Gain insights into essential algorithms, delve into recursion, backtracking, and graph theory, and enhance your problem-solving skills in C++ to confidently tackle complex challenges.

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 C++.

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 C++. 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 C++

# Task
Suppose we are given both an undirected graph $G$ with weighted edges and
a minimum spanning tree $T$ of $G$.
Provide code to update the minimum spanning tree when the weight of a single edge $e$ is decreased; we can follow the algorithm described below.

# Logic building

Here's the algorithm to update the minimum spanning tree $T$ when the weight of a single edge $e$ is decreased:

**Algorithm**





- Identify the two nodes $u$ and $v$ that the edge $e$ connects.
- Find the path $P$ in the minimum spanning tree $T$ that connects $u$ and $v$.
- Let $e'$ be the heaviest edge on the path $P$.
- If the weight of $e$ is less than the weight of $e'$, remove $e'$ from $T$.
- Add $e$ to $T$.
- Return $T$ as the updated minimum spanning tree.

Discuss the solution of minimum spanning trees in this lesson.

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

Solution: Minimum Spanning Trees

Task

Logic building