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.
Key Concepts
- Memoization: Store the results of expensive function calls and return the cached result when the same inputs occur again.
- Tabulation: Build up the solution iteratively using a table.
- Optimal Substructure: The optimal solution to the problem can be constructed from optimal solutions of its subproblems.
Example
Let's consider the Fibonacci sequence as an example.
- Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
- The Fibonacci number F(n) is the sum of the two preceding ones: F(n) = F(n-1) + F(n-2).
Dynamic Programming approach:
- Base cases: F(0) = 0, F(1) = 1
- Recursive relation: F(n) = F(n-1) + F(n-2)
Fibonacci Sequence
Resources
For further reading on Dynamic Programming, you can check out our Advanced Algorithms guide.