What are some applications of the Fibonacci sequence in C++?

What are some applications of the Fibonacci sequence in C++?

The Fibonacci sequence has several applications in C++, including algorithms for sorting, data structures like heaps, and even in graphics for creating natural-looking patterns.

Can you give me an example of how to implement it in C++?

Sure! Here's a simple implementation of the Fibonacci sequence using recursion in C++:

#include <iostream>
using namespace std;

int fibonacci(int n) {
    if (n <= 1) return n;
    return fibonacci(n - 1) + fibonacci(n - 2);
}

int main() {
    int n = 10; // Example: 10th Fibonacci number
    cout << "Fibonacci of " << n << " is " << fibonacci(n) << endl;
    return 0;
}

What are the limitations of this recursive approach?

The recursive approach can be inefficient for large values of n due to repeated calculations. It has an exponential time complexity of O(2^n). A better approach would be to use memoization or an iterative method.

How can I optimize it using memoization?

You can optimize the Fibonacci function using memoization by storing previously calculated values in an array. Here's an example:

#include <iostream>
#include <vector>
using namespace std;

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

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