Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable where the problem can be broken down into overlapping subproblems that can be solved independently.

Basic Concepts

  • Optimal Substructure: The problem can be solved by combining solutions to non-overlapping subproblems.
  • Overlapping Subproblems: The space of subproblems must be small, so that a recursive algorithm solves each subproblem only once.

Common Problems

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

Example: Fibonacci Numbers

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1.

def fibonacci(n):
    if n <= 1:
        return n
    else:
        return fibonacci(n-1) + fibonacci(n-2)

print(fibonacci(10))

Resources

For more information on dynamic programming, you can refer to our comprehensive guide on Algorithms.

Dynamic Programming