输入10个互不相同的数字并分成5对,问有多少种分法。
之前见到有人问输入10个互不相同的数字并分成5对有多少种分法,感觉这个问题有点意思就写了一个。
#include <iostream> #include <array> #include <vector> #include <cassert> template<int N> std::array<std::array<int, 2>, N + 1> append(const std::array<int, 2>& add, const std::array<std::array<int, 2>, N>& to){ std::array<std::array<int, 2>, N + 1> ret; for (int i = 0; i < N; ++i){ ret[i] = to[i]; } ret[N] = add; return ret; } template<int N> std::array<int, N - 1> pickout(const std::array<int, N>& lhs, int item){ std::array<int, N - 1> ret; for (int i = 0, j = 0; i < N - 1; ++i, ++j){ if (lhs[i] == item){ ++j; } ret[i] = lhs[j]; } return ret; } template<int N> std::vector<std::array<std::array<int, 2>, N / 2> > apply( const std::vector<std::array<std::array<int, 2>, N / 2> >& tmpl, const std::array<int, N>& data){ static_assert(N % 2 == 0, "should be multiply of 2"); std::vector<std::array<std::array<int, 2>, N / 2> > ret; for (auto entry : tmpl){ std::array<std::array<int, 2>, N / 2> record; for (int i = 0; i < N / 2; ++i){ record[i] = { { data[entry[i][0]], data[entry[i][1]] } }; } ret.push_back(record); } return ret; } template<int N> std::vector<std::array<std::array<int, 2>, N / 2> > get(){ static_assert(N % 2 == 0, "should be multiply of 2"); std::vector<std::array<std::array<int, 2>, N / 2> > ret; auto decay = get<N - 2>(); std::array<int, N> data; for (int i = 0; i < N; ++i)data[i] = i; for (int i = 1; i < N; ++i){ std::array<int, N - 2> d = pickout(pickout(data, 0), i); for (auto tail : apply(decay, d)){ ret.push_back(append(std::array<int, 2>{{ 0, i }}, tail)); } } return ret; } template<> std::vector<std::array<std::array<int, 2>, 1> > get<2>(){ return std::vector<std::array<std::array<int, 2>, 1> >{ std::array<std::array<int, 2>, 1>{{ std::array<int, 2>{{0, 1}} }} }; } template<typename T> std::ostream& operator << (std::ostream& out, const std::vector<T>& rhs){ out << "[ "; if (!rhs.empty())out << rhs[0]; for (int i = 1; i < rhs.size(); ++i){ out << ", " << rhs[i]; } return out << " ]"; } template<typename T, int N> std::ostream& operator << (std::ostream& out, const std::array<T, N>& rhs){ out << "[ " << rhs[0]; for (int i = 1; i < N; ++i){ out << ", " << rhs[i]; } return out << " ]"; } int main(){ std::array<int, 10> arr; std::cout << "input 10 numbers:" << std::endl; for (int i = 0; i < 10; ++i){ std::cin >> arr[i]; } for (auto i : apply(get<10>(), arr)){ std::cout << i << std::endl; } }