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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