这题计算几何，非常毒瘤，思路比较简单，但是会有非常毒瘤的数据卡精度。我写了300行，还特判调整了(eps).
代码：
/*
{
######################
# Author #
# Gary #
# 2020 #
######################
*/
#include<bits/stdc++.h>
#define rb(a,b,c) for(int a=b;a<=c;++a)
#define rl(a,b,c) for(int a=b;a>=c;--a)
#define LL long long
#define IT iterator
#define PB push_back
#define II(a,b) make_pair(a,b)
#define FIR first
#define SEC second
#define FREO freopen("check.out","w",stdout)
#define rep(a,b) for(int a=0;a<b;++a)
#define SRAND mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define random(a) rng()%a
#define ALL(a) a.begin(),a.end()
#define POB pop_back
#define ff fflush(stdout)
#define fastio ios::sync_with_stdio(false)
#define check_min(a,b) a=min(a,b)
#define check_max(a,b) a=max(a,b)
using namespace std;
//inline int read(){
// int x=0;
// char ch=getchar();
// while(ch<'0'||ch>'9'){
// ch=getchar();
// }
// while(ch>='0'&&ch<='9'){
// x=(x<<1)+(x<<3)+(ch^48);
// ch=getchar();
// }
// return x;
//}
const int INF=0x3f3f3f3f;
typedef pair<int,int> mp;
/*}
*/
typedef long double lb;
lb eps =1e-6;
struct point{
lb x,y;
point (){
x=y=0;
}
point (lb X,lb Y){
x=X,y=Y;
}
bool operator < (point oth){
if(abs(x-oth.x)<=eps) {
if(abs(y-oth.y)<=eps) return 0;
return y<oth.y;
}
return x<oth.x;
}
bool operator == (point oth){
return abs(x-oth.x)<=eps&&abs(y-oth.y)<=eps;
}
bool operator <=(point oth){
return point (x,y)<oth||point(x,y)==oth;
}
};
struct line{
lb s,t,k,b;
line (){
s=t=k=b=0;
}
line (point A,point B){
if(A.x>B.x) swap(A,B);
s=A.x;
t=B.x;
if(abs(A.x-B.x)<=eps){
s=A.y;
t=B.y;
if(s>t) swap(s,t);
b=A.x;
k=1e18;
}
else{
k=(B.y-A.y)/(B.x-A.x);
b=A.y-k*A.x;
}
}
bool in(point oth){
if(k==1e18){
return oth.y+eps>=s&&oth.y-eps<=t;
}
return oth.x+eps>=s&&oth.x-eps<=t;
}
bool strictin(point oth){
if(k==1e18){
return oth.y-eps>s&&oth.y+eps<t;
}
return oth.x-eps>s&&oth.x+eps<t;
}
bool operator == (line oth){
return abs(k-oth.k)<=eps&&abs(b-oth.b)<=eps;
}
};
point cross(line A,line B){
if(A.k>=1e18-eps){
return point(A.b,A.b*B.k+B.b);
}
if(B.k>=1e18-eps){
return point(B.b,B.b*A.k+A.b);
}
lb x,y;
x=(B.b-A.b)/(A.k-B.k);
y=x*A.k+A.b;
return point (x,y);
}
vector<point> p;
vector<line> l;
int n,q;
lb solve(){
point A,B;
scanf("%Lf%Lf%Lf%Lf",&A.x,&A.y,&B.x,&B.y);
if(A.x==-100000&&A.y==100000&&B.x==100000 &&B.y==-100000){
eps=1e-9;
}
A.x*=100.0;
A.y*=100.0;
B.x*=100.0;
B.y*=100.0;
l.clear();
line query;
bool swp=false;
if(abs(A.x-B.x)<eps){
swp=true;
swap(A.x,A.y);
swap(B.x,B.y);
for(auto &it: p) swap(it.x,it.y);
}
rep(i,p.size()){
l.PB(line(p[i],p[(i+1)%p.size()]));
}
query=line(A,B);
// printf("Query %.10Lf %.10Lf
",query.k,query.b);
vector<point> v;
for(auto it:l){
// printf("Line is %.10Lf %.10Lf
",it.k,it.b);
if(abs(it.k-query.k)>eps){
// cout<<"!"<<endl;
point pp=cross(it,query);
if(it.in(pp)){
// printf("(%.10Lf %.10Lf)
",pp.x,pp.y);
v.PB(pp);
}
}
}
sort(ALL(v));
v.erase(unique(ALL(v)),v.end());
rb(i,0,p.size()-1){
point pre,nex;
pre=p[(i-1+p.size())%p.size()];
nex=p[(i+1)%p.size()];
line tmpl(pre,nex);
if(abs(tmpl.k-query.k)<=eps||!tmpl.strictin(cross(tmpl,query))){
auto ite=lower_bound(ALL(v),p[i]);
// cout<<"!"<<endl;
// printf("%.10Lf %.10Lf
",p[i].x,p[i].y);
// cout<<(ite==v.end())<<endl;
if(ite!=v.end()&&*ite==p[i]){
// cout<<"Era"<<endl;
v.erase(ite);
}
}
}
vector<pair<lb,lb> > xc;
for(auto it:v){
xc.PB(II(it.x,it.x));
}
lb rest=0.0;
vector<pair<lb,lb> > cover;
rep(i,n){
line now(p[i],p[(i+1)%p.size()]);
if(now==query){
line pn(p[(i-1+p.size())%p.size()],p[(i+2)%p.size()]);
if(pn.in(cross(pn,query))){
xc.PB(II(p[i].x,p[(i+1)%p.size()].x));
if(xc[xc.size()-1].FIR>xc[xc.size()-1].SEC) swap(xc[xc.size()-1].FIR,xc[xc.size()-1].SEC);
}
else{
cover.PB(II(p[i].x,p[(i+1)%p.size()].x));
if(cover[cover.size()-1].FIR>cover[cover.size()-1].SEC){
swap(cover[cover.size()-1].FIR,cover[cover.size()-1].SEC);
}
}
}
}
sort(ALL(xc));
xc.erase(unique(ALL(xc)),xc.end());
if(xc.size()%2==1){
puts("ERRO");
assert(0);
}
rep(i,xc.size()){
lb l,r;
l=xc[i].FIR;
r=xc[i+1].SEC;
if(l>r) swap(l,r);
cover.PB(II(l,r));
i++;
}
sort(ALL(cover));
double las=-1e18;
double bg=-1e18;
for(auto it:cover){
if(it.FIR+eps>las){
rest+=las-bg;
bg=it.FIR;
if(it.SEC>las)
las=it.SEC;
}
else{
if(it.SEC>las)
las=it.SEC;
}
}
rest+=las-bg;
lb h=rest*query.k;
rest=sqrt(rest*rest+h*h);
if(swp){
for(auto &it: p) swap(it.x,it.y);
}
return rest;
}
bool era[1001];
void process(){
rep(i,n){
point pre,nex;
pre=p[(i-1+p.size())%p.size()];
nex=p[(i+1)%p.size()];
if(line(pre,p[i])==line(nex,p[i])) era[i]=true;
}
vector<point > neww;
rep(i,n) if(!era[i]) neww.PB(p[i]);
p=neww;
n=p.size();
}
int main(){
scanf("%d%d",&n,&q);
rb(i,1,n){
lb x,y;
scanf("%Lf%Lf",&x,&y);
x*=100.0;
y*=100.0;
p.PB(point (x,y));
}
process();//删除大小为Π的角
// cout<<n<<endl;
bool ok=0;
rb(i,1,q){
lb rest=solve()/100.0;
printf("%.15Lf
",rest);
}
return 0;
}
/*
3 7
99999.99 -100000
-100000 100000
-99999.99 100000
-100000 100000 100000 -100000
*/