Step by Step solution about How to resolve the algorithm First-class functions step by step in the C++ programming language

In this snippet, the goal is to compose functions and evaluate them on a set of input numbers.

Specifically, it combines functions from two vectors, A and B, using a template function called compose to create a new set of composed functions, which are stored in the composedFuns vector.

Then, for each input number in the exNums vector, it evaluates each composed function and prints the result. Here's a step-by-step explanation:

1. Function Composition Template (compose):

   • This template function takes three generic type parameters: A, B, and C. It is used to create a new function that composes two other functions.
   • The input to the new function is of type A, and the output is of type C.
   • The composition is done by applying the function g(x) to the input x, and then applying the function f(g(x)) to the result.

2. Vector of Functions (A and B):

   • A and B are vectors of function objects (FunType).
   • A contains functions like sin, cos, tan, and a lambda function that cubes its input.
   • B contains functions like asin, acos, atan, and a lambda function that takes the cube root of its input.

3. Composing Functions (transform):

   • The transform function is used to create the composedFuns vector.
   • It takes three iterators: the beginning of B, the beginning of A, and an output iterator (back_inserter(composedFuns)).
   • It calls the compose template function with the appropriate function objects from A and B and stores the result in composedFuns.

4. Evaluating Composed Functions:

   • The program iterates over the exNums vector, which contains input numbers for evaluation.
   • For each number, it iterates over the composedFuns vector.
   • For each composed function, it evaluates the function on the input number and prints the result.

5. Output Format:

   • The output follows this format for each composed function and input number: f\u207B\u00B9.f(num), where f\u207B is the composed function, and num is the input number.

#include <functional>
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
 
using std::cout;
using std::endl;
using std::vector;
using std::function;
using std::transform;
using std::back_inserter;

typedef function<double(double)> FunType;

vector<FunType> A = {sin, cos, tan, [](double x) { return x*x*x; } };
vector<FunType> B = {asin, acos, atan, [](double x) { return exp(log(x)/3); } };

template <typename A, typename B, typename C>
function<C(A)> compose(function<C(B)> f, function<B(A)> g) {
    return [f,g](A x) { return f(g(x)); };
}

int main() {
    vector<FunType> composedFuns;
    auto exNums = {0.0, 0.2, 0.4, 0.6, 0.8, 1.0};

    transform(B.begin(), B.end(),
                A.begin(),
                back_inserter(composedFuns),
                compose<double, double, double>);

    for (auto num: exNums)
        for (auto fun: composedFuns)
            cout << u8"f\u207B\u00B9.f(" << num << ") = " << fun(num) << endl;

    return 0;
}