What are some examples of memoization in C++?

Can you explain what memoization is in C++?

Memoization is an optimization technique used to speed up function calls by storing the results of expensive function calls and reusing them when the same inputs occur again.

Can you give me an example of memoization in C++?

Sure! Here's a simple example using Fibonacci numbers:

#include <iostream>
#include <unordered_map>

std::unordered_map<int, int> memo;

int fibonacci(int n) {
    if (n <= 1) return n;
    if (memo.find(n) != memo.end()) return memo[n];
    memo[n] = fibonacci(n - 1) + fibonacci(n - 2);
    return memo[n];
}

int main() {
    int n = 10;
    std::cout << "Fibonacci of " << n << " is " << fibonacci(n);
    return 0;
}

How does this example improve performance?

This example improves performance by avoiding redundant calculations. Without memoization, the Fibonacci function would have exponential time complexity, but with memoization, it reduces to linear time complexity.

Are there other use cases for memoization?

Yes, memoization can be used in various scenarios, such as dynamic programming problems, caching results of API calls, and optimizing recursive algorithms.