• kd-tree板子


    #include<iostream>
    #include<cstdio>
    #include<algorithm>
    #include<vector>
    #include<cmath>
    #define alpha (0.75)
    using namespace std;
    const int N = 6e5 + 5;
    const int INF = 0x3f3f3f3f;
    bool dimension;
    bool reg_dimension;
    int n, m, ans;
    struct Point
    {
        int x, y;
        Point(int X = 0, int Y = 0) :x(X), y(Y) {}
    };
    Point a[N];
    struct Node *null;
    struct Node
    {
        int cover;
        Point p, r1, r2;
        Node *son[2];
        inline void maintain()
        {
            r1.x = min(r1.x, min(son[0]->r1.x, son[1]->r1.x));
            r1.y = min(r1.y, min(son[0]->r1.y, son[1]->r1.y));
            r2.x = max(r2.x, max(son[0]->r2.x, son[1]->r2.x));
            r2.y = max(r2.y, max(son[0]->r2.y, son[1]->r2.y));
            cover = son[0]->cover + son[1]->cover + 1;
        }
        inline bool is_bad()
        {
            return max(son[0]->cover, son[1]->cover) > cover*alpha + 5;
        }
        inline int dis(Point p)
        {
            if (this == null)return INF;
            int res = 0;
            //曼哈顿距离
            if (p.x<r1.x || p.x>r2.x)res += p.x < r1.x ? r1.x - p.x : p.x - r2.x;
            if (p.y<r1.y || p.y>r2.y)res += p.y < r1.y ? r1.y - p.y : p.y - r2.y;
            return res;
        }
    };
    Node mempool[N];
    Node *tail;
    Node *root;
    inline bool cmp(Point p1, Point p2)
    {
        if (dimension == 0)return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y);
        return p1.y < p2.y || (p1.y == p2.y && p1.x < p2.x);
    }
    inline int Manhattan_dis(Point a, Point b)//曼哈顿距离
    {
        return abs(a.x - b.x) + abs(a.y - b.y);
    }
    inline double Oshi_dis(Point a,Point b)
    {
        return sqrt(1.0*(a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y));
    }
    inline void init()
    {
        tail = mempool;
        null = tail++;
        null->son[0] = null->son[1] = null;
        null->r1 = Point(INF, INF);
        null->r2 = Point(-INF, -INF);
        null->cover = 0;
        root = null;
    }
    inline Node* new_node(Point key)
    {
        Node *o;
        o = tail++;
        o->son[0] = o->son[1] = null;
        o->cover= 1;
        o->p = o->r1 = o->r2 = key;
        return o;
    }
    inline void travel(Node* p, vector<Node*>&x)
    {
        if (p == null)return;
        travel(p->son[0], x);
        x.push_back(p);
        travel(p->son[1], x);
    }
    inline Node* divide(vector<Node*>&x, int l, int r, bool d)
    {
        if (l >= r)return null;
        int mid = (l + r) >> 1;
        dimension = d;
        Node *o = x[mid];
        o->son[0] = divide(x, l, mid, d ^ 1);
        o->son[1] = divide(x, mid + 1, r, d ^ 1);
        o->maintain();
        return o;
    }
    inline void rebuild(Node *&o, bool d)
    {
        static vector<Node*>v;
        v.clear();
        travel(o, v);
        o = divide(v, 0, v.size(), d);
    }
    inline Node* build(int l, int r, bool d)
    {
        if (l >= r)return null;
        int mid = (l + r) >> 1;
        dimension = d;
        nth_element(a + l, a + mid, a + r, cmp);
        Node *o = new_node(a[mid]);
        o->son[0] = build(l, mid, d ^ 1);
        o->son[1] = build(mid + 1, r, d ^ 1);
        o->maintain();
        return o;
    }
    inline Node** __insert(Node *&o, Point key)
    {
        if (o == null)
        {
            o = new_node(key);
            reg_dimension = dimension;
            return &null;
        }
        else
        {
            o->cover++;
            bool dir = cmp(key, o->p) ^ 1;
            dimension ^= 1;
            Node** res = __insert(o->son[dir], key);
            if (o->is_bad())
            {
                res = &o;
                reg_dimension = dimension;//记录递归过程中最后一个较为不平衡的结点
            }
            o->maintain();
            return res;
        }
    }
    inline void insert(Point key)
    {
        reg_dimension = dimension = 0;
        Node** res = __insert(root, key);
        if (*res != null)rebuild(*res, reg_dimension);
    }
    inline void query(Node *o, Point key)
    {
        if (o == null)return;
        ans = min(ans, Manhattan_dis(key, o->p));
        int dir = o->son[0]->dis(key) > o->son[1]->dis(key);
        query(o->son[dir], key);
        if (o->son[dir ^ 1]->dis(key) < ans)
            query(o->son[dir ^ 1], key);
    }
    inline int read()
    {
        char ch = getchar();   int f = 1, x = 0;
        while (ch > '9' || ch < '0') { if (ch == '-')f = -1; ch = getchar(); }
        while (ch >= '0'&&ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); }
        return x * f;
    }
    int main()
    {
        init();
        n = read(); m = read();
        for (int i = 0; i < n; i++) a[i].x = read(), a[i].y = read();
        root = build(0, n, 0);
        while (m--)
        {
            int op = read(), x = read(), y = read();
            if (op == 1)insert(Point(x, y));
            else
            {
                ans = INF;
                query(root, Point(x, y));
                printf("%d
    ", ans);
            }
        }
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/King-of-Dark/p/12826972.html
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