2191 - Polygon Area.cpp

#include <bits/stdc++.h>
using namespace std;
#define ll long long

struct Point {
   ll x, y;
   void read() { cin >> x >> y; }
   Point operator-(const Point &b) const { return Point({x - b.x, y - b.y}); }
   ll operator*(const Point &b) const { return x * b.y - y * b.x; }
   ll cross(const Point &b, const Point &c) {
      return (b - *this) * (c - *this);
   }
};

void solve() {
   ll n;
   cin >> n;
   vector<Point> a(n);
   vector<bool> b(n, false);
   for (auto &i : a) i.read();

   auto next = [&](int idx) {
      int i = (idx + 1) % n;
      while (b[i]) i++, i %= n;
      return i;
   };

   int x = 0, y = 1, z = 2;
   ll ans = 0;
   for (int count = 0; n - count >= 3; count++) {
      b[y] = true;
      ans += (a[y].cross(a[x], a[z]));
      x = z;
      y = next(z);
      z = next(y);
   }

   cout << abs(ans) << "\n";
}

int main() {
   ios::sync_with_stdio(false);
   cin.tie(0);
   cout.tie(0);

   int t = 1;
   // cin >> t;
   while (t--) solve();
}