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Are you planning to take a course in data science? Do you want to create effective computer programming solutions that give accurate results? Are you a computer science beginner?

If you just said yes to any of these questions, then you must learn dynamic programming. It is a powerful technique used in computer science to solve certain categories of problems. It follows a simple concept - divide a problem into sub-parts, solve every sub-part one by one and save the solution of a sub-part to solve the subsequent sub-parts. This is done to prevent repetitive calculations.

Dynamic programming is a popular concept for solving optimisation problems, that is, when you are finding the minimum or maximum solution to a problem. With dynamic programming, you can definitely find the solution to a problem if its solution exists. For example, calculating the nth term of a Fibonacci series, 0/1 Knapsack problem, longest common sequence, palindrome sequence, matrix chain multiplication, etc. are some of the common examples of dynamic programming.

- Dynamic Programming vs Divide and Conquer Method
- Fibonacci sequence
- Matrix Chain Multiplication
- Matrix Chain Multiplication Example
- Matrix Chain Multiplication Algorithm
- Longest Common Sequence
- Longest Common Sequence Algorithm
- 0/1 Knapsack Problem

- Ugly numbers
- Fibonacci numbers
- nth Catalan Number
- Binomial Coefficient
- Largest divisible pairs subset
- Permutation Coefficient
- Tiling Problem
- Gold Mine Problem
- Maximum games played by the winner
- Coin change problem
- Friends Pairing Problem
- Subset Sum Problem
- Bell Numbers (Number of ways to Partition a Set)
- Subset with sum divisible by m
- Perfect Sum Problem (Print all subsets with the given sum)
- Cutting a Rod
- Tiling with Dominoes
- Painting Fence Algorithm

These are the steps the dynamic programming adheres to:

- You start with breaking down a complicated problem into smaller subproblems.
- Then, you have to identify the most effective solution to these sub-problems.
- You need to store the outcomes from subproblems. The process of keeping the outcomes of subproblems is also known as memorisation.
- Now, you can reuse the solutions so that similar sub-problems are calculated repeatedly.
- Then, find the solution to the complicated issue.

The steps listed above are the most fundamental steps to using dynamic programming. You can use dynamic programming for applications to programs that have characteristics like:

The problems that have overlapped sub-problems as well as optimal substructures. This is because optimal substructure implies that the optimisation problem's solution is obtained by combining the best solution for all subproblems.

In the scenario for dynamic programming, the complexity of space would be increased because we are keeping the intermediate results, but you will reduce the time complexity.

There are two ways to hover dynamic programming:

**Top-down method**

The top-down approach is based on the memorisation method, and the bottom-up approach is based on the tabulation technique. Memorisation is the total of both recursive and caching. Recursion calls the function by itself while caching stores the intermediate results.

**Bottom-Up method**

The bottom-up method is one of the methods employed to implement dynamic programming. It employs the tabulation technique to implement the dynamic programming method. It addresses the same types of issues, but it eliminates repetition.

If we eliminate the repetition, you will not have a stack overflow problem, and there is no overhead associated with function recursive. In this tabulation technique, we tackle the issues and save the results in a matrix.

A dynamic programming online tutor will help you grasp all the concepts with ease. The programming tutor will provide you with step by step explanations so that you can understand what dynamic programming is, why it is used and how you can use it to optimise solutions. You will be solving dynamic programming problems with your tutor regularly to strengthen your conceptual understanding.

Our tutors online will create a study plan for you based on your learning requirements. They will include doubt-solving sessions, revision sessions, practice tests and full tests to ensure that you make the most of our online tutoring program.

If you are studying a computer science course or if you are preparing for a certain certification, our tutors will guide you accordingly and prepare you for tests, assessments and examinations. They will explain the marking criteria and help you increase your problem-solving speed so that you can score maximum marks.

Dynamic Programming questions are often asked in coding interviews to test your knowledge about problem-solving and finding the optimal solution in a small time. Therefore, it is recommended that students must practise dynamic programming before going for an interview in the field of software development, software engineering or teaching.

**Experienced Tutors: **Each dynamic programming tutor at CrunchGrade is well-experienced. You can know more about their teaching experience through their tutor profile on our website. This profile also includes student ratings that specify what their students think of them.

**Personalised Tutoring Plans: **We will leave no stone unturned in creating a learning program that suits your needs. You can schedule the classes as per your availability and convenience. Take weekly sessions or everyday tutoring based on how you want to learn dynamic programming.

**Live, Online Classes: **We do not provide any pre-recorded study material in terms of online dynamic programming tuition. Every class will be live where you can interact with the tutor and actively participate in the study session.

**Affordable Prices: **When it comes to learning with CrunchGrade, tuition fees won’t be a problem because we provide highly-affordable online classes to students. Our tutors charge minimal rates per hour so that every student can afford to enhance their computer programming skills.