Can you explain the basics of principles and approaches of functional programming?

Functional programming (FP) is a programming paradigm based on the use of functions as the main building blocks and avoiding changing state and side effects.

Main principles and approaches of FP:

• Pure functions: a function always returns the same result for the same inputs and does not modify external state.
• Immutability: data does not change after creation; instead, new copies are created with modifications.
• Higher-order functions: functions that accept other functions as arguments or return them.
• Recursion instead of loops: recursion is often used for repeating operations.
• Absence of side effects: functions should not modify external variables, files, databases, etc.

Example in C++ (using lambda functions):

#include <iostream>
#include <vector>
#include <algorithm>

int main() {
    std::vector<int> numbers = {1, 2, 3, 4, 5};
    
    // Higher-order function: passing a lambda to std::for_each
    std::for_each(numbers.begin(), numbers.end(), [](int n) {
        std::cout << n * 2 << " ";
    });
    
    return 0;
}

Here, we do not modify the original vector but simply apply a function to each element for output, which aligns with the ideas of a functional approach.