P2093 [国家集训队]JZPFAR

 

P2093 [国家集训队]JZPFAR

https://www.luogu.org/problemnew/show/P2093

分析：

　　kdtree模板

　　维护一个小根堆，开始时插入k个-inf，每次取出最小的与当前更新，如果当前的更大一些，那么更新堆中的元素。

代码：

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;

inline int read() {
    int x=0,f=1;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-1;
    for (;isdigit(ch);ch=getchar())x=x*10+ch-'0';return x*f;
}

const int N = 200010;
const int DIM = 2;
const LL INF = 1e9;
 
struct Point{
    LL x[2];int id;
    Point() {x[0] = 0;x[1] = 0;}
    Point(LL a,LL b) {x[0] = a,x[1] = b;}
    LL& operator[](int c){return x[c];}
}P[N],Q;
struct KDtree{
    int ch[2],mn[2],mx[2];
    Point p;
}T[N<<1];
struct State{
    LL dis;int id;
    State() {}
    State(LL a,LL b) {dis = a,id = b;}
    bool operator < (const State &A) const {
        if (dis == A.dis) return id < A.id;
        return dis > A.dis;
    }
};
priority_queue <State> q;
int Cur,CntNode,Root;

#define lc T[rt].ch[0]
#define rc T[rt].ch[1]

bool cmp(Point a,Point b) {
    return a.x[Cur] < b.x[Cur];
}
void pushup(int rt) {
    for (int i=0; i<DIM; ++i) {
        if (lc) T[rt].mn[i] = min(T[rt].mn[i], T[lc].mn[i]), T[rt].mx[i] = max(T[rt].mx[i],T[lc].mx[i]);
        if (rc) T[rt].mn[i] = min(T[rt].mn[i], T[rc].mn[i]), T[rt].mx[i] = max(T[rt].mx[i],T[rc].mx[i]);
    }
}
void NewNode(int rt,Point p) {
    T[rt].p = p;
    T[rt].mn[0] = T[rt].mx[0] = p.x[0];
    T[rt].mn[1] = T[rt].mx[1] = p.x[1];
}
int build(int l,int r,int cd) {
    if (l > r) return 0;
    int m = (l + r) >> 1,rt = m;
    Cur = cd; nth_element(P+l, P+m, P+r+1, cmp);
    NewNode(rt,P[m]);
    lc = build(l, m-1, cd^1); 
    rc = build(m+1, r, cd^1);
    pushup(rt);
    return rt;
}
/*void Insert(Point p,int &rt,int cd) {
    if (!rt) {
        NewNode(rt = ++CntNode, p); return ;
    }
    if (p.x[cd] < T[rt].p.x[cd]) Insert(p, lc, cd^1);
    else Insert(p, rc, cd^1);
    pushup(rt);
}*/
LL sqr(LL x) {
    return x * x;
}
LL dis(Point a,Point b) {
    return sqr(a.x[0] - b.x[0]) + sqr(a.x[1] - b.x[1]);
}
LL dist(Point a,KDtree b) {
    LL res = 0;
    res += max(sqr(a.x[0] - b.mn[0]), sqr(a.x[0] - b.mx[0]));
    res += max(sqr(a.x[1] - b.mn[1]), sqr(a.x[1] - b.mx[1]));
    return res;
}
void query(Point p,int rt) {
    if (!rt) return ;
    LL d = dis(T[rt].p,p);
    if (d > q.top().dis || (d==q.top().dis && T[rt].p.id < q.top().id)) 
        q.pop(), q.push(State(d,T[rt].p.id));
    LL dl = lc ? dist(p,T[lc]) : 0; // --- T[rt] !!!
    LL dr = rc ? dist(p,T[rc]) : 0; // --- T[rt] !!!
    if (dl > dr) {
        if (dl >= q.top().dis) query(p,lc);
        if (dr >= q.top().dis) query(p,rc);
    }
    else {
        if (dr >= q.top().dis) query(p,rc);
        if (dl >= q.top().dis) query(p,lc);
    }
}
int main() {
    int n = read();
    for (int x,y,i=1; i<=n; ++i) {
        P[i].x[0] = read(),P[i].x[1] = read(); 
        P[i].id = i;
    }
    Root = build(1,n,0);
    int m = read();
    while (m--) {
        int x = read(),y = read(),k = read();
        for (int i=1; i<=k; ++i) q.push(State(-INF,0));
        query(Point(x,y),Root);
        printf("%d
",q.top().id);
        while (!q.empty()) q.pop();
    }
    return 0;
}