// SPDX-FileComment: This file is part of TNL - Template Numerical Library (https://tnl-project.org/)
// SPDX-License-Identifier: MIT

#pragma once

#include <TNL/Meshes/Topologies/SubentityVertexMap.h>
#include <TNL/Meshes/Topologies/Vertex.h>

namespace TNL::Meshes::Topologies {

template< int dimension_ >
struct Simplex
{
   static constexpr int dimension = dimension_;
};

namespace SimplexDetails {
template< unsigned int n, unsigned int k >
class NumCombinations;

template< unsigned int n, unsigned int k, unsigned int combinationIndex, unsigned int valueIndex >
class CombinationValue;
}  // namespace SimplexDetails

template< int dimension, int subtopologyDim >
class Subtopology< Simplex< dimension >, subtopologyDim >
{
   static_assert( 0 < subtopologyDim && subtopologyDim < dimension, "invalid subtopology dimension" );

   static constexpr int topologyVertexCount = Subtopology< Simplex< dimension >, 0 >::count;
   static constexpr int subtopologyVertexCount = Subtopology< Simplex< subtopologyDim >, 0 >::count;

public:
   using Topology = Simplex< subtopologyDim >;

   static constexpr int count = SimplexDetails::NumCombinations< topologyVertexCount, subtopologyVertexCount >::value;
};

template< int dimension >
class Subtopology< Simplex< dimension >, 0 >
{
   static_assert( 0 < dimension, "invalid dimension" );

public:
   using Topology = Vertex;

   static constexpr int count = dimension + 1;
};

template< int dimension, typename Subtopology, int subtopologyIndex, int vertexIndex >
struct SubentityVertexMap< Simplex< dimension >, Subtopology, subtopologyIndex, vertexIndex >
{
private:
   static constexpr int subtopologyCount = Topologies::Subtopology< Simplex< dimension >, Subtopology::dimension >::count;
   static constexpr int topologyVertexCount = Topologies::Subtopology< Simplex< dimension >, 0 >::count;
   static constexpr int subtopologyVertexCount = Topologies::Subtopology< Subtopology, 0 >::count;

   static_assert( 1 < dimension, "subtopology vertex can be specified for topologies of dimension 2 or higher" );
   static_assert( 0 <= subtopologyIndex && subtopologyIndex < subtopologyCount, "invalid subtopology index" );
   static_assert( 0 <= vertexIndex && vertexIndex < subtopologyVertexCount, "invalid subtopology vertex index" );

public:
   static constexpr int index =
      SimplexDetails::CombinationValue< topologyVertexCount, subtopologyVertexCount, subtopologyIndex, vertexIndex >::value;
};

template< unsigned int n, unsigned int k >
class NumCombinations
{
   static_assert( 0 < k && k < n, "invalid argument" );

public:
   static constexpr unsigned int value = NumCombinations< n - 1, k - 1 >::value + NumCombinations< n - 1, k >::value;
};

namespace SimplexDetails {

// Number of combinations (n choose k)
template< unsigned int n >
class NumCombinations< n, 0 >
{
   static_assert( 0 <= n, "invalid argument" );

public:
   static constexpr unsigned int value = 1;
};

template< unsigned int n >
class NumCombinations< n, n >
{
   static_assert( 0 < n, "invalid argument" );

public:
   static constexpr unsigned int value = 1;
};

//     Compile-time generation of combinations
// Combinations are generated in lexicographical order. The following example shows generation of 2-combinations from set {0, 1,
// 2}:
//   0, 1  <->  CombinationValue<3, 2, 0, 0>::VALUE, CombinationValue<3, 2, 0, 1>::VALUE
//   0, 2  <->  CombinationValue<3, 2, 1, 0>::VALUE, CombinationValue<3, 2, 1, 1>::VALUE
//   1, 2  <->  CombinationValue<3, 2, 2, 0>::VALUE, CombinationValue<3, 2, 2, 1>::VALUE
template< unsigned int n, unsigned int k, unsigned int combinationIndex >
class CombinationIncrement;

template< unsigned int n, unsigned int k, unsigned int combinationIndex, unsigned int valueIndex >
class CombinationValue
{
   static_assert( combinationIndex < NumCombinations< n, k >::value, "invalid combination index" );
   static_assert( valueIndex < k, "invalid value index" );

   static constexpr unsigned int incrementValueIndex = CombinationIncrement< n, k, combinationIndex - 1 >::valueIndex;

public:
   static constexpr unsigned int value =
      ( valueIndex < incrementValueIndex ? CombinationValue< n, k, combinationIndex - 1, valueIndex >::value
                                         : CombinationValue< n, k, combinationIndex - 1, incrementValueIndex >::value
                                              + valueIndex - incrementValueIndex + 1 );
};

template< unsigned int n, unsigned int k, unsigned int valueIndex >
class CombinationValue< n, k, 0, valueIndex >
{
   static_assert( valueIndex < k, "invalid value index" );

   static constexpr unsigned int incrementValueIndex = CombinationIncrement< n, k, 0 >::valueIndex;

public:
   static constexpr unsigned int value = valueIndex;
};

// The CombinationIncrement class determines value index of the particular combination which will be incremented when generating
// the next combination
template< unsigned int n, unsigned int k, unsigned int combinationIndex, unsigned int valueIndex_ >
class CombinationIncrementImpl
{
   static_assert( combinationIndex < NumCombinations< n, k >::value - 1, "nothing to increment" );

   static constexpr bool incrementPossible =
      ( CombinationValue< n, k, combinationIndex, valueIndex_ >::value + k - valueIndex_ < n );

public:
   static constexpr int valueIndex =
      ( incrementPossible ? valueIndex_ : CombinationIncrementImpl< n, k, combinationIndex, valueIndex_ - 1 >::valueIndex );
};

template< unsigned int n, unsigned int k, unsigned int combinationIndex >
class CombinationIncrementImpl< n, k, combinationIndex, 0 >
{
   static_assert( combinationIndex < NumCombinations< n, k >::value - 1, "nothing to increment" );

public:
   static constexpr int valueIndex = 0;
};

template< unsigned int n, unsigned int k, unsigned int combinationIndex >
class CombinationIncrement
{
   static_assert( combinationIndex < NumCombinations< n, k >::value - 1, "nothing to increment" );

public:
   static constexpr unsigned int valueIndex = CombinationIncrementImpl< n, k, combinationIndex, k - 1 >::valueIndex;
};

}  // namespace SimplexDetails

}  // namespace TNL::Meshes::Topologies
