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

# Logic building
In order to solve part (a) of the problem, we'll first begin by analyzing the algorithm below. After that, we'll move on to coding implementation.

**(a) Algorithm to compute $k$:**

- Initialize two pointers, left and right, to the beginning and end of the array, respectively ($left = 0, right = n - 1$).
- While $left < right$:
   - Calculate the middle index: $mid = (left + right) // 2$.
   - If $A[mid] > A[right]$, then the pivot (smallest element) is in the right half. Update the left pointer: $left = mid + 1$.
   - Else, the pivot is in the left half. Update the right pointer: $right = mid$.
- Return the index $left$ as $k$.
- Time complexity: $O( \log n)$, as we are essentially performing a binary search.

# Coding workspace for part (a)
The provided workspace contains the required libraries. Try to code the solution for the task (a) mentioned above.
 

Test your knowledge of recursion by solving this exercise.

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: Recursion

Logic building