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package kdtree
import (
"container/heap"
"github.com/hongshibao/go-algo"
)
type Point interface {
// Return the total number of dimensions
Dim() int
// Return the value X_{dim}, dim is started from 0
GetValue(dim int) float64
// Return the distance between two points
Distance(p Point) float64
// Return the distance between the point and the plane X_{dim}=val
PlaneDistance(val float64, dim int) float64
}
type PointBase struct {
Point
Vec []float64
}
func (b PointBase) Dim() int {
return len(b.Vec)
}
func (b PointBase) GetValue(dim int) float64 {
return b.Vec[dim]
}
func NewPointBase(vals []float64) PointBase {
ret := PointBase{}
for _, val := range vals {
ret.Vec = append(ret.Vec, val)
}
return ret
}
type kdTreeNode struct {
axis int
splittingPoint Point
leftChild *kdTreeNode
rightChild *kdTreeNode
}
type KDTree struct {
root *kdTreeNode
dim int
}
func (t *KDTree) Dim() int {
return t.dim
}
func (t *KDTree) KNN(target Point, k int) []Point {
hp := &kNNHeapHelper{}
t.search(t.root, hp, target, k)
ret := make([]Point, 0, hp.Len())
for hp.Len() > 0 {
item := heap.Pop(hp).(*kNNHeapNode)
ret = append(ret, item.point)
}
for i := len(ret)/2 - 1; i >= 0; i-- {
opp := len(ret) - 1 - i
ret[i], ret[opp] = ret[opp], ret[i]
}
return ret
}
func (t *KDTree) search(p *kdTreeNode,
hp *kNNHeapHelper, target Point, k int) {
stk := make([]*kdTreeNode, 0)
for p != nil {
stk = append(stk, p)
if target.GetValue(p.axis) < p.splittingPoint.GetValue(p.axis) {
p = p.leftChild
} else {
p = p.rightChild
}
}
for i := len(stk) - 1; i >= 0; i-- {
cur := stk[i]
dist := target.Distance(cur.splittingPoint)
if hp.Len() < k || (*hp)[0].distance >= dist {
heap.Push(hp, &kNNHeapNode{
point: cur.splittingPoint,
distance: dist,
})
if hp.Len() > k {
heap.Pop(hp)
}
}
if hp.Len() < k || target.PlaneDistance(
cur.splittingPoint.GetValue(cur.axis), cur.axis) <=
(*hp)[0].distance {
if target.GetValue(cur.axis) < cur.splittingPoint.GetValue(cur.axis) {
t.search(cur.rightChild, hp, target, k)
} else {
t.search(cur.leftChild, hp, target, k)
}
}
}
}
func NewKDTree(points []Point) *KDTree {
if len(points) == 0 {
return nil
}
ret := &KDTree{
dim: points[0].Dim(),
root: createKDTree(points, 0),
}
return ret
}
func createKDTree(points []Point, depth int) *kdTreeNode {
if len(points) == 0 {
return nil
}
dim := points[0].Dim()
ret := &kdTreeNode{
axis: depth % dim,
}
if len(points) == 1 {
ret.splittingPoint = points[0]
return ret
}
idx := selectSplittingPoint(points, ret.axis)
if idx == -1 {
return nil
}
ret.splittingPoint = points[idx]
ret.leftChild = createKDTree(points[0:idx], depth+1)
ret.rightChild = createKDTree(points[idx+1:len(points)], depth+1)
return ret
}
type selectionHelper struct {
axis int
points []Point
}
func (h *selectionHelper) Len() int {
return len(h.points)
}
func (h *selectionHelper) Less(i, j int) bool {
return h.points[i].GetValue(h.axis) < h.points[j].GetValue(h.axis)
}
func (h *selectionHelper) Swap(i, j int) {
h.points[i], h.points[j] = h.points[j], h.points[i]
}
func selectSplittingPoint(points []Point, axis int) int {
helper := &selectionHelper{
axis: axis,
points: points,
}
mid := len(points)/2 + 1
err := algo.QuickSelect(helper, mid)
if err != nil {
return -1
}
return mid - 1
}
type kNNHeapNode struct {
point Point
distance float64
}
type kNNHeapHelper []*kNNHeapNode
func (h kNNHeapHelper) Len() int {
return len(h)
}
func (h kNNHeapHelper) Less(i, j int) bool {
return h[i].distance > h[j].distance
}
func (h kNNHeapHelper) Swap(i, j int) {
h[i], h[j] = h[j], h[i]
}
func (h *kNNHeapHelper) Push(x interface{}) {
item := x.(*kNNHeapNode)
*h = append(*h, item)
}
func (h *kNNHeapHelper) Pop() interface{} {
old := *h
n := len(old)
item := old[n-1]
*h = old[0 : n-1]
return item
}
|
