new: CSES Geometry problems

Author: omar-besbes

solutions/CSES/Geometry/2192 - Point in Polygon.cpp

@@ -0,0 +1,59 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+
+struct P {
+   ll x, y;
+   void read() { cin >> x >> y; }
+   P operator-(P p) { return P{x - p.x, y - p.y}; }
+   ll cross(P p) { return x * p.y - y * p.x; }
+   ll cross(P a, P b) { return (a - *this).cross(b - *this); }
+};
+
+void solve() {
+   int n, m;
+   cin >> n >> m;
+   vector<P> v(n);
+   for (auto &i : v) i.read();
+
+   auto intersect = [](P cur, P p1, P p2) {
+      return cur.cross(p1, p2) == 0 &&
+             (min(p1.x, p2.x) <= cur.x && max(p1.x, p2.x) >= cur.x) &&
+             (min(p1.y, p2.y) <= cur.y && max(p1.y, p2.y) >= cur.y);
+   };
+
+   while (m--) {
+      P cur;
+      cur.read();
+
+      int crossings = 0;
+      bool isBoundary = false;
+      for (int i = 0; !isBoundary && i < n; i++) {
+         auto p1 = v[i], p2 = v[(i + 1) % n];
+         if (p1.y > p2.y) swap(p1, p2);
+
+         if (intersect(cur, p1, p2)) {
+            isBoundary = true;
+         } else {
+            auto isTouch = cur.cross(p1, p2) >= 0;
+            auto isBetween = (p1.y < cur.y) && (p2.y >= cur.y);
+            if (isTouch && isBetween) crossings++;
+         }
+      }
+
+      if (!isBoundary)
+         cout << (crossings & 1 ? "INSIDE\n" : "OUTSIDE\n");
+      else
+         cout << "BOUNDARY\n";
+   }
+}
+
+int main() {
+   ios::sync_with_stdio(false);
+   cin.tie(0);
+   cout.tie(0);
+
+   int t = 1;
+   // cin >> t;
+   while (t--) solve();
+}