C++: A Comprehensive Beginner’s Guide to Learn About the Realms of C++ From A-Z by Smith Benjamin

Author:Smith, Benjamin [Smith, Benjamin]
Language: eng
Format: epub
Published: 2020-04-24T16:00:00+00:00

Recursion

The function factorial is widely used in combinatorial analysis (counting theory in mathematics), probability theory, and statistics. The factorial of n is most times expressed as n!. The factorial for nonnegative integers can be expressed as:

n! = n . (n – 1) . (n – 2) . (n – 3) . . . 2 . 1

Mathematically, the definition of factorial is recursive because the ! function is being defined, but ! is also used in the definition. In C++, a function can be defined recursively as well. Consider code 5.10, which includes a factorial function that exactly models the mathematical definition.

Code 5.10

#include <iostream>

// Factorial (n)

// Computes n!

// Return the factorial of n;

int factorial(int n) {

if (n == 0)

return 1;

else

return n * factorial(n - 1);

}

int main() {

// Try out the factorial function

std::cout << " 0! = " << factorial(0) << '\n';

std::cout << " 1! = " << factorial(1) << '\n';

std::cout << " 6! = " << factorial(6) << '\n';

std::cout << "10! = " << factorial(10) << '\n';

}

So, a simple correct recursive function definition is based on four key concepts:

The function must not be able to call itself within a definition optionally. This is also known as the base case.

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