Approaches of Dynamic Programming (DP)
Dynamic programming can be achieved using two approaches:
1. Top-Down Approach (Memoization):
In the top-down approach, also known as memoization, we start with the final solution and recursively break it down into smaller subproblems. To avoid redundant calculations, we store the results of solved subproblems in a memoization table.
Let’s breakdown Top down approach:
- Starts with the final solution and recursively breaks it down into smaller subproblems.
- Stores the solutions to subproblems in a table to avoid redundant calculations.
- Suitable when the number of subproblems is large and many of them are reused.
2. Bottom-Up Approach (Tabulation):
In the bottom-up approach, also known as tabulation, we start with the smallest subproblems and gradually build up to the final solution. We store the results of solved subproblems in a table to avoid redundant calculations.
Let’s breakdown Bottom-up approach:
- Starts with the smallest subproblems and gradually builds up to the final solution.
- Fills a table with solutions to subproblems in a bottom-up manner.
- Suitable when the number of subproblems is small and the optimal solution can be directly computed from the solutions to smaller subproblems.
Dynamic Programming or DP
Dynamic Programming is a method used in mathematics and computer science to solve complex problems by breaking them down into simpler subproblems. By solving each subproblem only once and storing the results, it avoids redundant computations, leading to more efficient solutions for a wide range of problems. This article provides a detailed exploration of dynamic programming concepts, illustrated with examples.
Table of Content
- What is Dynamic Programming ?
- How Does Dynamic Programming Work?
- Examples of Dynamic Programming
- When to Use Dynamic Programming?
- Approaches of Dynamic Programming
- Dynamic Programming Algorithm
- Advantages of Dynamic Programming
- Applications of Dynamic Programming
- Learn Basic of Dynamic Programming
- Advanced Concepts in Dynamic Programming
- Dynamic Programming Problems