**FACTORIAL_COPY**

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**FACTORIAL**

The C++ program featured in this tutorial web page computes N factorial (**N!**) using recursion and using iteration. If N is a natural number, then N! is the product of exactly one instance of each unique natural number which is less than or equal to N. If N is zero, then N! is one.

*To view hidden text inside of the preformatted text boxes below, scroll horizontally.*

0! := 1. // base case: when N is zero N! := N * (N - 1)! // recursive case: when N is a natural number

**Software Application Files**

C++ source file: https://github.com/karlinarayberinger/karlina_object_ultimate_starter_pack/blob/main/factorial.cpp

plain-text file: https://github.com/karlinarayberinger/karlina_object_ultimate_starter_pack/blob/main/factorial_output.txt

**Program Compilation & Execution**

STEP_0: Copy and paste the C++ source code into a new text editor document and save that document as the following file name:

factorial.cpp

STEP_1: Open a Unix command line terminal application and set the current directory to wherever the C++ is located on the local machine (e.g. Desktop).

cd Desktop

STEP_2: Compile the C++ file into machine-executable instructions (i.e. object file) and then into an executable piece of software named **app** using the following command:

g++ factorial.cpp -o app

STEP_3: If the program compilation command does not work, then use the following command to install the C++ compiler:

sudo apt install build-essential

STEP_4: After running the **g++** command, run the executable file using the following command:

./app

STEP_5: Once the application is running, the following prompt will appear:

Enter a natural number which is no larger than 12:

STEP_6: Enter a value for N using the using the keyboard.

STEP_7: Observe program results on the command line terminal and in the output file.

**Program Source Code**

C++ source file: https://github.com/karlinarayberinger/karlina_object_ultimate_starter_pack/blob/main/factorial.cpp

*When copy-pasting the source code from the preformatted text box below into a text editor document, remove the spaces between the angle brackets and the library names in the preprocessing directives code block.*

/** * file: factorial.cpp * type: C++ (source file) * date: 22_JULY_2022 * author: Karlina Ray Beringer * license: PUBLIC_DOMAIN */ /* preprocessing directives */ #include < iostream > // command line input and output #include < fstream > // file input and 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 using a recursive algorithm. * Assume that N is an integer value and that output is an output stream object. * For each function call, print an algebriac 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 no smaller than 1 and when N is no larger than MAXIMUM_N. */ int compute_factorial_of_N_using_recursion(int N, std::ostream & output) { // base case: if N is less than 1 or if N is greater than MAXIMUM_N, then return 1. if ((N < 1) || (N > MAXIMUM_N)) { output << "\n\nfactorial(" << N << ") = 1. // base case"; return 1; } // recursive case: if N is not less than 1 and if N is not greater than MAXIMUM_N, then 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 natural number, then N! is the product of exactly one instance * of each unique natural number which is less than or equal to N. * N! := N * (N - 1) * (N - 2) * (N - 3) * ... * 3 * 2 * 1. * * 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 " * " to the output stream. if (i > 1) F *= i - 1; // If i is larger than 1, then 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, * then create a new file named factorial_output.txt. * * Then 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 less than 0 or larger than MAXIMUM_N, then set N to 0. N = ((N < 0) || (N > MAXIMUM_N)) ? 0 : N; // 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; }

**Sample Program Output**

plain-text file: https://github.com/karlinarayberinger/karlina_object_ultimate_starter_pack/blob/main/factorial_output.txt

-------------------------------- Start Of Program -------------------------------- The value which was entered for N is 12. N := 12. -------------------------------- Computing factorial N using recursion: factorial(12) = 12 * factorial(11). // recursive case factorial(11) = 11 * factorial(10). // recursive case factorial(10) = 10 * factorial(9). // recursive case factorial(9) = 9 * factorial(8). // recursive case factorial(8) = 8 * factorial(7). // recursive case factorial(7) = 7 * factorial(6). // recursive case factorial(6) = 6 * factorial(5). // recursive case factorial(5) = 5 * factorial(4). // recursive case factorial(4) = 4 * factorial(3). // recursive case factorial(3) = 3 * factorial(2). // recursive case factorial(2) = 2 * factorial(1). // recursive case factorial(1) = 1 * factorial(0). // recursive case factorial(0) = 1. // base case A := factorial(12) = 479001600. // 12! := 479001600. -------------------------------- Computing factorial N using iteration: factorial(12) = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 1. B := factorial(12) = 479001600. // 12! := 479001600. -------------------------------- End Of Program --------------------------------

This web page was last updated on 22_JULY_2022. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.

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This web page was last updated on 09_SEPTEMBER_2022. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.