Dynamic Programming (DP) is a method for solving a complex problem by breaking it down into a collection of simpler subproblems. It is applicable where the problem can be broken down into overlapping subproblems that can be solved independently.

Basic Concept

Dynamic Programming is applicable in scenarios where:

  • The problem can be broken down into overlapping subproblems.
  • Optimal substructure property is present.

Example

Consider the Fibonacci series. The series is defined as:

F(0) = 0
F(1) = 1
F(n) = F(n-1) + F(n-2) for n > 1

The Fibonacci series can be computed using a recursive approach or an iterative approach. However, the iterative approach is more efficient due to the overlapping subproblems.

Why Use Dynamic Programming?

  • Efficiency: Dynamic Programming provides an efficient way to solve problems by breaking them down into smaller subproblems.
  • Optimal Substructure: It is useful in solving problems that exhibit optimal substructure property.

Common Dynamic Programming Problems

  • Fibonacci Series
  • Longest Common Subsequence
  • Knapsack Problem
  • Matrix Chain Multiplication

Resources

For more information on Dynamic Programming, you can read our detailed Dynamic Programming Guide.

Dynamic Programming Concept