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