CSES Point In Polygon
// compile: make data
// run: time ./data < big.in > big.out
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#ifdef LOCAL
#include <debug/codeforces.h>
#define debug(x...) _debug_print(#x, x);
#define Debug(x...) _debug_print_format(#x, x);
std::ifstream terminal("/dev/tty");
#define PP cerr<<"\033[1;30mpause...\e[0m",terminal.ignore();
#else
#define debug(x...)
#define Debug(x...)
#define PP
#endif
template<typename...Args> void print_(Args...args){((cout<<args<<" "),...)<<endl;}
#define rep(i,a,b) for(int i=(a);i<(int)(b);++i)
#define sz(v) ((int)(v).size())
#define print(...) print_(__VA_ARGS__);
#define FIND(a, x) ((find(a.begin(),a.end(),(x))!=a.end())?1:0)
#define cmin(x,...) x=min({(x),__VA_ARGS__})
#define cmax(x,...) x=max({(x),__VA_ARGS__})
#define INTMAX (int)(9223372036854775807)
#define INF (int)(1152921504606846976)
#define NaN (int)(0x8b88e1d0595d51d1)
#define double long double
#define int long long
#define uint unsigned long long
#define MAXN 200010

template <typename T> struct point2d {
    T x, y;
    point2d() {}
    point2d(int X, int Y): x(X), y(Y) {}
    point2d<T> operator+(const point2d<T> &rhs) const {
        point2d<T> res(x + rhs.x, y + rhs.y);
        return res;
    }
    point2d<T> operator-(const point2d<T> &rhs) const {
        point2d<T> res(x - rhs.x, y - rhs.y);
        return res;
    }
    bool operator==(const point2d<T> &rhs) const {
        return x == rhs.x && y == rhs.y;
    }
    T dot(const point2d<T> &rhs) const {
        return x * rhs.x + y * rhs.y;
    }
    T cross2(const point2d<T> &rhs) const {
        return x * rhs.y - y * rhs.x;
    }
    double norm() const {
        return sqrt(x * x + y * y);
    }
};

template <typename T> struct line2d {
    point2d<T> a, b;
    line2d() {}
    line2d(point2d<T> A, point2d<T> B): a(A), b(B) {}
    bool on(point2d<T> p, bool ica = 1, bool icb = 1) {
        if (!ica && a == p) return false;
        if (!icb && b == p) return false;
        point2d<T> v1 = p - a, v2 = p - b;
        return v1.cross2(v2) == 0 && v1.dot(v2) <= 0;
    }
    bool intersect(line2d<T> &rhs, bool ica = 1, bool icb = 1) {
        line2d<T> &lhs = *this;
        if (!ica && rhs.on(lhs.a)) return false;
        if (!icb && rhs.on(lhs.b)) return false;
        if (lhs.on(rhs.a, ica, icb) || lhs.on(rhs.b, ica, icb)) return true;
        if ((ica && rhs.on(lhs.a)) || (icb && rhs.on(lhs.b))) return true;
        auto mul = [](T A, T B) -> T {
            if (A == 0 || B == 0) return 0;
            if ((A > 0 && B > 0) || (A < 0 && B < 0)) return 1;
            return -1;
        };
        point2d<T> ab = lhs.b - lhs.a;
        point2d<T> ac = rhs.a - lhs.a;
        point2d<T> ad = rhs.b - lhs.a;
        point2d<T> cd = rhs.b - rhs.a;
        point2d<T> ca = lhs.a - rhs.a;
        point2d<T> cb = lhs.b - rhs.a;
        if (mul(ab.cross2(ac), ab.cross2(ad)) < 0 && mul(cd.cross2(ca), cd.cross2(cb)) < 0) return true;
        return false;
    }
};

template <typename T> struct polygon2d {
    vector<point2d<T>> p;
    polygon2d() {}
    polygon2d(vector<point2d<T>> a): p(a) {}
    void add(const point2d<T> q) {p.push_back(q); }
    T area() const {
        T res = 0;
        rep(i, 0, p.size()) {
            int j = (i + 1) % p.size();
            res += p[i].cross2(p[j]);
        }
        return abs(res);
    }
    int in(const point2d<T> &q) const {
        line2d l(q, point2d<T>((T)(1e9+7), q.y));
        int cnt = 0;
        rep(i, 0, sz(p)) {
            point2d<T> a = p[i], b = p[(i+1) % sz(p)];
            line2d m(a, b);
            if (m.on(q)) return 0;
            if (!m.intersect(l)) continue;
            int maxy = max(a.y, b.y);
            if (maxy > q.y) ++cnt;
        }
        return cnt&1 ? 1 : -1;
    }
};

int32_t main() {
    ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);

    int n, m; cin >> n >> m;
    polygon2d<int> p;
    rep(i, 0, n) {
        int x, y; cin >> x >> y;
        p.add(point2d<int>(x, y));
    }
    rep(i, 0, m) {
        int x, y; cin >> x >> y;
        int res = p.in(point2d<int>(x, y)); 
        if (res == 1) printf("INSIDE\n");
        else if (res == -1) printf("OUTSIDE\n");
        else printf("BOUNDARY\n");
    }

    return 0;
}
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Source: github.com/k4yt3x/flowerhd
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