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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 namespace Acts {
 
 template <SatisfyCandidateConcept external_space_point_t>
 inline void CandidatesForMiddleSp<external_space_point_t>::setMaxElements(
     std::size_t nLow, std::size_t nHigh) {
   m_maxSizeHigh = nHigh;
   m_maxSizeLow = nLow;
 
   // protection against default numbers
   // it may cause std::bad_alloc if we don't protect
   if (nHigh == std::numeric_limits<std::size_t>::max() ||
       nLow == std::numeric_limits<std::size_t>::max()) {
     return;
   }
 
   // Reserve enough memory for all collections
   m_storage.reserve(nLow + nHigh);
   m_indicesHigh.reserve(nHigh);
   m_indicesLow.reserve(nLow);
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 inline void CandidatesForMiddleSp<external_space_point_t>::pop(
     std::vector<std::size_t>& indices, std::size_t& currentSize) {
   // Remove the candidate with the lowest weight in the collection
   // By construction, this element is always the first element in the
   // collection.
   // The removal works this way: the first element of the collection
   // is overwritten with the last element of the collection.
   // The number of stored elements (currentSize) is lowered by 1
   // The new first element is moved down in the tree to its correct position
   std::swap(indices[0], indices[currentSize - 1]);
   bubbledw(indices, 0, --currentSize);
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 inline bool CandidatesForMiddleSp<external_space_point_t>::exists(
     const std::size_t n, const std::size_t maxSize) const {
   // If the element exists, its index is lower than the current number
   // of stored elements
   return n < maxSize;
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 inline float CandidatesForMiddleSp<external_space_point_t>::weight(
     const std::vector<std::size_t>& indices, std::size_t n) const {
   // Get the weight of the n-th element
   return m_storage[indices[n]].weight;
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 inline void CandidatesForMiddleSp<external_space_point_t>::clear() {
   // do not clear max size, this is set only once
   // reset to 0 the number of stored elements
   m_nHigh = 0;
   m_nLow = 0;
   // Reset all values to default
   m_storage.clear();
   m_indicesHigh.clear();
   m_indicesLow.clear();
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 bool CandidatesForMiddleSp<external_space_point_t>::push(
     external_space_point_t& SpB, external_space_point_t& SpM,
     external_space_point_t& SpT, float weight, float zOrigin, bool isQuality) {
   // Decide in which collection this candidate may be added to according to the
   // isQuality boolean
   if (isQuality) {
     return push(m_indicesHigh, m_nHigh, m_maxSizeHigh, SpB, SpM, SpT, weight,
                 zOrigin, isQuality);
   }
   return push(m_indicesLow, m_nLow, m_maxSizeLow, SpB, SpM, SpT, weight,
               zOrigin, isQuality);
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 bool CandidatesForMiddleSp<external_space_point_t>::push(
     std::vector<std::size_t>& indices, std::size_t& n, const std::size_t nMax,
     external_space_point_t& SpB, external_space_point_t& SpM,
     external_space_point_t& SpT, float weight, float zOrigin, bool isQuality) {
   // If we do not want to store candidates, returns
   if (nMax == 0) {
     return false;
   }
 
   // if there is still space, add anything
   if (n < nMax) {
     addToCollection(indices, n, nMax,
                     value_type(SpB, SpM, SpT, weight, zOrigin, isQuality));
     return true;
   }
 
   // if no space, replace one if quality is enough
   // compare to element with lowest weight
   if (float lowestWeight = this->weight(indices, 0); weight <= lowestWeight) {
     return false;
   }
 
   // remove element with lower weight and add this one
   pop(indices, n);
   addToCollection(indices, n, nMax,
                   value_type(SpB, SpM, SpT, weight, zOrigin, isQuality));
   return true;
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 void CandidatesForMiddleSp<external_space_point_t>::addToCollection(
     std::vector<std::size_t>& indices, std::size_t& n, const std::size_t nMax,
     value_type&& element) {
   // adds elements to the end of the collection
   if (indices.size() == nMax) {
     m_storage[indices[n]] = std::move(element);
   } else {
     m_storage.push_back(std::move(element));
     indices.push_back(m_storage.size() - 1);
   }
   // Move the added element up in the tree to its correct position
   bubbleup(indices, n++);
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 void CandidatesForMiddleSp<external_space_point_t>::bubbledw(
     std::vector<std::size_t>& indices, std::size_t n, std::size_t actualSize) {
   while (n < actualSize) {
     // The collection of indexes are sorted as min heap trees
     // left child : 2 * n + 1
     // right child: 2 * n + 2
     float current = weight(indices, n);
     std::size_t leftChild = 2 * n + 1;
     std::size_t rightChild = 2 * n + 2;
 
     // We have to move the current node down the tree to its correct position.
     // This is done by comparing its weight with the weights of its two
     // children. Few things can happen:
     //   - there are no children
     //   - the current weight is lower than the weight of the children
     //   - at least one of the children has a lower weight
     // In the first two cases we stop, since we are already in the correct
     // position
 
     // if there is no left child, that also means no right child is present.
     // We do nothing
     if (!exists(leftChild, actualSize)) {
       break;
     }
 
     // At least one of the child is present. Left child for sure, right child we
     // have to check. We take the lowest weight of the children. By default this
     // is the weight of the left child, and we then check for the right child
 
     float weightLeftChild = weight(indices, leftChild);
 
     std::size_t selectedChild = leftChild;
     float selectedWeight = weightLeftChild;
 
     // Check which child has the lower weight
     if (exists(rightChild, actualSize)) {
       float weightRightChild = weight(indices, rightChild);
       if (weightRightChild <= weightLeftChild) {
         selectedChild = rightChild;
         selectedWeight = weightRightChild;
       }
     }
 
     // At this point we have the minimum weight of the children
     // We can compare this to the current weight
     // If weight of the children is higher we stop
     if (selectedWeight >= current) {
       break;
     }
 
     // swap and repeat the process
     std::swap(indices[n], indices[selectedChild]);
     n = selectedChild;
   }  // while loop
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 void CandidatesForMiddleSp<external_space_point_t>::bubbleup(
     std::vector<std::size_t>& indices, std::size_t n) {
   while (n != 0) {
     // The collection of indexes are sorted as min heap trees
     // parent: (n - 1) / 2;
     // this works because it is an integer operation
     std::size_t parentIdx = (n - 1) / 2;
 
     float weightCurrent = weight(indices, n);
     // If weight of the parent is lower than this one, we stop
     if (float weightParent = weight(indices, parentIdx);
         weightParent <= weightCurrent) {
       break;
     }
 
     // swap and repeat the process
     std::swap(indices[n], indices[parentIdx]);
     n = parentIdx;
   }
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 std::vector<typename CandidatesForMiddleSp<external_space_point_t>::value_type>
 CandidatesForMiddleSp<external_space_point_t>::storage() {
   // this will retrieve the entire storage
   // the resulting vector is already sorted from high to low quality
   std::vector<value_type> output(m_nHigh + m_nLow);
   std::size_t outIdx = output.size() - 1;
 
   // rely on the fact that m_indices* are both min heap trees
   // Sorting comes naturally by popping elements one by one and
   // placing this element at the end of the output vector
   while (m_nHigh != 0 || m_nLow != 0) {
     // no entries in collection high, we attach the entire low collection
     if (m_nHigh == 0) {
       std::size_t idx = m_nLow;
       for (std::size_t i(0); i < idx; i++) {
         output[outIdx--] = std::move(m_storage[m_indicesLow[0]]);
         pop(m_indicesLow, m_nLow);
       }
       break;
     }
 
     // no entries in collection low, we attach the entire high collection
     if (m_nLow == 0) {
       std::size_t idx = m_nHigh;
       for (std::size_t i(0); i < idx; i++) {
         output[outIdx--] = std::move(m_storage[m_indicesHigh[0]]);
         pop(m_indicesHigh, m_nHigh);
       }
       break;
     }
 
     // Both have entries, get the minimum
     if (descendingByQuality(m_storage[m_indicesLow[0]],
                             m_storage[m_indicesHigh[0]])) {
       output[outIdx--] = std::move(m_storage[m_indicesHigh[0]]);
       pop(m_indicesHigh, m_nHigh);
     } else {
       output[outIdx--] = std::move(m_storage[m_indicesLow[0]]);
       pop(m_indicesLow, m_nLow);
     }
 
   }  // while loop
 
   clear();
   return output;
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 bool CandidatesForMiddleSp<external_space_point_t>::descendingByQuality(
     const value_type& i1, const value_type& i2) {
   if (i1.weight != i2.weight) {
     return i1.weight > i2.weight;
   }
 
   // This is for the case when the weights from different seeds
   // are same. This makes cpu & cuda results same
 
   const auto& bottomL1 = i1.bottom;
   const auto& middleL1 = i1.middle;
   const auto& topL1 = i1.top;
 
   const auto& bottomL2 = i2.bottom;
   const auto& middleL2 = i2.middle;
   const auto& topL2 = i2.top;
 
   float seed1_sum = 0.;
   float seed2_sum = 0.;
 
   seed1_sum += bottomL1->y() * bottomL1->y() + bottomL1->z() * bottomL1->z();
   seed1_sum += middleL1->y() * middleL1->y() + middleL1->z() * middleL1->z();
   seed1_sum += topL1->y() * topL1->y() + topL1->z() * topL1->z();
 
   seed2_sum += bottomL2->y() * bottomL2->y() + bottomL2->z() * bottomL2->z();
   seed2_sum += middleL2->y() * middleL2->y() + middleL2->z() * middleL2->z();
   seed2_sum += topL2->y() * topL2->y() + topL2->z() * topL2->z();
 
   return seed1_sum > seed2_sum;
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 bool CandidatesForMiddleSp<external_space_point_t>::ascendingByQuality(
     const value_type& i1, const value_type& i2) {
   return !descendingByQuality(i1, i2);
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 std::size_t
 CandidatesForMiddleSp<external_space_point_t>::nLowQualityCandidates() const {
   return m_nLow;
 }
 
 template <SatisfyCandidateConcept external_space_point_t>
 std::size_t
 CandidatesForMiddleSp<external_space_point_t>::nHighQualityCandidates() const {
   return m_nHigh;
 }
 
 }  // namespace Acts

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