Kd树迭代实现(C++)

Question

你好，有人有 C++ 中 Kd-Tree 的迭代实现吗？ 我尝试过，但当节点数量为奇数时，它会失败。 到目前为止，这是我的代码。我正在参考 http://ldots.org/kdtree/#buildingAkDTree 网站了解详细信息。

#include <stdio.h>
#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <stack>
#include <queue>
#include <iomanip>


struct Point {
    double pt[2];
    int id;
};

typedef std::vector<Point> TPointVector;

struct KdNode {
    double point[2];
    int id;
    double desc;
    bool leaf;

    KdNode *left;
    KdNode *right;
    KdNode *parent;
    KdNode(KdNode *parent_):parent(parent_),leaf(false){}
    KdNode(KdNode *parent_,TPointVector::iterator itr, int depth, TPointVector &pv);
    KdNode(KdNode *t, TPointVector &pv);

};

KdNode::KdNode(KdNode *parent_,TPointVector::iterator itr, int depth, TPointVector &pv) {
    parent = parent_ ;
    left   = 0;
    right  = 0;
    desc   = itr->pt[depth % 2 ];
    leaf   = false;
}

KdNode::KdNode(KdNode *t, TPointVector &pv) {
    id       = pv[0].id;
    point[0] = pv[0].pt[0];
    point[1] = pv[0].pt[1];
    left     = 0;
    right    = 0;
    parent   = t;
    leaf     = true;
}

KdNode *pRoot = 0;


struct ComparePoints {
    int cord;
    ComparePoints(int  cord_) : cord(cord_ % 2) { };
    bool operator()(const Point& lhs, const Point& rhs) const {
        return lhs.pt[cord] < rhs.pt[cord];
    }
};
void buildLeftTree(std::stack<TPointVector > &stackL) {
    KdNode *pCurrent = pRoot;
    KdNode **pNode  = &(pCurrent->left);
    int depth      = 0; 
    bool changeDirection = false;
    while (! stackL.empty()) {
        TPointVector pv = stackL.top(); 
        stackL.pop();
        if ( pv.size() != 1 ) { 
            std::sort(pv.begin(), pv.end(), ComparePoints(++depth));

            *pNode = new KdNode(pCurrent, pv.begin() + pv.size()/2, depth, pv);

            TPointVector lvp,rvp;
            std::size_t median = pv.size() / 2;
            std::copy(pv.begin(), pv.begin() + median, std::back_inserter(lvp));
            std::copy(pv.begin() + median, pv.end(), std::back_inserter(rvp));

            stackL.push(rvp); 
            stackL.push(lvp);

            if ( changeDirection ) {
                pCurrent = pCurrent->right;
                changeDirection = false;
            } else {
                pCurrent = pCurrent->left;
            }           
            pNode = &(pCurrent->left);

        } else {
            KdNode **pNodeLeft   = &(pCurrent->left);
            *pNodeLeft  = new KdNode(pCurrent, pv);
            pv = stackL.top();
            stackL.pop();

            KdNode **pNodeRight   = &(pCurrent->right);
            *pNodeRight  = new KdNode(pCurrent,pv);

            pCurrent = pCurrent->parent;
            pNode  = &(pCurrent->right);
            changeDirection = true;
            depth--;
        }           
    }
}

void buildRightTree(std::stack<TPointVector > &stackR) {
    KdNode *pCurrent = pRoot;
    KdNode **pNode  = &(pCurrent->right);
    int depth      = 0; 
    bool changeDirection = true;
    while (! stackR.empty()) {
        TPointVector pv = stackR.top(); 
        stackR.pop();

        if ( pv.size() != 1 ) { 
            std::sort(pv.begin(), pv.end(), ComparePoints(++depth));
            *pNode = new KdNode(pCurrent, pv.begin() + pv.size()/2, depth, pv);

            TPointVector lvp,rvp;
            std::size_t median = pv.size() / 2;
            std::copy(pv.begin(), pv.begin() + median, std::back_inserter(lvp));
            std::copy(pv.begin() + median, pv.end(), std::back_inserter(rvp));

            stackR.push(rvp); 
            stackR.push(lvp);       

            if ( changeDirection ) {
                pCurrent = pCurrent->right;
                changeDirection = false;
            } else {
                pCurrent = pCurrent->left;
            }       
            pNode = &(pCurrent->left);

        } else {
            KdNode **pNodeLeft   = &(pCurrent->left);
            *pNodeLeft  = new KdNode(pCurrent, pv);
            pv = stackR.top();
            stackR.pop();

            KdNode **pNodeRight   = &(pCurrent->right);
            *pNodeRight  = new KdNode(pCurrent,pv);

            pCurrent = pCurrent->parent;
            pNode  = &(pCurrent->right);
            depth--;
            changeDirection = true;
        }           
    }
}


void constructKD(TPointVector &pv) {
    int depth = 0;
    std::sort(pv.begin(), pv.end(), ComparePoints(depth));

    pRoot        = new KdNode(0);
    pRoot->desc  = ( pv.begin() + pv.size()/2)->pt[0];
    pRoot->left  = 0;
    pRoot->right = 0;

    TPointVector lvp, rvp;
    std::copy(pv.begin(), pv.begin() + pv.size()/2, std::back_inserter(lvp));
    std::copy(pv.begin() + pv.size()/2, pv.end(), std::back_inserter(rvp));

    std::stack<TPointVector > stackL, stackR;
    stackL.push(lvp);
    stackR.push(rvp);

    buildLeftTree(stackL);
    buildRightTree(stackR);

}
void readPoints(const char* fileName, TPointVector& points) {
    std::ifstream input(fileName);

    if ( input.peek() != EOF ) {
        while(!input.eof()) {
            int id = 0;
            double x_cord, y_cord;
            input >> id >> x_cord >> y_cord;

            Point t ;
            t.pt[0] = x_cord;
            t.pt[1] = y_cord;
            t.id    = id;

            points.push_back(t);
        }
        input.close();
    }   
}
void _printLevelWise(KdNode *node, std::queue<KdNode *> Q) {
    int depth = 0;
    while ( ! Q.empty()) {
        KdNode *qNode = Q.front();Q.pop();
        if ( qNode->leaf ) {
            std::cout << "[" << qNode->id << "]" << std::setprecision (25) << "(" << qNode->point[0] << "," << qNode->point[1] << ")" << std::endl;
        } else {
            std::cout << std::setprecision (25) << qNode->desc << std::endl;
        }       
        if (qNode->left != 0)
            Q.push(qNode->left);
        if (qNode->right != 0)
            Q.push(qNode->right);
    }
}
void PrintLevelWise(KdNode *node) {
    std::queue<KdNode *> Q;
    Q.push(node);
    _printLevelWise(node, Q);
}
int main ( int argc, char **argv ) {
    if ( argc <= 1 ) {
        return 0;
    }
    TPointVector points;
    readPoints(argv[1], points);
    for ( TPointVector::iterator itr = points.begin(); itr != points.end(); ++itr) {
        std::cout << "(" << itr->pt[0] << "," << itr->pt[1] << ")" << std::endl;
    }
    if ( points.size() == 0 )
        return 0;
    constructKD(points);
    PrintLevelWise(pRoot);
    std::cout << "Construction of KD Tree Done " << std::endl;
}

失败的示例输入：

1 6 1 
2 5 5 
3 9 6 
4 3 6 
5 4 9

有效的示例输入：

1 6 1 
2 5 5 
3 9 6 
4 3 6 
5 4 9 
6 4 0 
7 7 9 
8 2 9

Answer 1

buildLeftTree 和 buildRightTree 中的 else 不处理右子树上有奇数个节点的情况。在您的 5 点示例中，buildRightTree 中的 else 情况最终在 stackR 上得到三个点，第一个点用于 left 节点，后两个它默默地分配给 right 节点，就好像它是唯一的节点一样。

这是由于您的中值选择所使用的标准与您引用的网站上列出的标准不同。

std::size_t median = pv.size() / 2; // degenerates in cases where size() is odd

您的选择标准应该基于 x 或 y 值的中位数，并使用基于该标准的子列表（不假定任何给定的大小）。

Answer 2

在 buildLeftTree 和 buildRightTree 的 else 中。

在堆栈的 top 和 pop 函数之间添加

if (pv.size() > 1)
{
    pNode = &(pCurrent->right);
    continue;
}

。会没事的。

我还有一个问题，当点数达到百万级时，建树会很慢，如何提高性能？