determinant.h

#include <array>
#include <numeric>
#include <algorithm>
#include <utility>

template<typename T, int N, std::size_t... I>
constexpr std::array<T, N> istoarr(std::index_sequence<I...>) {
    return std::array<T, N>{ {I...} };
}

template<typename T, int N>
constexpr std::array<T, N> create_array() {
    return istoarr<T, N>(std::make_index_sequence<N>{});
}

template<int N>
constexpr int determinant(const std::array<std::array<int, N>, N>& a) {
    int det = 0;
    std::array<int, N> perm = create_array<int, N>();
    int sign = 1;
    do {
        int det_perm = sign;
        for (int i = 0; i < N; ++i) {
            det_perm *= a[i][perm[i]];
        }
        det += det_perm;
        sign *= -1;
    } while (std::next_permutation(perm.begin(), perm.end()));
    return det;
}