rooted at $s$ that contains all the desired shortest paths.

It’s not hard to see that if shortest paths are unique, then they form a tree because any subpath of the shortest path is itself the shortest path. If there are multiple shortest paths to some vertices, we can always choose one shortest path to each vertex so that the union of the paths is a tree. If there are shortest paths from $s$ to two vertices $u$ and $v$ that diverge, then meet, then diverge again, we can modify one of the paths without changing its length so that the two paths only diverge once.


Understand the fundamental concepts of shortest paths 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

Introduction to Shortest Paths

Weighted directed graph (two vertices)