The factorial of a non-negative integer n, written n!, is the product of every positive integer up to n:
n! = n × (n-1) × (n-2) × ... × 1
By definition, 0! = 1. Factorial appears throughout combinatorics, probability, and algorithm analysis.
Implementations Both versions use the same recursive strategy: return 1 for the base cases n == 0 and n == 1, and multiply n by the factorial of n - 1 for every other input.
FactorialRecursivo.cpp
FactorialRecursivo.py
#include <bits/stdc++.h> using namespace std ; int n; int factorial ( int n ){ return (n == 1 || n == 0 ) ? 1 : n * factorial (n - 1 ); } int main (){ cout << "Ingresa un numero: " ; cin >> n; cout << factorial (n); return 0 ; }
Recursive logic The function reduces the problem by one at every call:
Base case — when n == 0 or n == 1, the function returns 1 immediately without making another call.Recursive case — for any n > 1, the function returns n * factorial(n - 1), deferring the rest of the computation down the call stack.
For n = 5 the call chain looks like:
factorial(5) → 5 * factorial(4) → 4 * factorial(3) → 3 * factorial(2) → 2 * factorial(1) → 1
The stack then unwinds, multiplying each value on the way back: 1 → 2 → 6 → 24 → 120.
How to run
Compile and run the C++ version
g++ -o factorial FactorialRecursivo.cpp && ./factorial
You will be prompted to enter a number. The program prints the result and exits.
Run the Python version
python3 FactorialRecursivo.py
You will be prompted to enter a number. The program prints the result and exits. Example values Input (n) Output (n!) 0 1 1 1 5 120 10 3628800
Limitations Naive recursion pushes one stack frame for each decrement of n. For large values of n this exhausts the call stack and causes a stack overflow . The C++ version also uses int, which overflows for n ≥ 13. If you need to handle large inputs, consider an iterative approach or arbitrary-precision arithmetic.