Point in Polygon

input/code.cpp: In function 'void Test()':
input/code.cpp:128:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  128 |     freopen("temp\\in.txt", "r", stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~
input/code.cpp: In member function 'void Point::Input()':
input/code.cpp:23:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   23 |         scanf("%lld%lld", &x_, &y_);
      |         ~~~~~^~~~~~~~~~~~~~~~~~~~~~

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N=10005;

inline int Sign(const LL& x)
{
    if(abs(x)==0)       return 0;
    if(x < 0)           return -1;
    else                return 1;
}

struct Point
{
    LL x_, y_;
    Point(){}
    Point(LL x, LL y)
    {
        x_ = x;
        y_ = y;
    }
    void Input() {
        scanf("%lld%lld", &x_, &y_);
    }

    bool operator == (const Point& P)const {
        return Sign(x_ - P.x_) == 0 && Sign(y_ - P.y_) == 0;
    }
    bool operator < (const Point& P)const {
        return Sign(x_ - P.x_) == 0? Sign(y_ - P.y_)<0 : x_<P.x_;
    }
    LL operator ^ (const Point& P)const {
        return x_*P.y_ - y_*P.x_;
    }
    LL operator * (const Point& P)const {
        return x_*P.x_ + y_*P.y_;
    }
    Point operator + (const Point& P)const {
        return Point(x_+P.x_, y_+P.y_);
    }
    Point operator - (const Point& P)const {
        return Point(x_-P.x_, y_-P.y_);
    }
    Point operator * (const LL& k)const {
        return Point(x_*k, y_*k);
    }
    Point operator / (const LL& k)const {
        return Point(x_/k, y_/k);
    }

    LL len() {
        return hypot(x_, y_);
    }
};

struct Line
{
    Point s_, e_;
    Line(){}
    Line(Point s, Point e)
    {
        s_ = s;
        e_ = e;
    }
    // 3(O) 2(R) 1(L)
    int Relation(Point p) 
    {
        int c = Sign((p-s_)^(e_-s_));
        if(c < 0)       return 1;
        else if(c > 0)  return 2;
        else            return 3;
    }
    bool OnSeg(Point p) {
        return Sign((p-s_)^(e_-s_)) == 0 && Sign((p-s_)*(p-e_)) <= 0;
    }
};


struct Polygon
{
    int n_;
    Point p_[N];
    Line l_[N];
    void Input(int n)
    {
        n_ = n;
        for(int i=0; i<n_; i++)
            p_[i].Input();
        InitLines();
    }
    void InitLines()
    {
        for(int i=0; i<n_; i++)
            l_[i] = Line(p_[i], p_[(i+1)%n_]);
    }

    LL Area()
    {
        LL ret = 0;
        for(int i=0; i<n_; i++)
            ret += (p_[i] ^ p_[(i+1)%n_]);
        return fabs(ret)/2;
    }
    // 3(P) 2(E) 1(I) 0(O)
    int Relation(Point p)
    {
        for(int i=0; i<n_; i++)
            if(p_[i] == p)      return 3;
        for(int i=0; i<n_; i++)
            if(l_[i].OnSeg(p))  return 2;
        int cnt = 0;
        for(int i=0; i<n_; i++)
        {
            int j = (i+1)%n_;
            int k = Sign((p-p_[j])^(p_[i]-p_[j]));
            int u = Sign(p_[i].y_ - p.y_);
            int v = Sign(p_[j].y_ - p.y_);
            if(k > 0 && u < 0 && v >= 0) cnt++;
            if(k < 0 && v < 0 && u >= 0) cnt--;
        }
        return cnt != 0;
    }
};


void Test()
{
    freopen("temp\\in.txt", "r", stdin);
}
int main()
{
    // Test();
    int n, m;
    cin >> n >> m;
    Polygon G;
    G.Input(n);

    while(m--)
    {
        Point x;
        x.Input();
        int r = G.Relation(x);
        switch (r)
        {
        case 0:
            cout << "OUTSIDE" <<endl;
            break;
        case 1:
            cout << "INSIDE" <<endl;
            break;
        default:
            cout << "BOUNDARY" <<endl;
            break;
        }
    }
    return 0;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED