When to Use Dynamic Programming (DP)?
Dynamic programming is an optimization technique used when solving problems that consists of the following characteristics:
1. Optimal Substructure:
Optimal substructure means that we combine the optimal results of subproblems to achieve the optimal result of the bigger problem.
Example:
Consider the problem of finding the minimum cost path in a weighted graph from a source node to a destination node. We can break this problem down into smaller subproblems:
- Find the minimum cost path from the source node to each intermediate node.
- Find the minimum cost path from each intermediate node to the destination node.
The solution to the larger problem (finding the minimum cost path from the source node to the destination node) can be constructed from the solutions to these smaller subproblems.
2. Overlapping Subproblems:
The same subproblems are solved repeatedly in different parts of the problem.
Example:
Consider the problem of computing the Fibonacci series. To compute the Fibonacci number at index n, we need to compute the Fibonacci numbers at indices n-1 and n-2. This means that the subproblem of computing the Fibonacci number at index n-1 is used twice in the solution to the larger problem of computing the Fibonacci number at index n.
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.
Dynamic Programming
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