Factorial Implementations — Tutorial

Factorial Implementations — Advanced Tutorial

Two ready-to-build C++ examples included in this folder: a simple recursive example using native types and an iterative big-integer example using a digit vector.

Files

  • recursive_simple.cpp — Recursive version using unsigned long long. Short and didactic; overflows for n > 20.
  • bigint_iterative.cpp — Iterative big-integer version using a vector of base-10 digits. Computes exact factorials for much larger n without external libraries.
  • factorial_comparison.md — Comparison notes and guidance for publication.

How to build

GCC / Clang

g++ -std=c++17 -O2 recursive_simple.cpp -o recursive_simple
./recursive_simple

g++ -std=c++17 -O2 bigint_iterative.cpp -o bigint_iterative
./bigint_iterative

MSVC (Developer Command Prompt)

cl /EHsc recursive_simple.cpp
recursive_simple.exe

cl /EHsc bigint_iterative.cpp
bigint_iterative.exe
Note: If you open the Visual Studio solution included in this folder, ensure only one file with main() is built per project, or keep these examples in separate projects to avoid multiple-definition linker errors.

Quick comparison

  • Recursive (native): minimal code; limited by 64-bit overflow and recursion depth.
  • Big-int (digit vector): exact results for large n; simple implementation but not optimized for thousands of digits — prefer boost::multiprecision::cpp_int or GMP for production.

Suggested tutorial flow

  1. Introduce factorial mathematically.
  2. Show recursive native implementation and explain overflow and stack-depth limits.
  3. Show iterative native implementation and discuss limits.
  4. Present big-integer approach (this repo) and explain complexity.
  5. Demonstrate using boost::multiprecision::cpp_int and compare performance.
  6. Optional: link to advanced algorithms (prime-swing, binary splitting) for very large factorials.

Ready to publish. If you want, I can also generate an HTML page that embeds full source code blocks, or produce a single combined ZIP containing both examples and the tutorial HTML.

Here it is a simple Hello, World source code in C and C++ languages:

C Version:

#include<stdio.h>
main()
{
printf(“Hello, World!\n”);
}

C++ Version:

#include<iostream>
using namespace std;
main()  // This is a comment( using double slash ” //” make the code disable after that. Note that if main() function is not declared with return type,  as void, int or char, the compiler will automatically assume as int.
{
cout << “Hello, World!” << endl;
}

Hello world!

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