mirror of https://github.com/OpenTTD/OpenTTD.git
484 lines
17 KiB
C++
484 lines
17 KiB
C++
/*
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* This file is part of OpenTTD.
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* OpenTTD is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, version 2.
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* OpenTTD is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
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* See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with OpenTTD. If not, see <http://www.gnu.org/licenses/>.
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*/
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/** @file kdtree.hpp K-d tree template specialised for 2-dimensional Manhattan geometry */
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#ifndef KDTREE_HPP
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#define KDTREE_HPP
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#include "../stdafx.h"
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/**
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* K-dimensional tree, specialised for 2-dimensional space.
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* This is not intended as a primary storage of data, but as an index into existing data.
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* Usually the type stored by this tree should be an index into an existing array.
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*
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* This implementation assumes Manhattan distances are used.
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*
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* Be careful when using this in game code, depending on usage pattern, the tree shape may
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* end up different for different clients in multiplayer, causing iteration order to differ
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* and possibly having elements returned in different order. The using code should be designed
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* to produce the same result regardless of iteration order.
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*
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* The element type T must be less-than comparable for FindNearest to work.
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*
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* @tparam T Type stored in the tree, should be cheap to copy.
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* @tparam TxyFunc Functor type to extract coordinate from a T value and dimension index (0 or 1).
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* @tparam CoordT Type of coordinate values extracted via TxyFunc.
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* @tparam DistT Type to use for representing distance values.
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*/
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template <typename T, typename TxyFunc, typename CoordT, typename DistT>
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class Kdtree {
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/** Type of a node in the tree */
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struct node {
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T element; ///< Element stored at node
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size_t left; ///< Index of node to the left, INVALID_NODE if none
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size_t right; ///< Index of node to the right, INVALID_NODE if none
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node(T element) : element(element), left(INVALID_NODE), right(INVALID_NODE) { }
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};
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static const size_t INVALID_NODE = SIZE_MAX; ///< Index value indicating no-such-node
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std::vector<node> nodes; ///< Pool of all nodes in the tree
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std::vector<size_t> free_list; ///< List of dead indices in the nodes vector
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size_t root; ///< Index of root node
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TxyFunc xyfunc; ///< Functor to extract a coordinate from an element
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size_t unbalanced; ///< Number approximating how unbalanced the tree might be
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/** Create one new node in the tree, return its index in the pool */
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size_t AddNode(const T &element)
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{
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if (this->free_list.empty()) {
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this->nodes.emplace_back(element);
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return this->nodes.size() - 1;
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} else {
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size_t newidx = this->free_list.back();
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this->free_list.pop_back();
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this->nodes[newidx] = node{ element };
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return newidx;
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}
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}
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/** Find a coordinate value to split a range of elements at */
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template <typename It>
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CoordT SelectSplitCoord(It begin, It end, int level)
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{
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It mid = begin + (end - begin) / 2;
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std::nth_element(begin, mid, end, [&](T a, T b) { return this->xyfunc(a, level % 2) < this->xyfunc(b, level % 2); });
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return this->xyfunc(*mid, level % 2);
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}
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/** Construct a subtree from elements between begin and end iterators, return index of root */
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template <typename It>
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size_t BuildSubtree(It begin, It end, int level)
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{
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ptrdiff_t count = end - begin;
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if (count == 0) {
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return INVALID_NODE;
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} else if (count == 1) {
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return this->AddNode(*begin);
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} else if (count > 1) {
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CoordT split_coord = SelectSplitCoord(begin, end, level);
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It split = std::partition(begin, end, [&](T v) { return this->xyfunc(v, level % 2) < split_coord; });
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size_t newidx = this->AddNode(*split);
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this->nodes[newidx].left = this->BuildSubtree(begin, split, level + 1);
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this->nodes[newidx].right = this->BuildSubtree(split + 1, end, level + 1);
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return newidx;
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} else {
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NOT_REACHED();
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}
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}
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/** Rebuild the tree with all existing elements, optionally adding or removing one more */
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bool Rebuild(const T *include_element, const T *exclude_element)
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{
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size_t initial_count = this->Count();
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if (initial_count < 8) return false; // arbitrary value for "not worth rebalancing"
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T root_element = this->nodes[this->root].element;
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std::vector<T> elements = this->FreeSubtree(this->root);
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elements.push_back(root_element);
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if (include_element != nullptr) {
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elements.push_back(*include_element);
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initial_count++;
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}
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if (exclude_element != nullptr) {
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typename std::vector<T>::iterator removed = std::remove(elements.begin(), elements.end(), *exclude_element);
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elements.erase(removed, elements.end());
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initial_count--;
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}
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this->Build(elements.begin(), elements.end());
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assert(initial_count == this->Count());
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return true;
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}
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/** Insert one element in the tree somewhere below node_idx */
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void InsertRecursive(const T &element, size_t node_idx, int level)
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{
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/* Dimension index of current level */
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int dim = level % 2;
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/* Node reference */
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node &n = this->nodes[node_idx];
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/* Coordinate of element splitting at this node */
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CoordT nc = this->xyfunc(n.element, dim);
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/* Coordinate of the new element */
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CoordT ec = this->xyfunc(element, dim);
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/* Which side to insert on */
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size_t &next = (ec < nc) ? n.left : n.right;
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if (next == INVALID_NODE) {
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/* New leaf */
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size_t newidx = this->AddNode(element);
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/* Vector may have been reallocated at this point, n and next are invalid */
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node &nn = this->nodes[node_idx];
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if (ec < nc) nn.left = newidx; else nn.right = newidx;
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} else {
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this->InsertRecursive(element, next, level + 1);
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}
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}
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/**
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* Free all children of the given node
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* @return Collection of elements that were removed from tree.
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*/
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std::vector<T> FreeSubtree(size_t node_idx)
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{
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std::vector<T> subtree_elements;
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node &n = this->nodes[node_idx];
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/* We'll be appending items to the free_list, get index of our first item */
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size_t first_free = this->free_list.size();
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/* Prepare the descent with our children */
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if (n.left != INVALID_NODE) this->free_list.push_back(n.left);
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if (n.right != INVALID_NODE) this->free_list.push_back(n.right);
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n.left = n.right = INVALID_NODE;
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/* Recursively free the nodes being collected */
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for (size_t i = first_free; i < this->free_list.size(); i++) {
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node &fn = this->nodes[this->free_list[i]];
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subtree_elements.push_back(fn.element);
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if (fn.left != INVALID_NODE) this->free_list.push_back(fn.left);
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if (fn.right != INVALID_NODE) this->free_list.push_back(fn.right);
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fn.left = fn.right = INVALID_NODE;
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}
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return subtree_elements;
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}
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/**
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* Find and remove one element from the tree.
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* @param element The element to search for
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* @param node_idx Sub-tree to search in
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* @param level Current depth in the tree
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* @return New root node index of the sub-tree processed
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*/
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size_t RemoveRecursive(const T &element, size_t node_idx, int level)
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{
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/* Node reference */
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node &n = this->nodes[node_idx];
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if (n.element == element) {
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/* Remove this one */
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this->free_list.push_back(node_idx);
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if (n.left == INVALID_NODE && n.right == INVALID_NODE) {
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/* Simple case, leaf, new child node for parent is "none" */
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return INVALID_NODE;
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} else {
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/* Complex case, rebuild the sub-tree */
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std::vector<T> subtree_elements = this->FreeSubtree(node_idx);
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return this->BuildSubtree(subtree_elements.begin(), subtree_elements.end(), level);;
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}
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} else {
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/* Search in a sub-tree */
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/* Dimension index of current level */
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int dim = level % 2;
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/* Coordinate of element splitting at this node */
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CoordT nc = this->xyfunc(n.element, dim);
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/* Coordinate of the element being removed */
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CoordT ec = this->xyfunc(element, dim);
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/* Which side to remove from */
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size_t next = (ec < nc) ? n.left : n.right;
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assert(next != INVALID_NODE); // node must exist somewhere and must be found before a leaf is reached
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/* Descend */
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size_t new_branch = this->RemoveRecursive(element, next, level + 1);
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if (new_branch != next) {
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/* Vector may have been reallocated at this point, n and next are invalid */
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node &nn = this->nodes[node_idx];
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if (ec < nc) nn.left = new_branch; else nn.right = new_branch;
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}
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return node_idx;
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}
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}
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DistT ManhattanDistance(const T &element, CoordT x, CoordT y) const
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{
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return abs((DistT)this->xyfunc(element, 0) - (DistT)x) + abs((DistT)this->xyfunc(element, 1) - (DistT)y);
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}
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/** A data element and its distance to a searched-for point */
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using node_distance = std::pair<T, DistT>;
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/** Ordering function for node_distance objects, elements with equal distance are ordered by less-than comparison */
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static node_distance SelectNearestNodeDistance(const node_distance &a, const node_distance &b)
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{
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if (a.second < b.second) return a;
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if (b.second < a.second) return b;
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if (a.first < b.first) return a;
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if (b.first < a.first) return b;
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NOT_REACHED(); // a.first == b.first: same element must not be inserted twice
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}
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/** Search a sub-tree for the element nearest to a given point */
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node_distance FindNearestRecursive(CoordT xy[2], size_t node_idx, int level, DistT limit = std::numeric_limits<DistT>::max()) const
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{
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/* Dimension index of current level */
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int dim = level % 2;
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/* Node reference */
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const node &n = this->nodes[node_idx];
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/* Coordinate of element splitting at this node */
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CoordT c = this->xyfunc(n.element, dim);
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/* This node's distance to target */
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DistT thisdist = ManhattanDistance(n.element, xy[0], xy[1]);
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/* Assume this node is the best choice for now */
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node_distance best = std::make_pair(n.element, thisdist);
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/* Next node to visit */
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size_t next = (xy[dim] < c) ? n.left : n.right;
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if (next != INVALID_NODE) {
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/* Check if there is a better node down the tree */
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best = SelectNearestNodeDistance(best, this->FindNearestRecursive(xy, next, level + 1));
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}
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limit = std::min(best.second, limit);
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/* Check if the distance from current best is worse than distance from target to splitting line,
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* if it is we also need to check the other side of the split. */
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size_t opposite = (xy[dim] >= c) ? n.left : n.right; // reverse of above
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if (opposite != INVALID_NODE && limit >= abs((int)xy[dim] - (int)c)) {
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node_distance other_candidate = this->FindNearestRecursive(xy, opposite, level + 1, limit);
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best = SelectNearestNodeDistance(best, other_candidate);
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}
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return best;
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}
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template <typename Outputter>
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void FindContainedRecursive(CoordT p1[2], CoordT p2[2], size_t node_idx, int level, const Outputter &outputter) const
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{
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/* Dimension index of current level */
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int dim = level % 2;
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/* Node reference */
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const node &n = this->nodes[node_idx];
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/* Coordinate of element splitting at this node */
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CoordT ec = this->xyfunc(n.element, dim);
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/* Opposite coordinate of element */
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CoordT oc = this->xyfunc(n.element, 1 - dim);
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/* Test if this element is within rectangle */
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if (ec >= p1[dim] && ec < p2[dim] && oc >= p1[1 - dim] && oc < p2[1 - dim]) outputter(n.element);
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/* Recurse left if part of rectangle is left of split */
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if (p1[dim] < ec && n.left != INVALID_NODE) this->FindContainedRecursive(p1, p2, n.left, level + 1, outputter);
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/* Recurse right if part of rectangle is right of split */
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if (p2[dim] > ec && n.right != INVALID_NODE) this->FindContainedRecursive(p1, p2, n.right, level + 1, outputter);
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}
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/** Debugging function, counts number of occurrences of an element regardless of its correct position in the tree */
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size_t CountValue(const T &element, size_t node_idx) const
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{
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if (node_idx == INVALID_NODE) return 0;
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const node &n = this->nodes[node_idx];
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return CountValue(element, n.left) + CountValue(element, n.right) + ((n.element == element) ? 1 : 0);
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}
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void IncrementUnbalanced(size_t amount = 1)
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{
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this->unbalanced += amount;
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}
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/** Check if the entire tree is in need of rebuilding */
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bool IsUnbalanced()
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{
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size_t count = this->Count();
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if (count < 8) return false;
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return this->unbalanced > this->Count() / 4;
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}
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/** Verify that the invariant is true for a sub-tree, assert if not */
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void CheckInvariant(size_t node_idx, int level, CoordT min_x, CoordT max_x, CoordT min_y, CoordT max_y)
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{
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if (node_idx == INVALID_NODE) return;
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const node &n = this->nodes[node_idx];
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CoordT cx = this->xyfunc(n.element, 0);
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CoordT cy = this->xyfunc(n.element, 1);
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assert(cx >= min_x);
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assert(cx < max_x);
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assert(cy >= min_y);
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assert(cy < max_y);
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if (level % 2 == 0) {
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// split in dimension 0 = x
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CheckInvariant(n.left, level + 1, min_x, cx, min_y, max_y);
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CheckInvariant(n.right, level + 1, cx, max_x, min_y, max_y);
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} else {
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// split in dimension 1 = y
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CheckInvariant(n.left, level + 1, min_x, max_x, min_y, cy);
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CheckInvariant(n.right, level + 1, min_x, max_x, cy, max_y);
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}
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}
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/** Verify the invariant for the entire tree, does nothing unless KDTREE_DEBUG is defined */
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void CheckInvariant()
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{
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#ifdef KDTREE_DEBUG
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CheckInvariant(this->root, 0, std::numeric_limits<CoordT>::min(), std::numeric_limits<CoordT>::max(), std::numeric_limits<CoordT>::min(), std::numeric_limits<CoordT>::max());
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#endif
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}
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public:
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/** Construct a new Kdtree with the given xyfunc */
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Kdtree(TxyFunc xyfunc) : root(INVALID_NODE), xyfunc(xyfunc), unbalanced(0) { }
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/**
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* Clear and rebuild the tree from a new sequence of elements,
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* @tparam It Iterator type for element sequence.
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* @param begin First element in sequence.
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* @param end One past last element in sequence.
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*/
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template <typename It>
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void Build(It begin, It end)
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{
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this->nodes.clear();
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this->free_list.clear();
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this->unbalanced = 0;
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if (begin == end) return;
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this->nodes.reserve(end - begin);
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this->root = this->BuildSubtree(begin, end, 0);
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CheckInvariant();
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}
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/**
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* Clear the tree.
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*/
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void Clear()
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{
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this->nodes.clear();
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this->free_list.clear();
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this->unbalanced = 0;
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return;
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}
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/**
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* Reconstruct the tree with the same elements, letting it be fully balanced.
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*/
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void Rebuild()
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{
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this->Rebuild(nullptr, nullptr);
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}
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/**
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* Insert a single element in the tree.
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* Repeatedly inserting single elements may cause the tree to become unbalanced.
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* Undefined behaviour if the element already exists in the tree.
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*/
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void Insert(const T &element)
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{
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if (this->Count() == 0) {
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this->root = this->AddNode(element);
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} else {
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if (!this->IsUnbalanced() || !this->Rebuild(&element, nullptr)) {
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this->InsertRecursive(element, this->root, 0);
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this->IncrementUnbalanced();
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}
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CheckInvariant();
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}
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}
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/**
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* Remove a single element from the tree, if it exists.
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* Since elements are stored in interior nodes as well as leaf nodes, removing one may
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* require a larger sub-tree to be re-built. Because of this, worst case run time is
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* as bad as a full tree rebuild.
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*/
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void Remove(const T &element)
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{
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size_t count = this->Count();
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if (count == 0) return;
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if (!this->IsUnbalanced() || !this->Rebuild(nullptr, &element)) {
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/* If the removed element is the root node, this modifies this->root */
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this->root = this->RemoveRecursive(element, this->root, 0);
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this->IncrementUnbalanced();
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}
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CheckInvariant();
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}
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/** Get number of elements stored in tree */
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size_t Count() const
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{
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assert(this->free_list.size() <= this->nodes.size());
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return this->nodes.size() - this->free_list.size();
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}
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/**
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* Find the element closest to given coordinate, in Manhattan distance.
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* For multiple elements with the same distance, the one comparing smaller with
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* a less-than comparison is chosen.
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*/
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T FindNearest(CoordT x, CoordT y) const
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{
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assert(this->Count() > 0);
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CoordT xy[2] = { x, y };
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return this->FindNearestRecursive(xy, this->root, 0).first;
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}
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/**
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* Find all items contained within the given rectangle.
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* @note Start coordinates are inclusive, end coordinates are exclusive. x1<x2 && y1<y2 is a precondition.
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* @param x1 Start first coordinate, points found are greater or equals to this.
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* @param y1 Start second coordinate, points found are greater or equals to this.
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* @param x2 End first coordinate, points found are less than this.
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* @param y2 End second coordinate, points found are less than this.
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* @param outputter Callback used to return values from the search.
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*/
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template <typename Outputter>
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void FindContained(CoordT x1, CoordT y1, CoordT x2, CoordT y2, const Outputter &outputter) const
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{
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assert(x1 < x2);
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assert(y1 < y2);
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if (this->Count() == 0) return;
|
|
|
|
CoordT p1[2] = { x1, y1 };
|
|
CoordT p2[2] = { x2, y2 };
|
|
this->FindContainedRecursive(p1, p2, this->root, 0, outputter);
|
|
}
|
|
|
|
/**
|
|
* Find all items contained within the given rectangle.
|
|
* @note End coordinates are exclusive, x1<x2 && y1<y2 is a precondition.
|
|
*/
|
|
std::vector<T> FindContained(CoordT x1, CoordT y1, CoordT x2, CoordT y2) const
|
|
{
|
|
std::vector<T> result;
|
|
this->FindContained(x1, y1, x2, y2, [&result](T e) {result.push_back(e); });
|
|
return result;
|
|
}
|
|
};
|
|
|
|
#endif
|