Kit polígono

#include "bits/stdc++.h"
using namespace std;

using cord = long double;
const long double PI = acos(-1);
const long double EPS = 1e-8;

int signal(cord x) { return (x > EPS) - (x < -EPS); }

struct point {
    cord x,y;

    // Constructor
    point(cord _x, cord _y): x(_x), y(_y) {}
    point(): x(0), y(0) {}

    // Very basic operations
    void operator=  (const point& p){x = p.x; y = p.y; }
    point operator+ (const point& q){ return {x + q.x, y + q.y}; }
    point operator- (const point& q){ return {x - q.x, y - q.y}; }
    point operator* (const cord& s) { return {x*s, y*s}; }
    point operator/ (const cord& s) { return {x/s, y/s}; }

    // Basic operations
    cord cross (const point &p){ return (x*p.y - y*p.x); }
    cord dot (const point& p)  { return (x*p.x + y*p.y); }

    /* TRANSFORMA EM DOUBLE
    point proj(const point& p) { return(p*(dot(p)/p.norm()))}
    */

    // Length operations
    cord norm()       { return (x*x + y*y); }
    long double len() { return hypot(x, y); }

    // Rotation operations
    point rotate90()              { return {-y,x}; }
    // TRANSFORMA PRA DOUBLE point rotate(long double ang) { return {cos(ang)*x - sin(ang)*y, sin(ang)*x + cos(ang)*y}; }

};

#define pb push_back
#define mp make_pair
#define fst first
#define snd second

#define fr(i,n)     for(int i=0;i<n;i++)
#define frr(i,n)    for(int i=1;i<=n;i++)

#define ms(x,i) memset(x,i,sizeof(x))
#define dbg(x)  cout << #x << " = " << x << endl
#define all(x)  x.begin(),x.end()

#define gnl cout << endl
#define olar cout << "olar" << endl
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL);cout.tie(NULL)

typedef long long int ll;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<pii> vii;
typedef pair<ll,ll> pll;

const int INF = 0x3f3f3f3f;
const ll llINF = 0x3f3f3f3f3f3f3f;
const int MOD = 1e9+7;

long double memo[100100][2][2][2][2];
point A,B;

int cc;
int n;
vector<point> v;
/*
memo[i][j][k][l][h]:
    ponto i;
    projetei o v_0;
    projetei o v_{i-2};
    projetei o v_{i-1};

    area > 0;

    bool 1 = B
         0 = A

*/

long double pd(int i,int pri,int pen,int ult, int posi){
    point a,b;
    if(pen == 0) a = v[i-2] + A;
    else a = v[i-2] + B;
    if(ult == 0) b = v[i-1] + A;
    else b = v[i-1] + B;
    a=a/2;b=b/2;

    point v0;
    if(pri == 0) v0 = v[0] + A;
    else v0 = v[0] + B;
    v0=v0/2;

    if(i == n){

        if(signal((b-a).cross(v0 - b))*cc < 0) return (long double)llINF;

        if(posi == 1) return (long double)0;
        else return (long double)llINF;
    }

    long double& pdm = memo[i][pri][pen][ult][posi];
    if(signal(pdm + 1) > 0) return pdm;
    pdm = (long double)llINF;



    point tentA,tentB;
    tentA = v[i] + A;
    tentB = v[i] + B;
    tentA = tentA/2;
    tentB = tentB/2;

    if(signal((b - a).cross(tentA - b))*cc >= 0){
        long double area = abs((b - v0).cross(tentA - v0));
        int p;
        if (posi > 0 || signal(area) > 0) p = 1;
        else p = 0;
        pdm = min(pdm, area + pd(i + 1,pri,ult,0,p));
        dbg(pdm);
    }

    if(signal((b - a).cross(tentB - b))*cc >= 0){
        long double area = abs((b - v0).cross(tentB - v0));
        int p;
        if (posi > 0 || signal(area) > 0) p = 1;
        else p = 0;
        pdm = min(pdm, area + pd(i + 1,pri,ult,1,p));
        dbg(pdm);
    }

    //if(signal(pdm) < 0) pdm = (long double)llINF;

    return pdm;

}


int main(){

    fastio;

    cout << setprecision(3) << fixed;

    cin >> n;

    fr(i,n){
        point p;
        cin >> p.x >> p.y;
        v.pb(p);
    }


    fr(i,n){
        if(signal((v[1] - v[0]).cross(v[i] - v[1])) != 0){
            cc = signal((v[1] - v[0]).cross(v[i] - v[1]));
            break;
        }
    }


    cin >> A.x >> A.y >> B.x >> B.y;

    long double ans = (long double)llINF;

    ms(memo,-1);

    ans = min(ans,pd(2,0,0,0,0));
    dbg(ans);
    //return 0;
    ans = min(ans,pd(2,1,1,0,0));
    ans = min(ans,pd(2,0,0,1,0));
    ans = min(ans,pd(2,1,1,1,0));

    reverse(all(v));
    ms(memo,-1);

    ans = min(ans,pd(2,0,0,0,0));
    ans = min(ans,pd(2,1,1,0,0));
    ans = min(ans,pd(2,0,0,1,0));
    ans = min(ans,pd(2,1,1,1,0));

    ans*= 4;
    ans += 0.5;
    ans = (ll)ans;


    cout << ans/8 << endl;




}