【ZOJ】4012 Your Bridge is under Attack

【ZOJ】4012 Your Bridge is under Attack

平面上随机n个点，然后给出m条直线，问直线上有几个点

\(n,m \leq 10^{5}\)

由于共线的点不会太多，于是我们可以建KD树出来直接查询，这条直线和某个矩形不相交则不搜索这个子树

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
#define pb push_back
#define space putchar(' ')
#define enter putchar('\n')
#define eps 1e-10
#define ba 47
#define MAXN 100005
//#define ivorysi
using namespace std;
typedef long long int64;
typedef unsigned int u32;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;T f = 1;char c = getchar();
    while(c < '0' || c > '9') {
    if(c == '-') f = -1;
    c = getchar();
    }
    while(c >= '0' && c <= '9') {
    res = res * 10 +c - '0';
    c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) {
    out(x / 10);
    }
    putchar('0' + x % 10);
}
int N,M,d;
pii p[MAXN];
#define lc(u) tr[u].lc
#define rc(u) tr[u].rc
#define siz(u) tr[u].siz
struct node {
    int lc,rc,siz,x,y;
    int x1,y1,x2,y2;
}tr[MAXN];
int rt,Ncnt;

void upmin(int &x,int y) {x = min(x,y);}
void upmax(int &x,int y) {x = max(x,y);}
void update(int u) {
    siz(u) = siz(lc(u)) + siz(rc(u)) + 1;
    tr[u].x1 = tr[u].x2 = tr[u].x;
    tr[u].y1 = tr[u].y2 = tr[u].y;
    upmin(tr[u].x1,min(tr[lc(u)].x1,tr[rc(u)].x1));
    upmax(tr[u].x2,max(tr[lc(u)].x2,tr[rc(u)].x2));
    upmin(tr[u].y1,min(tr[lc(u)].y1,tr[rc(u)].y1));
    upmax(tr[u].y2,max(tr[lc(u)].y2,tr[rc(u)].y2));
}
bool cmp(pii a,pii b) {
    if(d == 0) return a.fi < b.fi || (a.fi == b.fi && a.se < b.se);
    else return a.se < b.se || (a.se == b.se && a.fi < b.fi);
}
bool check(int u,int a,int b) {
    if(1LL * (tr[u].x2 - a) * b + 1LL * tr[u].y2 * a < 0) return false;
    if(1LL * (tr[u].x1 - a) * b + 1LL * tr[u].y1 * a > 0) return false;
    return true;
}
void build(int &u,int l,int r,int D) {
    if(l > r) return;
    u = ++Ncnt;
    if(l == r) {
	lc(u) = rc(u) = 0;
	tr[u].x = p[l].fi;tr[u].y = p[l].se;
	update(u);return;
    }
    d = D;
    int mid = (l + r) >> 1;
    nth_element(p + l,p + mid,p + r + 1,cmp);
    tr[u].x = p[mid].fi;tr[u].y = p[mid].se;
    build(lc(u),l,mid - 1,D ^ 1);
    build(rc(u),mid + 1,r,D ^ 1);
    update(u);
}
int Query(int u,int a,int b) {
    if(!check(u,a,b)) return 0;
    int res = 0;
    if(1LL * (tr[u].x - a) * b + 1LL * a * tr[u].y == 0) ++res;
    res += Query(lc(u),a,b);
    res += Query(rc(u),a,b);
    return res;
}
void Solve() {
    Ncnt = 0;rt = 0;
    tr[0].x1 = tr[0].y1 = 1e9 + 10;
    tr[0].y2 = tr[0].y2 = -1;
    read(N);read(M);
    for(int i = 1 ; i <= N ; ++i) {
	read(p[i].fi);read(p[i].se);
    }
    build(rt,1,N,0);
    int a,b;
    for(int i = 1 ; i <= M ; ++i) {
	read(a);read(b);
	out(Query(rt,a,b));enter;
    }
}
int main(){
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    int T;
    read(T);
    for(int i = 1 ; i <= T ; ++i) Solve();

    return 0;
}