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.
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0! := 1. // base case: when N is zero N! := N * (N - 1)! // recursive case: when N is any natural number
SOFTWARE_APPLICATION_COMPONENTS
C++_source_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_summer_2023_starter_pack/main/factorial.cpp
plain-text_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_summer_2023_starter_pack/main/factorial_output.txt
PROGRAM_COMPILATION_AND_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++ program file 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 commands (in top-down order) to install the C/C++ compiler (which is part of the GNU Compiler Collection (GCC)):
sudo apt install build-essential
sudo apt-get install g++
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 nonnegative integer which is no larger than 12:
STEP_6: Enter a value for N using the keyboard.
STEP_7: Observe program results on the command line terminal and in the output file.
PROGRAM_SOURCE_CODE
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A computer interprets a C++ source code as a series of programmatic instructions (i.e. software) which govern how the hardware of that computer behaves).
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C++_source_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_summer_2023_starter_pack/main/factorial.cpp
/**
* 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;
}
SAMPLE_PROGRAM_OUTPUT
The text in the preformatted text box below was generated by one use case of the C++ program featured in this computer programming tutorial web page.
plain-text_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_summer_2023_starter_pack/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 06_NOVEMBER_2024. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.