double factorial Algorithm
(possibly the earliest publication to use double factorial notation) states that the double factorial was originally introduced in order to simplify the expression of certain trigonometric integrals arise in the derivation of the Wallis merchandise. The term odd factorial is sometimes used for the double factorial of an odd number.
#include <iostream>
#include <cassert>
/* Double factorial of a non-negative integer n, is defined as the product of
all the integers from 1 to n that have the same parity (odd or even) as n.
It is also called as semifactorial of a number and is denoted by !! */
uint64_t double_factorial_iterative(uint64_t n) {
uint64_t res = 1;
for ( uint64_t i = n; i >= 0; i -= 2 ) {
if (i == 0 || i == 1) return res;
res *= i;
}
}
/* Recursion can be costly for large numbers */
uint64_t double_factorial_recursive(uint64_t n) {
if (n <= 1) return 1;
return n * double_factorial_recursive(n - 2);
}
int main() {
uint64_t n{};
std::cin >> n;
assert(n >= 0);
std::cout << double_factorial_iterative(n);
}
