Dynamic Programming Solutions

This repository contains a variety of solutions to problems that utilize the Dynamic Programming (DP) technique. Dynamic Programming is a method for solving problems by breaking them down into smaller subproblems and solving each subproblem just once, storing its result to avoid redundant computations. It is widely used in algorithm design and problem-solving, especially in optimization problems.

About This Repository

The goal of this repository is to provide efficient solutions to various algorithmic challenges that can be solved using Dynamic Programming. Each solution includes an explanation of the approach, the logic behind the implementation, and the actual code.

Whether you're a beginner looking to understand the basics of DP, or an advanced coder aiming to practice and refine your skills, this repository is designed to help you enhance your problem-solving abilities.

Key Concepts

This repository covers the following key Dynamic Programming concepts:

• Memoization (Top-Down Approach): Solving problems recursively and storing the results of subproblems to avoid recomputation.
• Tabulation (Bottom-Up Approach): Iteratively solving subproblems using a table (array) to store intermediate results.
• Optimal Substructure: Breaking down problems into smaller subproblems that can be solved independently.
• Overlapping Subproblems: Reusing previously solved subproblems to improve efficiency.

Features

• Efficient Solutions: Solutions implemented with an emphasis on time complexity optimization.
• Code in Java: The repository is primarily written in Java, utilizing its features for optimal implementation.
• Clear Explanation: Each solution includes a detailed explanation of the approach used, with comments in the code to help users understand the logic.
• Reusable Code: Functions are designed to be modular and reusable for similar problems.

Structure

The repository is organized as follows:

• Each problem is implemented in its own Java file.
• Every file contains a problem description, a solution approach, and the actual code.
• The README.md explains the general concepts and how to run the solutions.

How to Use

1. Clone the Repository

   To get started, clone the repository to your local machine using the following command:

   git clone https://github.com/NirmalsaiswaroopJ/Dynamic-programming.git

2. Run the Solutions Navigate to the directory where the code is stored:

   cd Dynamic-programming

   javac <filename>.java
   java <classname>

3. Learn and Modify