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’ve just been appointed as the new organizer of the first annual mandatory
holiday party at Giggle (a subsidiary of Abugida). Giggle employees are
organized into a strict hierarchy a tree with the company president at the
root. The all-knowing oracles in Human Resources have assigned a real
number to each employee measuring how “fun” the employee is. To keep
things social, there is one restriction on the guest list: 

An employee cannot attend the party if their immediate supervisor is also present. On the other hand, the president of the company must attend the party, even though she has a negative fun rating; it’s her company, after all. 

Given an algorithm that
makes a guest list for the party that maximizes the sum of the “fun” ratings
of the guests, write the code in the coding playground.

# Logic building
Before jumping to the coding implementation. let's understand the algorithm to solve this problem.

We can use a dynamic programming approach! We'll represent the employee hierarchy as a tree where each node contains the employee's fun rating. The algorithm will be based on a recursive function that traverses the tree and calculates the maximum fun for each subtree, considering two cases: when the root of the subtree is included in the guest list or when it's excluded.

Here's a step-by-step algorithm to make a guest list for the party:

- Create a function `max_fun(node)` that takes a tree node as input. This node represents an employee, and contains the employee's fun rating and a list of children nodes (subordinates).
- **Base case:** If the given node is null (no employee), return `0`.
- Calculate the maximum fun when the current employee (node) is included in the guest list:
   - Initialize a variable `include_fun` with the fun rating of the current employee.
   - Iterate over the children of the current employee. For each child, iterate over its children (the current employee's grandchildren) and call the `max_fun` function. Sum up the results and add it to `include_fun`.
- Calculate the maximum fun when the current employee (node) is excluded from the guest list:
    - Initialize a variable `exclude_fun` with `0`.
    - Iterate over the children of the current employee. For each child, call the `max_fun` function. Sum up the results and store it in `exclude_fun`.
- Return the maximum value between `include_fun` and `exclude_fun`.
- Call the function `max_fun(root)` to start the algorithm with the company president as the root.

# Coding workspace
As we now understand the basic algorithm to solve the problem, let's implement this algorithm in the following coding workspace and write code in C++:


Challenge yourself by solving a coding-based question related to dynamic programming.

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

Challenge: Dynamic Programming

Task