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

We just discovered our best friend from elementary school on Twitbook. We both want to meet as soon as possible, but we live in two different cites that are far apart. To minimize travel time, we agree to meet at an intermediate city, and then we simultaneously hop in our cars and start driving toward each other. But where exactly should we meet? We are given a weighted graph $G = (V, E)$, where the vertices $V$ represent cities and the edges $E$ represent roads that directly connect cities. Each edge $e$ has a weight $w(e)$ equal to the time required to travel between the two cities. We're also given a vertex $p$, representing our starting location, and a vertex $q$, representing our friend’s starting location. 
To find the optimal meeting point for two people traveling along a weighted graph, we can use Dijkstra's algorithm. We start by computing the shortest paths from both the starting vertices $p$ and $q$ to every other vertex in the graph. Then, we iterate through all the vertices in the graph and compute the sum of the shortest path distances from $p$ and $q$ to each vertex. The vertex with the minimum sum of distances is the optimal meeting point. Analyze the given algorithm and then give its C++ code implementation in the coding workspace provided.

# Logic building

The following is the algorithm that can be used to solve this problem.

**Algorithm** 



Solution to the shortest paths computations problem.

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: Shortest Paths