What is memoization in Java and how can I implement it?

What is memoization in Java and how can I implement it?

Memoization is an optimization technique used to speed up recursive algorithms by storing previously computed results. In Java, you can implement it using a HashMap to cache results.

Can you show me a simple example of memoization in a Fibonacci sequence?

Sure! Here's a simple example:

import java.util.HashMap;

public class Fibonacci {
    private HashMap<Integer, Integer> memo = new HashMap<>();

    public int fib(int n) {
        if (n <= 1) return n;
        if (memo.containsKey(n)) return memo.get(n);
        int result = fib(n - 1) + fib(n - 2);
        memo.put(n, result);
        return result;
    }
}

How does this improve performance compared to a regular recursive approach?

Using memoization reduces the time complexity from exponential O(2^n) to linear O(n) by avoiding redundant calculations.

Are there any downsides to using memoization?

Yes, the main downside is increased memory usage due to storing results, which can be significant for large inputs.