相关链接
题目传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=4829
解题报告
首先我们可以把每一条射线等价为一条垂直于$x$轴的射线
此时问题变成了$Flappy \ Bird$那样
然后我们发现问题就是上下两个凸包互相卡
然后用两个队列瞎搞搞就好了
另外这题精度巨坑
之前用$long double$各种判$EPS$还是挂成狗
所以建议安心用$long long$
Code
#include<bits/stdc++.h>
#define LL long long
using namespace std;
const int N = 1000009;
const int LEN = 1e4;
const double PI = acos(-1);
int n,tot,st[N],head[2],tail[2];
struct Point{
LL x,y; Point *nxt; int pt;
inline Point() {}
inline Point(LL a, LL b):x(a),y(b) {}
inline Point operator + (const Point &P) {return Point(x + P.x, y + P.y);}
inline Point operator - (const Point &P) {return Point(x - P.x, y - P.y);}
inline Point operator * (double t) {return Point(x * t, y * t);}
inline LL operator ^ (const Point &P) {return x * P.x + y * P.y;}
inline LL operator * (const Point &P) {return x * P.y - y * P.x;}
inline bool operator < (const Point &P) const {return x < P.x;}
inline bool operator != (const Point &P) const {return x != P.x || y != P.y;}
inline double len() {return sqrt(x * x + y * y);}
}ss,tt,p[N],vout[N],*que[2][N];
inline int read() {
char c=getchar(); int f=1,ret=0;
while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
while (c<='9'&&c>='0') {ret=ret*10+c-'0';c=getchar();}
return ret * f;
}
inline bool NotInRange(double div, double a, double b) {
if (div >= -PI / 2 && div <= PI / 2) return (a < div || a > PI / 2) && (b < div || b > PI / 2);
else if (div < 0) return a > div && a < PI / 2 && b > div && b < PI / 2;
else return (a > div || a < PI / 2) && (b > div || b < PI / 2);
}
int main() {
n = read(); tt.x = read(); tt.y = read();
for (int i=1;i<=n;i++) {
p[i].x = read(); p[i].y = read();
double r1,r2,r3; scanf("%lf",&r1);
r2 = atan2((ss-p[i]).y, (ss-p[i]).x);
r3 = atan2((tt-p[i]).y, (tt-p[i]).x);
if (NotInRange(r1, r2, r3)) p[i].pt = 1; //射线朝上
else p[i].pt = 0; //射线朝下
}
sort(p+1, p+1+n);
int lim = n; n = 0;
for (int i=1;i<=lim;i++) {
if (p[i].x < ss.x || tt.x < p[i].x) continue;
p[++n] = p[i];
}
p[++n] = tt;
que[0][tail[0] = head[0] = 1] = &ss;
que[1][tail[1] = head[1] = 1] = &ss;
for (int i=1;i<=n;i++) {
int &h1 = head[p[i].pt], &h2 = head[p[i].pt ^ 1], &t1 = tail[p[i].pt], &t2 = tail[p[i].pt ^ 1];
Point **a1 = que[p[i].pt], **a2 = que[p[i].pt ^ 1];
if (h2 < t2 && ((p[i] - *a2[h2]) * (*a2[h2 + 1] - *a2[h2])) * (p[i].pt==1? 1: -1) >= 0) {
while (h2 < t2 && ((p[i] - *a2[h2]) * (*a2[h2 + 1] - *a2[h2])) * (p[i].pt==1? 1: -1) >= 0) {
++h2;
}
p[i].nxt = a2[h2];
a1[h1 = t1 = t1 + 1] = a2[h2];
} else {
while (h1 < t1 && ((p[i] - *a1[t1 - 1]) * (*a1[t1] - *a1[t1 - 1])) * (p[i].pt==1? 1: -1) >= 0) {
--t1;
}
p[i].nxt = a1[t1];
}
a1[++t1] = &p[i];
}
double ans = 0;
for (Point *cur=&p[n],*last;*cur!=ss;) {
last = cur; cur = cur->nxt;
ans += (*cur - *last).len();
}
printf("%.10lf\n",ans);
return 0;
}
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