题意:
\(n\)个点,\(q\)个询问,每次问包含询问点的直角三角形有几个
思路:
代码:
#include<bits/stdc++.h>
using namespace std;
const int maxn = 8000 + 10;
typedef long long ll;
const ll mod = 998244353;
typedef unsigned long long ull;
struct Point{
ll x, y;
int flag;
}be[maxn], p[maxn];
int Qua(Point a){
if(a.x > 0 && a.y >= 0) return 1;
if(a.x <= 0 && a.y > 0) return 2;
if(a.x < 0 && a.y <= 0) return 3;
if(a.x >= 0 && a.y < 0) return 4;
}
int cmp1(Point a, Point b) {
ll d = a.x * b.y - b.x * a.y;
if(d == 0) {
return a.x < b.x;
}
else{
return d > 0;
}
}
bool cmp(const Point &a, const Point &b){
int qa = Qua(a), qb = Qua(b);
if(qa == qb){
return cmp1(a, b);
}
return qa < qb;
}
int angle(Point a, Point b){ //爆ll
ull now = (ull)(a.x - b.x) * (a.x - b.x) + (ull)(a.y - b.y) * (a.y - b.y);
ull exc = a.x * a.x + a.y * a.y + b.x * b.x + b.y * b.y;
if(now == exc) return 0; //直角
if(now < exc) return -1; //锐角
return 1; //钝角
}
ll cross(Point a, Point b){
return a.x * b.y - a.y * b.x;
}
ll ans[maxn];
int main(){
int n, q;
scanf("%d%d", &n, &q);
int cnt = 0;
for(int i = 1; i <= n; i++){
cnt++;
scanf("%lld%lld", &be[cnt].x, &be[cnt].y);
be[cnt].flag = 0;
p[cnt] = be[cnt];
}
for(int i = 1; i <= q; i++){
cnt++;
scanf("%lld%lld", &be[cnt].x, &be[cnt].y);
be[cnt].flag = i;
p[cnt] = be[cnt];
}
for(int i = n + 1; i <= cnt; i++){
p[0] = be[i]; //直角点
int tot = 0;
for(int j = 1; j <= n; j++){
p[j].x = be[j].x - be[i].x;
p[j].y = be[j].y - be[i].y;
p[j].flag = be[j].flag;
}
sort(p + 1, p + n + 1, cmp);
for(int j = 1; j <= n; j++){
p[j + n] = p[j];
}
int R = 2;
for(int L = 1; L <= n; L++){
while(R <= 2 * n){
if(cross(p[L], p[R]) < 0) break;
if(angle(p[L], p[R]) >= 0) break;
R++;
}
int tR = R;
while(tR <= 2 * n){
if(cross(p[L], p[tR]) <= 0) break;
if(angle(p[L], p[tR]) != 0) break;
ans[be[i].flag]++;
tR++;
}
}
}
for(int i = 1; i <= n; i++){
p[0] = be[i]; //非直角点
int tot = 0;
for(int j = 1; j <= cnt; j++){
if(j == i) continue;
tot++;
p[tot].x = be[j].x - be[i].x;
p[tot].y = be[j].y - be[i].y;
p[tot].flag = be[j].flag;
}
sort(p + 1, p + tot + 1, cmp);
for(int j = 1; j <= tot; j++){
p[j + tot] = p[j];
}
int R = 2;
for(int L = 1; L <= tot; L++){
while(R <= 2 * tot){
if(cross(p[L], p[R]) < 0) break;
if(angle(p[L], p[R]) >= 0) break;
R++;
}
int tR = R;
while(tR <= 2 * tot){
if(cross(p[L], p[tR]) <= 0) break;
if(angle(p[L], p[tR]) != 0) break;
if(p[L].flag && p[tR].flag == 0){
ans[p[L].flag]++;
}
else if(p[L].flag == 0 && p[tR].flag){
ans[p[tR].flag]++;
}
tR++;
}
}
}
for(int i = 1; i <= q; i++) printf("%lld\n", ans[i]);
return 0;
}
原文地址:https://www.cnblogs.com/KirinSB/p/11634347.html
时间: 2024-10-03 22:08:34