What is the difference between memoization and dynamic programming?

What is the difference between memoization and dynamic programming?

Memoization is an optimization technique that stores the results of expensive function calls and returns the cached result when the same inputs occur again. Dynamic programming, on the other hand, is a method for solving complex problems by breaking them down into simpler subproblems, solving each subproblem just once, and storing their solutions.

Can you give me an example of each?

Sure! For memoization, consider the Fibonacci sequence. Instead of recalculating Fibonacci(n) multiple times, you store the results of Fibonacci(n-1) and Fibonacci(n-2) in a cache. For dynamic programming, the same Fibonacci problem can be solved using a bottom-up approach, where you iteratively calculate Fibonacci numbers from the base cases up to n.

When should I use one over the other?

Use memoization when you have a recursive solution that recalculates the same values multiple times. Use dynamic programming when you can solve the problem iteratively and want to optimize both time and space complexity.

Are there any downsides to using these techniques?

Yes, memoization can lead to high memory usage if the cache grows large, while dynamic programming can be complex to implement for certain problems. It's important to analyze the problem to choose the right approach.