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 been hired to store a sequence of $n$ books on shelves in a library. The order of the books is fixed by the cataloging system and can't be changed; each shelf must store a contiguous interval of the given sequence of books. We are given two arrays $H[1 .. n]$ and $T[1 .. n]$, where $H[i]$ and $T[i]$ are respectively the height and thickness of the $i$-th book in the sequence. All shelves in this library have the same length $L$; the total thickness of all books on any single shelf can't exceed $L$. Suppose all the books have the same height $h$ and the shelves have heights larger than $h$, so every book fits on every shelf. Analyze the greedy algorithm to store the books in as few shelves as possible and write its code in the coding workspace given below.

# Logic building
Let's go through the greedy algorithm so that we can easily write its code. Let's begin!

In the case where all the books have the same height $h$ and the shelves have heights larger than $h$, so every book fits on every shelf, we can use the following greedy algorithm to store the books in as few shelves as possible.

**Algorithm**

- Initialize the count of shelves, $shelf_-count$, to $1$.
- Initialize the current shelf thickness, $current_-thickness$, to $0$.
- Iterate through the books, for each book $i$ ($1$ to $n$):
    - Check if the thickness of the current book, $T[i]$, can be added to the current shelf without exceeding the length $L$. If yes, add the book to the current shelf by updating $current_-thickness$ with $current_-thickness + T[i]$.
    - If the book doesn't fit in the current shelf, increment the $shelf_-count$, and reset the $current_-thickness$ to the thickness of the current book $T[i]$.
- Return the $shelf_-count$.

This greedy algorithm works by trying to fill each shelf to its maximum capacity before moving on to the next shelf. Since the books are in a fixed order and have the same height, we can place as many books as possible on each shelf until their total thickness exceeds the shelf length.

# Time complexity
The time complexity of this algorithm is $O(n)$, where $n$ is the number of books, as we iterate through the books once. The space complexity is $O(1)$ since we only use a few variables to keep track of the current shelf state and the total number of shelves used.

# Solution

The following coding workspace contains the solution to the problem and its line-by-line explanation.

Solution to the problem related to greedy algorithms.

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: Greedy Algorithms

Task