/**
 * file: factorial.cpp
 * type: C++ (source file)
 * date: 14_JUNE_2023
 * author: karbytes
 * license: PUBLIC_DOMAIN
 */

/* preprocessing directives */
#include <iostream> // library for defining objects which handle command line input and command line output
#include <fstream> // library for defining objects which handle file input and file output
#define MAXIMUM_N 12 // constant which represents maximum N value

/* function prototypes */
int compute_factorial_of_N_using_recursion(int N, std::ostream & output);
int compute_factorial_of_N_using_iteration(int N, std::ostream & output);

/**
 * Compute N factorial (N!) using a recursive algorithm.
 * 
 * Assume that N is an integer value and that output is an output stream object.
 * 
 * For each compute_factorial_of_N_using_recursion function call, 
 * print an algebraic expression which represents N factorial.
 * 
 * 0! := 1. // base case: when N is smaller than 1 or when N is larger than MAXIMUM_N.
 * N! := N * (N - 1)! // recursive case: when N is larger than or equal to 1 and when N is smaller than or equal to MAXIMUM_N.
 */
int compute_factorial_of_N_using_recursion(int N, std::ostream & output)
{
    // base case: if N is smaler than 1 or if N is larger than MAXIMUM_N, return 1.
    if ((N < 1) || (N > MAXIMUM_N))
    {
        output << "\n\nfactorial(" << N << ") = 1. // base case";
        return 1;
    }
    // recursive case: if N is larger than or equal to 1 and if N is smaller than or equal to MAXIMUM_N, return N multiplied by (N - 1) factorial.
    else
    {
        output << "\n\nfactorial(" << N << ") = " << N << " * factorial(" << N - 1 << "). // recursive case" ;
        return N * compute_factorial_of_N_using_recursion(N - 1, output);
    }
}

/**
 * Compute N factorial using an iterative algorithm.
 * 
 * Assume that N is an integer value and that output is an output stream object.
 * 
 * For each while loop iteration, i,  print the ith multiplicative term of N factorial.
 * 
 * ---------------------------------------------------------------------------------------------------------------------------------------------------------------
 * If N is a larger than or equal to 1 and if N is smaller than or equal to MAXIMUM_N, 
 * N! is the product of exactly one instance of each unique natural number which is smaller than or equal to N. 
 * 
 * N! := N * (N - 1) * (N - 2) * (N - 3) * ... * 3 * 2 * 1. // if N is an arbitrarily large natural number (which, in this line, is equal to or larger than 7)
 * ---------------------------------------------------------------------------------------------------------------------------------------------------------------
 * 
 * If N is zero, then N! is one.
 * 
 * 0! := 1.
 * ---------------------------------------------------------------------------------------------------------------------------------------------------------------
 */
int compute_factorial_of_N_using_iteration(int N, std::ostream & output)
{
    int i = 0, F = 0; 
    i = ((N > 0) && (N <= MAXIMUM_N)) ? N : 0; 
    F = (N > 0) ? N : 1; 
    output << "\n\nfactorial(" << i << ") = ";
    while (i > 0) // Execute the code block encapsulated by the while loop while the condition "i > 0" is true.
    {
        output << i << " * "; // Print the value of i followed by " * " to the output stream.
        if (i > 1) F *= i - 1; // If i is larger than 1, multiply F by (i - 1).
        i -= 1; // Decrement i by 1.
    }
    output << "1.";
    return F;
}

/* program entry point */
int main()
{
    // Declare three int type variables and set each of their initial values to 0.
    int N = 0, A = 0, B = 0;

    // Declare a file output stream object.
    std::ofstream file;

    /**
     * If factorial_output.txt does not already exist in the same directory as factorial.cpp, 
     * create a new file named factorial_output.txt.
     * 
     * Open the plain-text file named factorial_output.txt 
     * and set that file to be overwritten with program data.
     */
    file.open("factorial_output.txt");

    // Print an opening message to the command line terminal.
    std::cout << "\n\n--------------------------------";
    std::cout << "\nStart Of Program";
    std::cout << "\n--------------------------------";

    // Print an opening message to the file output stream.
    file << "--------------------------------";
    file << "\nStart Of Program";
    file << "\n--------------------------------";

    // Print "Enter a nonnegative integer which is no larger than {MAXIMUM_N}: " to the command line terminal.
    std::cout << "\n\nEnter a nonnegative integer which is no larger than " << MAXIMUM_N << ": ";

    // Scan the command line terminal for the most recent keyboard input value.
    std::cin >> N;

    // Print "The value which was entered for N is {N}." to the command line terminal.
    std::cout << "\nThe value which was entered for N is " << N << ".";

    // Print "The value which was entered for N is {N}." to the file output stream.
    file << "\n\nThe value which was entered for N is " << N << ".";

    // If N is smaller than 0 or if N is larger than MAXIMUM_N, set N to 0.
    N = ((N < 0) || (N > MAXIMUM_N)) ? 0 : N; // A tertiary operation (using the tertiary operator (?)) is an alternative to using if-else statements.

    // Print "N := {N}." to the command line terminal.
    std::cout << "\n\nN := " << N << ".";

    // Print "N := {N}." to the file output stream.
    file << "\n\nN := " << N << ".";

    // Print a horizontal line to the command line terminal.
    std::cout << "\n\n--------------------------------";

    // Print a horizontal line to the command line terminal.
    file << "\n\n--------------------------------";

    // Print "Computing factorial N using recursion:" to the command line terminal.
    std::cout << "\n\nComputing factorial N using recursion:";

    // Print "Computing factorial N using recursion:" to the file output stream.
    file << "\n\nComputing factorial N using recursion:";

    // Compute N factorial using recursion, store the result in A, and print each function call in the recursive function call chain to the command line terminal.
    A = compute_factorial_of_N_using_recursion(N, std::cout);

    // Compute N factorial using recursion and print each function call in the recursive function call chain to the file output stream.
    compute_factorial_of_N_using_recursion(N, file);

    // Print the value of A to the command line terminal.
    std::cout << "\n\nA = factorial(" << N << ") = " << A << ". // " << N << "! = " << A << ".";

    // Print the value of A to the file output stream.
    file << "\n\nA = factorial(" << N << ") = " << A << ". // " << N << "! = " << A << ".";

    // Print a horizontal line to the command line terminal.
    std::cout << "\n\n--------------------------------";

    // Print a horizontal line to the command line terminal.
    file << "\n\n--------------------------------";

    // Print "Computing factorial N using iteration:" to the command line terminal.
    std::cout << "\n\nComputing factorial N using iteration:";

    // Print "Computing factorial N using iteration:" to the file output stream.
    file << "\n\nComputing factorial N using iteration:";

    // Compute N factorial using iteration and print each multiplicative term of N! to the command line terminal.
    B = compute_factorial_of_N_using_iteration(N, std::cout);

    // Compute N factorial using iteration and print each multiplicative term of N! to the file output stream.
    compute_factorial_of_N_using_iteration(N, file);

    // Print the value of B to the command line terminal.
    std::cout << "\n\nB = factorial(" << N << ") = " << B << ". // " << N << "! = " << B << ".";

    // Print the value of B to the file output stream.
    file << "\n\nB = factorial(" << N << ") = " << B << ". // " << N << "! = " << B << ".";

    // Print a closing message to the command line terminal.
    std::cout << "\n\n--------------------------------";
    std::cout << "\nEnd Of Program";
    std::cout << "\n--------------------------------\n\n";

    // Print a closing message to the file output stream.
    file << "\n\n--------------------------------";
    file << "\nEnd Of Program";
    file << "\n--------------------------------";

    // Close the file output stream.
    file.close();

    // Exit the program.
    return 0;
}