[CF gym 101471A][LOJ6470]Airport Construction

题面

http://codeforces.com/gym/101471/attachments A题

题解

前置知识

• 判线段是否在多边形内 https://www.cnblogs.com/zhangshu/archive/2011/08/08/2130694.html

肉眼目测答案线段至少通过两个多边形顶点。

枚举这两个顶点，判线段是否在多边形内。

若是，将其两边延长直到碰到多边形的边，然后用延长后的边更新答案。

代码

#include<bits/stdc++.h>

using namespace std;

#define rg register
#define In inline
#define ld long double

const ld eps = 1e-7;
const int N = 200;

In int read(){
	int s = 0,ww = 1;
	char ch = getchar();
	while(ch < '0' || ch > '9'){if(ch == '-')ww = -1;ch = getchar();}
	while('0' <= ch && ch <= '9'){s = 10 * s + ch - '0';ch = getchar();}
	return s * ww;
}

In int sgn(ld x){return x < -eps ? -1 : x > eps;}

In ld sqr(ld x){return x * x;}

struct vec{
	ld x,y;
	vec(){}
	vec(ld _x,ld _y){x = _x,y = _y;}
	In friend vec operator + (vec a,vec b){
		return vec(a.x + b.x,a.y + b.y);
	}
	In friend vec operator - (vec a,vec b){
		return vec(a.x - b.x,a.y - b.y);
	}
	In friend vec operator * (vec a,ld k){
		return vec(a.x * k,a.y * k);
	}
	In friend vec operator / (vec a,ld k){
		return vec(a.x / k,a.y / k);
	}
	In friend ld Dot(vec a,vec b){
		return a.x * b.x + a.y * b.y;
	}
	In friend ld Cross(vec a,vec b){
		return a.x * b.y - a.y * b.x;
	}
	In friend bool InUpper(vec a){
		return sgn(a.y) > 0 || (sgn(a.y) == 0 && sgn(a.x) > 0);
	}
	In friend bool prl(vec a,vec b){
		return sgn(Cross(a,b)) == 0;
	}
	In friend bool samedir(vec a,vec b){
		return prl(a,b) && sgn(Dot(a,b)) >= 0;
	}
	In friend ld len(vec a){
		return sqrt(sqr(a.x) + sqr(a.y));
	}
};

struct seg{
	vec p,q;
	seg(){}
	seg(vec _p,vec _q){p = _p,q = _q;}
	In friend bool prl(seg a,seg b){
		return prl(a.q - a.p,b.q - b.p);
	}
	In friend bool samedir(seg a,seg b){
		return samedir(a.q - a.p,b.q - b.p);
	}
	In friend bool OnSeg(seg a,vec p){
		return samedir(p - a.p,a.q - a.p) && samedir(p - a.q,a.p - a.q);
	}
	In friend vec Its(seg a,seg b){
		ld x = Cross(b.q - b.p,a.p - b.p);
		ld y = Cross(a.q - a.p,b.q - b.p);
		return a.p + (a.q - a.p) * x / y;
	}
};

vec p[N+5];
seg a[N+5],t[N+5];
int n;
ld ans;

In bool cmp(seg a,seg b){
	int k = sgn(Cross(a.q-a.p,b.q-b.p));
	if(k != 0)return k > 0;
	return len(a.q - a.p) < len(b.q - b.p);
}

bool inside(vec p,seg a[],int n){ //2:in,1:on,0:out
	bool rt = 0;
	for(rg int i = 1;i <= n;i++){
		seg s = a[i];
		if(OnSeg(s,p))return 1;
		if(sgn(s.p.y-s.q.y) < 0)swap(s.p,s.q);
		if(sgn(p.y-s.p.y) >= 0 || sgn(p.y-s.q.y) < 0)continue;
		rt ^= (sgn(Cross(s.p-p,s.q-p)) > 0);
	}
	return rt << 1;
}

vec P[N+5];
int Pn;

In bool cmp2(vec a,vec b){
	return a.x == b.x ? a.y < b.y : a.x < b.x;
}

void check(seg s,seg a[],int n){
	Pn = 0;
	for(rg int i = 1;i <= n;i++){
		if(prl(s,a[i]))continue;
		vec p = Its(s,a[i]);
		if(OnSeg(a[i],p))P[++Pn] = p;
	}
	if(Pn)sort(P + 1,P + Pn + 1,cmp2);
	int l = 1,r = 0;
	while(l < Pn && !OnSeg(s,P[l]))l++;
	r = l;
	while(r < Pn && OnSeg(s,P[r+1]))r++;
	for(rg int i = l;i < r;i++)
		if(!inside((P[i]+P[i+1])/2,a,n))return;
	while(l > 1 && inside((P[l-1]+P[l])/2,a,n))l--;
	while(r < Pn && inside((P[r+1]+P[r])/2,a,n))r++;
	ans = max(ans,len(P[r]-P[l]));
}

int main(){
	n = read();
	for(rg int i = 1;i <= n;i++){
		int x = read(),y = read();
		p[i] = vec(x,y);
	}	
	for(rg int i = 1;i < n;i++)a[i] = seg(p[i],p[i+1]);
	a[n] = seg(p[n],p[1]);
	for(rg int i = 1;i <= n;i++){
		int cur = 0;
		for(rg int j = 1;j <= n;j++){
			if(i == j || InUpper(p[j]-p[i]))continue;
			t[++cur] = seg(p[i],p[j]);
		}
		sort(t + 1,t + cur + 1,cmp);
		for(rg int j = 1;j <= cur;j++){
			if(j > 1 && samedir(t[j-1],t[j]))continue;
			check(t[j],a,n);
		}
	}
	printf("%.9lf
",(double)ans);
	return 0;
}