Task: K-d tree


C++: #include <algorithm>
#include <array>
#include <cmath>
#include <iostream>
#include <random>
#include <vector>


template<typename coordinate_type, size_t dimensions>
class point {
public:
    point(std::array<coordinate_type, dimensions> c) : coords_(c) {}
    point(std::initializer_list<coordinate_type> list) {
        size_t n = std::min(dimensions, list.size());
        std::copy_n(list.begin(), n, coords_.begin());
    }
    
    coordinate_type get(size_t index) const {
        return coords_[index];
    }
    
    double distance(const point& pt) const {
        double dist = 0;
        for (size_t i = 0; i < dimensions; ++i) {
            double d = get(i) - pt.get(i);
            dist += d * d;
        }
        return dist;
    }
private:
    std::array<coordinate_type, dimensions> coords_;
};

template<typename coordinate_type, size_t dimensions>
std::ostream& operator<<(std::ostream& out, const point<coordinate_type, dimensions>& pt) {
    out << '(';
    for (size_t i = 0; i < dimensions; ++i) {
        if (i > 0)
            out << ", ";
        out << pt.get(i);
    }
    out << ')';
    return out;
}


template<typename coordinate_type, size_t dimensions>
class kdtree {
public:
    typedef point<coordinate_type, dimensions> point_type;
private:
    struct node {
        node(const point_type& pt) : point_(pt), left_(nullptr), right_(nullptr) {}
        coordinate_type get(size_t index) const {
            return point_.get(index);
        }
        double distance(const point_type& pt) const {
            return point_.distance(pt);
        }
        point_type point_;
        node* left_;
        node* right_;
    };
    node* root_ = nullptr;
    node* best_ = nullptr;
    double best_dist_ = 0;
    size_t visited_ = 0;
    std::vector<node> nodes_;

    struct node_cmp {
        node_cmp(size_t index) : index_(index) {}
        bool operator()(const node& n1, const node& n2) const {
            return n1.point_.get(index_) < n2.point_.get(index_);
        }
        size_t index_;
    };

    node* make_tree(size_t begin, size_t end, size_t index) {
        if (end <= begin)
            return nullptr;
        size_t n = begin + (end - begin)/2;
        auto i = nodes_.begin();
        std::nth_element(i + begin, i + n, i + end, node_cmp(index));
        index = (index + 1) % dimensions;
        nodes_[n].left_ = make_tree(begin, n, index);
        nodes_[n].right_ = make_tree(n + 1, end, index);
        return &nodes_[n];
    }

    void nearest(node* root, const point_type& point, size_t index) {
        if (root == nullptr)
            return;
        ++visited_;
        double d = root->distance(point);
        if (best_ == nullptr || d < best_dist_) {
            best_dist_ = d;
            best_ = root;
        }
        if (best_dist_ == 0)
            return;
        double dx = root->get(index) - point.get(index);
        index = (index + 1) % dimensions;
        nearest(dx > 0 ? root->left_ : root->right_, point, index);
        if (dx * dx >= best_dist_)
            return;
        nearest(dx > 0 ? root->right_ : root->left_, point, index);
    }
public:
    kdtree(const kdtree&) = delete;
    kdtree& operator=(const kdtree&) = delete;
    
    template<typename iterator>
    kdtree(iterator begin, iterator end) : nodes_(begin, end) {
        root_ = make_tree(0, nodes_.size(), 0);
    }
    
    
    template<typename func>
    kdtree(func&& f, size_t n) {
        nodes_.reserve(n);
        for (size_t i = 0; i < n; ++i)
            nodes_.push_back(f());
        root_ = make_tree(0, nodes_.size(), 0);
    }

    
    bool empty() const { return nodes_.empty(); }

    
    size_t visited() const { return visited_; }

    
    double distance() const { return std::sqrt(best_dist_); }

    
    const point_type& nearest(const point_type& pt) {
        if (root_ == nullptr)
            throw std::logic_error("tree is empty");
        best_ = nullptr;
        visited_ = 0;
        best_dist_ = 0;
        nearest(root_, pt, 0);
        return best_->point_;
    }
};

void test_wikipedia() {
    typedef point<int, 2> point2d;
    typedef kdtree<int, 2> tree2d;

    point2d points[] = { { 2, 3 }, { 5, 4 }, { 9, 6 }, { 4, 7 }, { 8, 1 }, { 7, 2 } };

    tree2d tree(std::begin(points), std::end(points));
    point2d n = tree.nearest({ 9, 2 });

    std::cout << "Wikipedia example data:\n";
    std::cout << "nearest point: " << n << '\n';
    std::cout << "distance: " << tree.distance() << '\n';
    std::cout << "nodes visited: " << tree.visited() << '\n';
}

typedef point<double, 3> point3d;
typedef kdtree<double, 3> tree3d;

struct random_point_generator {
    random_point_generator(double min, double max)
        : engine_(std::random_device()()), distribution_(min, max) {}

    point3d operator()() {
        double x = distribution_(engine_);
        double y = distribution_(engine_);
        double z = distribution_(engine_);
        return point3d({x, y, z});
    }

    std::mt19937 engine_;
    std::uniform_real_distribution<double> distribution_;
};

void test_random(size_t count) {
    random_point_generator rpg(0, 1);
    tree3d tree(rpg, count);
    point3d pt(rpg());
    point3d n = tree.nearest(pt);

    std::cout << "Random data (" << count << " points):\n";
    std::cout << "point: " << pt << '\n';
    std::cout << "nearest point: " << n << '\n';
    std::cout << "distance: " << tree.distance() << '\n';
    std::cout << "nodes visited: " << tree.visited() << '\n';
}

int main() {
    try {
        test_wikipedia();
        std::cout << '\n';
        test_random(1000);
        std::cout << '\n';
        test_random(1000000);
    } catch (const std::exception& e) {
        std::cerr << e.what() << '\n';
    }
    return 0;
}



Go: 


package main

import (
    "fmt"
    "math"
    "math/rand"
    "sort"
    "time"
)


type point []float64


func (p point) sqd(q point) float64 {
    var sum float64
    for dim, pCoord := range p {
        d := pCoord - q[dim]
        sum += d * d
    }
    return sum
}




type kdNode struct {
    domElt      point
    split       int
    left, right *kdNode
}   

type kdTree struct {
    n      *kdNode
    bounds hyperRect
}
    
type hyperRect struct {
    min, max point
}



func (hr hyperRect) copy() hyperRect {
    return hyperRect{append(point{}, hr.min...), append(point{}, hr.max...)}
}   
    



func newKd(pts []point, bounds hyperRect) kdTree {
    var nk2 func([]point, int) *kdNode
    nk2 = func(exset []point, split int) *kdNode {
        if len(exset) == 0 {
            return nil
        }
        
        
        
        sort.Sort(part{exset, split})
        m := len(exset) / 2
        d := exset[m]
        for m+1 < len(exset) && exset[m+1][split] == d[split] {
            m++
        }
        
        s2 := split + 1
        if s2 == len(d) {
            s2 = 0
        }
        return &kdNode{d, split, nk2(exset[:m], s2), nk2(exset[m+1:], s2)}
    }
    return kdTree{nk2(pts, 0), bounds}
}



type part struct {
    pts   []point
    dPart int
}


func (p part) Len() int { return len(p.pts) }
func (p part) Less(i, j int) bool {
    return p.pts[i][p.dPart] < p.pts[j][p.dPart]
}
func (p part) Swap(i, j int) { p.pts[i], p.pts[j] = p.pts[j], p.pts[i] }





func (t kdTree) nearest(p point) (best point, bestSqd float64, nv int) {
    return nn(t.n, p, t.bounds, math.Inf(1))
}



func nn(kd *kdNode, target point, hr hyperRect,
    maxDistSqd float64) (nearest point, distSqd float64, nodesVisited int) {
    if kd == nil {
        return nil, math.Inf(1), 0
    }
    nodesVisited++
    s := kd.split
    pivot := kd.domElt
    leftHr := hr.copy()
    rightHr := hr.copy()
    leftHr.max[s] = pivot[s]
    rightHr.min[s] = pivot[s]
    targetInLeft := target[s] <= pivot[s]
    var nearerKd, furtherKd *kdNode
    var nearerHr, furtherHr hyperRect
    if targetInLeft {
        nearerKd, nearerHr = kd.left, leftHr
        furtherKd, furtherHr = kd.right, rightHr
    } else {
        nearerKd, nearerHr = kd.right, rightHr
        furtherKd, furtherHr = kd.left, leftHr
    }
    var nv int
    nearest, distSqd, nv = nn(nearerKd, target, nearerHr, maxDistSqd)
    nodesVisited += nv
    if distSqd < maxDistSqd {
        maxDistSqd = distSqd
    }
    d := pivot[s] - target[s]
    d *= d
    if d > maxDistSqd {
        return
    }
    if d = pivot.sqd(target); d < distSqd {
        nearest = pivot
        distSqd = d
        maxDistSqd = distSqd
    }
    tempNearest, tempSqd, nv := nn(furtherKd, target, furtherHr, maxDistSqd)
    nodesVisited += nv
    if tempSqd < distSqd {
        nearest = tempNearest
        distSqd = tempSqd
    }
    return
}

func main() {
    rand.Seed(time.Now().Unix())
    kd := newKd([]point{{2, 3}, {5, 4}, {9, 6}, {4, 7}, {8, 1}, {7, 2}},
        hyperRect{point{0, 0}, point{10, 10}})
    showNearest("WP example data", kd, point{9, 2})
    kd = newKd(randomPts(3, 1000), hyperRect{point{0, 0, 0}, point{1, 1, 1}})
    showNearest("1000 random 3d points", kd, randomPt(3))
}   
    
func randomPt(dim int) point {
    p := make(point, dim)
    for d := range p {
        p[d] = rand.Float64()
    }
    return p
}   
    
func randomPts(dim, n int) []point {
    p := make([]point, n)
    for i := range p {
        p[i] = randomPt(dim) 
    } 
    return p
}
    
func showNearest(heading string, kd kdTree, p point) {
    fmt.Println()
    fmt.Println(heading)
    fmt.Println("point:           ", p)
    nn, ssq, nv := kd.nearest(p)
    fmt.Println("nearest neighbor:", nn)
    fmt.Println("distance:        ", math.Sqrt(ssq))
    fmt.Println("nodes visited:   ", nv)
}