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December 20, 2016 17:01
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#include <iostream> | |
#include <vector> | |
#include <array> | |
#include <unordered_set> | |
#include <algorithm> | |
#include <functional> | |
using std::cout; | |
using std::unordered_set; | |
// we need to represent the circular table | |
template<int N> | |
struct circular_table { | |
// initialize the table with N couples | |
circular_table() { | |
for( int i = 0; i < N; ++i ) { | |
ap[i*2] = (i+1); | |
ap[i*2+1] = -(i+1); | |
} | |
std::sort(ap.begin(), ap.end()); | |
} | |
bool is_valid() const { | |
if ( std::abs(first()) == std::abs(last()) ) return false; | |
for( int i = 0; i < N*2-1; ++i ) { | |
if ( std::abs(ap[i]) == std::abs(ap[i+1]) ) return false; | |
} | |
return true; | |
} | |
int first() const { return ap[0]; } | |
int last () const { return ap[N*2-1]; } | |
void print() { | |
for( auto && i: ap ) cout << i << " "; | |
cout << "\n"; | |
} | |
bool operator==(circular_table<N> const & o) const { | |
auto b = std::find(o.ap.begin(), o.ap.end(), ap[0]); | |
container_type ap2; | |
auto o2 = std::rotate_copy(o.ap.begin(), b, o.ap.end(), ap2.begin()); | |
return ap == ap2; | |
} | |
typedef std::array<int, N*2> container_type; | |
container_type ap; | |
}; | |
namespace std { | |
template<int N> | |
struct hash<circular_table<N>> { | |
auto operator()(circular_table<N> const & ct) const -> std::size_t { | |
// return the same number to force operator== usage. | |
return 0; | |
} | |
}; | |
} | |
template<int N> | |
int count_valid_permutations() { | |
int i = 0; | |
circular_table<N> t; | |
unordered_set<circular_table<N>> tset; | |
while ( std::next_permutation(t.ap.begin(), t.ap.end()) ) { | |
if ( t.is_valid() ) | |
tset.insert(t); | |
} | |
return tset.size(); | |
} | |
int main(int argc, char* argv[]) { | |
cout << "n=1: " << count_valid_permutations<1>() << '\n'; | |
cout << "n=2: " << count_valid_permutations<2>() << '\n'; | |
cout << "n=3: " << count_valid_permutations<3>() << '\n'; | |
cout << "n=4: " << count_valid_permutations<4>() << '\n'; | |
} |
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