Pascal triangle calculation without using for/while loop - c++

Question

I would like to generate Pascal pyramid data from a given data set that looks like this
Pyramid(1,2,3,4,5,6,7,8,9);
This is what I have been doing but it reaches only the second layer while I want it to recursively loop till the top.
template<typename T>
const T Pyramid(T a, T b)
{
return a + b;
}
template<typename T, typename ...A>
const T Pyramid(T t1, T t2, A...a)
{
return Pyramid(t1, t2) + Pyramid(t2, a...);
}
Could you help me fill up the next layers ? ;)

Answer 1

C++17
Here is the C++17 solution (using fold expressions):
#include <iostream>
#include <stdexcept>
#include <utility>
using Integer = std::uint64_t;
constexpr auto Factorial(const Integer n)
{
Integer factorial = 1;
for (Integer i = 2; i <= n; ++i)
{
factorial *= i;
}
return factorial;
}
constexpr auto Binom(const Integer n, const Integer m)
{
if (n < m)
{
throw std::invalid_argument("Binom: n should not be less than m");
}
return Factorial(n) / Factorial(m) / Factorial(n - m);
}
template <Integer... indices, typename... Types>
constexpr auto PyramidImplementation(std::integer_sequence<Integer, indices...>, Types... values)
{
return ((Binom(sizeof...(values), indices) * values) + ...);
}
template <typename... Types>
constexpr auto Pyramid(Types... values)
{
return PyramidImplementation(std::make_integer_sequence<Integer, sizeof...(values)>{}, values...);
}
// ...
constexpr auto pyramid = Pyramid(1, 2, 3, 4, 5, 6, 7, 8, 9);
std::cout << "Pyramid = " << pyramid << std::endl;
Live demo
This solution doesn't use the recursion, because the needed result for a[i] (i = 0 ... n - 1) can be calculated as a sum of binom(n, i) * a[i] (for i = 0 ... n - 1), where binom(n, m) is the binomial coefficient. The Binom function is implemented in the simplest way, so it will work only for small values of n.
C++14
The code can be made C++14-compatible via the following PyramidImplementation function implementation:
#include <type_traits>
template <Integer... indices, typename... Types>
constexpr auto PyramidImplementation(std::integer_sequence<Integer, indices...>, Types... values)
{
using Do = int[];
std::common_type_t<Types...> pyramid{};
(void)Do{0, (pyramid += Binom(sizeof...(values), indices) * values, 0)...};
return pyramid;
}
Live demo