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

# Task
An addition chain for an integer $n$ is an increasing sequence of integers that starts with 1 and ends with $n$, such that each entry after the first is the sum of two earlier entries. More formally, the integer sequence $x_0 < x_1 < x_2 < ··· < x_l$ is an addition chain for $n$ if and only if 
- $x_0 = 1$ 
- $x_l = n$ 
- For every index $k > 0$, there are indices $i <= j < k$ such that $x_k = x_i + x_j$

The $l$ength of an addition chain is the number of elements minus 1; we don’t bother to count the first entry. For example, $1, 2, 3, 5, 10, 20, 23, 46, 92, 184, 187, 374$ is an addition chain for $374$ of length $11$.

We described a recursive backtracking algorithm to compute a minimum length addition chain for a given positive integer $n$. Don’t analyze or optimize your algorithm’s running time, except to satisfy your own curiosity. A correct algorithm whose running time is exponential in $n$ is sufficient for full credit. Then implement the algorithm to write code in C++.


Solution to the problem related to backtracking.

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: Backtracking

Task