C++: Dynamic Programming vs Recursion

What is the difference between dynamic programming and recursion in C++?

Dynamic programming is an optimization technique that solves problems by breaking them down into simpler subproblems and storing the results to avoid redundant calculations. Recursion, on the other hand, is a method where a function calls itself to solve smaller instances of the same problem.

Can you give me an example of a problem that can be solved using both methods?

Sure! The Fibonacci sequence is a classic example. You can calculate it using recursion, but it can be inefficient due to repeated calculations. Dynamic programming can solve it more efficiently by storing previously computed values.

Which method is generally more efficient?

Dynamic programming is generally more efficient for problems with overlapping subproblems, as it avoids redundant calculations by storing results. Recursion can be simpler to implement but may lead to exponential time complexity in such cases.

Are there any downsides to using dynamic programming?

Yes, dynamic programming can require more memory to store the results of subproblems, which may not be ideal for problems with large input sizes. Additionally, it can be more complex to implement compared to straightforward recursion.