What is memoization in C++ dynamic programming?

Can you explain what memoization is in the context of C++ dynamic programming?

Sure! Memoization is an optimization technique used in dynamic programming to store the results of expensive function calls and reuse them when the same inputs occur again.

How does memoization improve performance in C++?

It reduces the time complexity by avoiding repeated calculations for the same inputs, which can significantly speed up algorithms like Fibonacci sequence calculations.

Can you provide a simple example of memoization in C++?

Absolutely! Here's a basic example:

#include <iostream>
#include <vector>

int fib(int n, std::vector<int>& memo) {
    if (n <= 1) return n;
    if (memo[n] != -1) return memo[n];
    memo[n] = fib(n - 1, memo) + fib(n - 2, memo);
    return memo[n];
}

int main() {
    int n = 10;
    std::vector<int> memo(n + 1, -1);
    std::cout << "Fibonacci of " << n << " is " << fib(n, memo);
    return 0;
}

This code uses a vector to store previously computed Fibonacci values.

What are the limitations of using memoization?

While memoization is powerful, it can consume a lot of memory if the input space is large, and it may not be suitable for problems with a high number of unique states.