interval_tree.cpp

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#ifndef HPP_FCL_INTERVAL_TREE_INL_H
#define HPP_FCL_INTERVAL_TREE_INL_H

#include "hpp/fcl/broadphase/detail/interval_tree.h"

#include <algorithm>

namespace hpp {
namespace fcl {
namespace detail {

//==============================================================================
IntervalTree::IntervalTree() {
  nil = new IntervalTreeNode;
  nil->left = nil->right = nil->parent = nil;
  nil->red = false;
  nil->key = nil->high = nil->max_high =
      -(std::numeric_limits<FCL_REAL>::max)();
  nil->stored_interval = nullptr;

  root = new IntervalTreeNode;
  root->parent = root->left = root->right = nil;
  root->key = root->high = root->max_high =
      (std::numeric_limits<FCL_REAL>::max)();
  root->red = false;
  root->stored_interval = nullptr;

  recursion_node_stack_size = 128;
  recursion_node_stack = (it_recursion_node*)malloc(recursion_node_stack_size *
                                                    sizeof(it_recursion_node));
  recursion_node_stack_top = 1;
  recursion_node_stack[0].start_node = nullptr;
}

//==============================================================================
IntervalTree::~IntervalTree() {
  IntervalTreeNode* x = root->left;
  std::deque<IntervalTreeNode*> nodes_to_free;

  if (x != nil) {
    if (x->left != nil) {
      nodes_to_free.push_back(x->left);
    }
    if (x->right != nil) {
      nodes_to_free.push_back(x->right);
    }

    delete x;
    while (nodes_to_free.size() > 0) {
      x = nodes_to_free.back();
      nodes_to_free.pop_back();
      if (x->left != nil) {
        nodes_to_free.push_back(x->left);
      }
      if (x->right != nil) {
        nodes_to_free.push_back(x->right);
      }
      delete x;
    }
  }
  delete nil;
  delete root;
  free(recursion_node_stack);
}

//==============================================================================
void IntervalTree::leftRotate(IntervalTreeNode* x) {
  IntervalTreeNode* y;

  y = x->right;
  x->right = y->left;

  if (y->left != nil) y->left->parent = x;

  y->parent = x->parent;

  if (x == x->parent->left)
    x->parent->left = y;
  else
    x->parent->right = y;

  y->left = x;
  x->parent = y;

  x->max_high =
      std::max(x->left->max_high, std::max(x->right->max_high, x->high));
  y->max_high = std::max(x->max_high, std::max(y->right->max_high, y->high));
}

//==============================================================================
void IntervalTree::rightRotate(IntervalTreeNode* y) {
  IntervalTreeNode* x;

  x = y->left;
  y->left = x->right;

  if (nil != x->right) x->right->parent = y;

  x->parent = y->parent;
  if (y == y->parent->left)
    y->parent->left = x;
  else
    y->parent->right = x;

  x->right = y;
  y->parent = x;

  y->max_high =
      std::max(y->left->max_high, std::max(y->right->max_high, y->high));
  x->max_high = std::max(x->left->max_high, std::max(y->max_high, x->high));
}

//==============================================================================
void IntervalTree::recursiveInsert(IntervalTreeNode* z) {
  IntervalTreeNode* x;
  IntervalTreeNode* y;

  z->left = z->right = nil;
  y = root;
  x = root->left;
  while (x != nil) {
    y = x;
    if (x->key > z->key)
      x = x->left;
    else
      x = x->right;
  }
  z->parent = y;
  if ((y == root) || (y->key > z->key))
    y->left = z;
  else
    y->right = z;
}

//==============================================================================
void IntervalTree::fixupMaxHigh(IntervalTreeNode* x) {
  while (x != root) {
    x->max_high =
        std::max(x->high, std::max(x->left->max_high, x->right->max_high));
    x = x->parent;
  }
}

//==============================================================================
IntervalTreeNode* IntervalTree::insert(SimpleInterval* new_interval) {
  IntervalTreeNode* y;
  IntervalTreeNode* x;
  IntervalTreeNode* new_node;

  x = new IntervalTreeNode(new_interval);
  recursiveInsert(x);
  fixupMaxHigh(x->parent);
  new_node = x;
  x->red = true;
  while (x->parent->red) {
    if (x->parent == x->parent->parent->left) {
      y = x->parent->parent->right;
      if (y->red) {
        x->parent->red = true;
        y->red = true;
        x->parent->parent->red = true;
        x = x->parent->parent;
      } else {
        if (x == x->parent->right) {
          x = x->parent;
          leftRotate(x);
        }
        x->parent->red = false;
        x->parent->parent->red = true;
        rightRotate(x->parent->parent);
      }
    } else {
      y = x->parent->parent->left;
      if (y->red) {
        x->parent->red = false;
        y->red = false;
        x->parent->parent->red = true;
        x = x->parent->parent;
      } else {
        if (x == x->parent->left) {
          x = x->parent;
          rightRotate(x);
        }
        x->parent->red = false;
        x->parent->parent->red = true;
        leftRotate(x->parent->parent);
      }
    }
  }
  root->left->red = false;
  return new_node;
}

//==============================================================================
IntervalTreeNode* IntervalTree::getSuccessor(IntervalTreeNode* x) const {
  IntervalTreeNode* y;

  if (nil != (y = x->right)) {
    while (y->left != nil) y = y->left;
    return y;
  } else {
    y = x->parent;
    while (x == y->right) {
      x = y;
      y = y->parent;
    }
    if (y == root) return nil;
    return y;
  }
}

//==============================================================================
IntervalTreeNode* IntervalTree::getPredecessor(IntervalTreeNode* x) const {
  IntervalTreeNode* y;

  if (nil != (y = x->left)) {
    while (y->right != nil) y = y->right;
    return y;
  } else {
    y = x->parent;
    while (x == y->left) {
      if (y == root) return nil;
      x = y;
      y = y->parent;
    }
    return y;
  }
}

//==============================================================================
void IntervalTree::recursivePrint(IntervalTreeNode* x) const {
  if (x != nil) {
    recursivePrint(x->left);
    x->print(nil, root);
    recursivePrint(x->right);
  }
}

//==============================================================================
void IntervalTree::print() const { recursivePrint(root->left); }

//==============================================================================
void IntervalTree::deleteFixup(IntervalTreeNode* x) {
  IntervalTreeNode* w;
  IntervalTreeNode* root_left_node = root->left;

  while ((!x->red) && (root_left_node != x)) {
    if (x == x->parent->left) {
      w = x->parent->right;
      if (w->red) {
        w->red = false;
        x->parent->red = true;
        leftRotate(x->parent);
        w = x->parent->right;
      }
      if ((!w->right->red) && (!w->left->red)) {
        w->red = true;
        x = x->parent;
      } else {
        if (!w->right->red) {
          w->left->red = false;
          w->red = true;
          rightRotate(w);
          w = x->parent->right;
        }
        w->red = x->parent->red;
        x->parent->red = false;
        w->right->red = false;
        leftRotate(x->parent);
        x = root_left_node;
      }
    } else {
      w = x->parent->left;
      if (w->red) {
        w->red = false;
        x->parent->red = true;
        rightRotate(x->parent);
        w = x->parent->left;
      }
      if ((!w->right->red) && (!w->left->red)) {
        w->red = true;
        x = x->parent;
      } else {
        if (!w->left->red) {
          w->right->red = false;
          w->red = true;
          leftRotate(w);
          w = x->parent->left;
        }
        w->red = x->parent->red;
        x->parent->red = false;
        w->left->red = false;
        rightRotate(x->parent);
        x = root_left_node;
      }
    }
  }
  x->red = false;
}

//==============================================================================
void IntervalTree::deleteNode(SimpleInterval* ivl) {
  IntervalTreeNode* node = recursiveSearch(root, ivl);
  if (node) deleteNode(node);
}

//==============================================================================
IntervalTreeNode* IntervalTree::recursiveSearch(IntervalTreeNode* node,
                                                SimpleInterval* ivl) const {
  if (node != nil) {
    if (node->stored_interval == ivl) return node;

    IntervalTreeNode* left = recursiveSearch(node->left, ivl);
    if (left != nil) return left;
    IntervalTreeNode* right = recursiveSearch(node->right, ivl);
    if (right != nil) return right;
  }

  return nil;
}

//==============================================================================
SimpleInterval* IntervalTree::deleteNode(IntervalTreeNode* z) {
  IntervalTreeNode* y;
  IntervalTreeNode* x;
  SimpleInterval* node_to_delete = z->stored_interval;

  y = ((z->left == nil) || (z->right == nil)) ? z : getSuccessor(z);
  x = (y->left == nil) ? y->right : y->left;
  if (root == (x->parent = y->parent)) {
    root->left = x;
  } else {
    if (y == y->parent->left) {
      y->parent->left = x;
    } else {
      y->parent->right = x;
    }
  }

  if (y != z) {
    y->max_high = -(std::numeric_limits<FCL_REAL>::max)();
    y->left = z->left;
    y->right = z->right;
    y->parent = z->parent;
    z->left->parent = z->right->parent = y;
    if (z == z->parent->left)
      z->parent->left = y;
    else
      z->parent->right = y;

    fixupMaxHigh(x->parent);
    if (!(y->red)) {
      y->red = z->red;
      deleteFixup(x);
    } else
      y->red = z->red;
    delete z;
  } else {
    fixupMaxHigh(x->parent);
    if (!(y->red)) deleteFixup(x);
    delete y;
  }

  return node_to_delete;
}

//==============================================================================
bool overlap(FCL_REAL a1, FCL_REAL a2, FCL_REAL b1, FCL_REAL b2) {
  if (a1 <= b1) {
    return (b1 <= a2);
  } else {
    return (a1 <= b2);
  }
}

//==============================================================================
std::deque<SimpleInterval*> IntervalTree::query(FCL_REAL low, FCL_REAL high) {
  std::deque<SimpleInterval*> result_stack;
  IntervalTreeNode* x = root->left;
  bool run = (x != nil);

  current_parent = 0;

  while (run) {
    if (overlap(low, high, x->key, x->high)) {
      result_stack.push_back(x->stored_interval);
      recursion_node_stack[current_parent].try_right_branch = true;
    }
    if (x->left->max_high >= low) {
      if (recursion_node_stack_top == recursion_node_stack_size) {
        recursion_node_stack_size *= 2;
        recursion_node_stack = (it_recursion_node*)realloc(
            recursion_node_stack,
            recursion_node_stack_size * sizeof(it_recursion_node));
        if (recursion_node_stack == nullptr) abort();
      }
      recursion_node_stack[recursion_node_stack_top].start_node = x;
      recursion_node_stack[recursion_node_stack_top].try_right_branch = false;
      recursion_node_stack[recursion_node_stack_top].parent_index =
          current_parent;
      current_parent = recursion_node_stack_top++;
      x = x->left;
    } else
      x = x->right;

    run = (x != nil);
    while ((!run) && (recursion_node_stack_top > 1)) {
      if (recursion_node_stack[--recursion_node_stack_top].try_right_branch) {
        x = recursion_node_stack[recursion_node_stack_top].start_node->right;
        current_parent =
            recursion_node_stack[recursion_node_stack_top].parent_index;
        recursion_node_stack[current_parent].try_right_branch = true;
        run = (x != nil);
      }
    }
  }
  return result_stack;
}

}  // namespace detail
}  // namespace fcl
}  // namespace hpp

#endif