KD-Tree解决空间最短距离的利器

KD-Tree解决空间最短距离的利器

本文作者：Caozhijie

/**************************************************************
    Problem: 2648
    User: Cardinal
    Language: C++
    Result: Accepted
    Time:14476 ms
    Memory:40356 kb
****************************************************************/

#include <cstdio>
#include <cstring>
#include <climits>
#include <iostream>
#include <algorithm>
using namespace std;

#define Min(a, b) ((a)<(b)?(a):(b))
#define Max(a, b) ((a)>(b)?(a):(b))
#define Abs(x) ((x)>0?(x):-(x))

#define N 500010
#define M 500010
int n, m;

struct Point {
    int x, y;
    Point(int _x = 0, int _y = 0):x(_x),y(_y){}
    void set(int _, int __) {
        x = _, y = __;
    }
}P[N + M];
int Dis(const Point &A, const Point &B) {
    return Abs(A.x - B.x) + Abs(A.y - B.y);
}

bool sign;
inline bool cmp(const Point &A, const Point &B) {
    if (sign)
        return A.x < B.x || (A.x == B.x && A.y < B.y);
    else
        return A.y < B.y || (A.y == B.y && A.x < B.x);
}

struct Node {
    Node *l, *r;
    int x[2], y[2];
    Point p;

    void SetP(const Point &P) {
        p = P;
        x[0] = x[1] = P.x;
        y[0] = y[1] = P.y;
    }
    int Dis(const Point &p) const {
        int res = 0;
        if (p.x < x[0] || p.x > x[1])
            res += (p.x < x[0]) ? x[0] - p.x : p.x - x[1];
        if (p.y < y[0] || p.y > y[1])
            res += (p.y < y[0]) ? y[0] - p.y : p.y - y[1];
        return res;
    }
    void up(Node *B) {
        x[0] = Min(x[0], B->x[0]);
        x[1] = Max(x[1], B->x[1]);
        y[0] = Min(y[0], B->y[0]);
        y[1] = Max(y[1], B->y[1]);
    }
}mem[N + M], *C = mem, Tnull, *null = &Tnull;

Node *Build(int tl, int tr, bool d) {
    if (tl > tr)
        return null;

    int mid = (tl + tr) >> 1;
    sign = d;
    std::nth_element(P + tl + 1, P + mid + 1, P + tr + 1, cmp);

    Node *q = C++;
    q->SetP(P[mid]);
    q->l = Build(tl, mid - 1, d ^ 1);
    q->r = Build(mid + 1, tr, d ^ 1);
    if (q->l != null)
        q->up(q->l);
    if (q->r != null)
        q->up(q->r);
    return q;
}

#define INF 0x3f3f3f3f
int res;
void Ask(Node *q, const Point &p) {
    res = Min(res, Dis(q->p, p));
    int DisL = q->l != null ? q->l->Dis(p) : INF;
    int DisR = q->r != null ? q->r->Dis(p) : INF;
    if (DisL < DisR) {
        if (q->l != null)
            Ask(q->l, p);
        if (DisR < res && q->r != null)
            Ask(q->r, p);
    }
    else {
        if (q->r != null)
            Ask(q->r, p);
        if (DisL < res && q->l != null)
            Ask(q->l, p);
    }
}

void Insert(Node *root, const Point &p) {
    Node *q = C++;
    q->l = q->r = null;
    q->SetP(p);

    sign = 0;
    while(1) {
        root->up(q);
        if (cmp(q->p, root->p)) {
            if (root->l == null) {
                root->l = q;
                break;
            }
            else
                root = root->l;
        }
        else {
            if (root->r == null) {
                root->r = q;
                break;
            }
            else
                root = root->r;
        }
        sign ^= 1;
    }
}

int main() {
    #ifndef ONLINE_JUDGE
    //freopen("tt.in", "r", stdin);
    //freopen("tt.out", "w", stdout);
    #endif

    scanf("%d%d", &n, &m);

    register int i;
    int ope, x, y;
    for(i = 1; i <= n; ++i) {
        scanf("%d%d", &x, &y);
        P[i] = Point(x, y);
    }

    Node* root = Build(1, n, 0);

    while(m--) {
        scanf("%d%d%d", &ope, &x, &y);
        if (ope == 1)
            Insert(root, Point(x, y));
        else {
            res = INF;
            Ask(root, Point(x, y));
            printf("%d\n", res);
        }
    }

    return 0;
}