Welcome to DPX, your go-to repository for learning and practicing dynamic programming (DP) concepts through well-explained problems and solutions.
Dynamic programming is a powerful algorithmic technique used to solve problems by breaking them down into simpler subproblems, solving each subproblem just once, and storing their solutions — usually using a table — to avoid redundant computations. It is especially useful for optimization problems and problems with overlapping subproblems and optimal substructure properties.
You will learn when to apply DP, such as in problems involving sequences, subsets, and resource allocation, where naive recursive approaches would be too slow.
By studying the examples and explanations in this repository, you will:
- Understand the core concepts of dynamic programming, including memoization and tabulation.
- Learn to identify problems that can be solved using DP.
- Gain practical experience implementing classical DP algorithms like Fibonacci sequence and 0/1 Knapsack.
- Analyze the time and space complexity improvements over naive recursive solutions.
- Build a foundation to tackle more advanced DP problems confidently.
This repo currently contains the following folders:
-
explanations/
Markdown files that explain classic dynamic programming problems, including theory and approach.fibonacci.md- Explanation of the Fibonacci sequence using DP.knapsack_01.md- Explanation of the 0/1 Knapsack problem.longest_common_subsequence.md- Explanation of the Longest Common Subsequence problem.longest_increasing_subsequence.md- Explanation of the Longest Increasing Subsequence problem.
-
problems/
Python implementations of the corresponding problems described in the explanations folder.fibonacci.py- DP solution for the Fibonacci sequence.knapsack_01.py- DP solution for the 0/1 Knapsack problem.longest_common_subsequence.py- DP solution for Longest Common Subsequence.longest_increasing_subsequence.py- DP solution for Longest Increasing Subsequence.
Clone the repository:
git clone https://github.com/PyPartners/dpx.git
cd dpxRun the Python scripts from the problems/ folder using:
python problems/fibonacci.pyor
python problems/knapsack_01.pyor
python problems/longest_common_subsequence.pyor
python problems/longest_increasing_subsequence.pyTo deepen your understanding of dynamic programming, you might find these resources helpful:
- Dynamic Programming on GeeksforGeeks
- TopCoder Tutorial: Dynamic Programming
- HackerRank Challenges: Dynamic Programming
We plan to continuously add:
- More classic and advanced dynamic programming problems
- Optimized solutions and alternative approaches
- Visual explanations and diagrams
- Integration with tutorials and educational content
Stay tuned!
Contributions are welcome! Feel free to open issues or submit pull requests to improve the explanations or add new problem solutions.
This project is licensed under the MIT License. See the LICENSE file for details.
Happy Coding! 🚀