G. Geoplano.cpp

#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "debug.cpp"
#else
#define dbg(...) 42
#endif
#define endl '\n'
#define fastio                      \
  ios_base::sync_with_stdio(false); \
  cin.tie(0);                       \
  cout.tie(0);
#define len(__x) (int)__x.size()
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using vll = vector<ll>;
using pll = pair<ll, ll>;
using vll2d = vector<vll>;
using vi = vector<int>;
using vi2d = vector<vi>;
using pii = pair<int, int>;
using vii = vector<pii>;
using vc = vector<char>;
#define all(a) a.begin(), a.end()
#define pb(___x) push_back(___x)
#define mp(___a, ___b) make_pair(___a, ___b)
#define eb(___x) emplace_back(___x)
int lg2(ll x) {
  return __builtin_clzll(1) - __builtin_clzll(x);
}

// vector<string> dir({"LU", "U", "RU", "R", "RD", "D",
// "LD", "L"}); int dx[] = {-1, -1, -1, 0, 1, 1, 1, 0}; int
// dy[] = {-1, 0, 1, 1, 1, 0, -1, -1};
vector<string> dir({"U", "R", "D", "L"});
int dx[] = {-1, 0, 1, 0};
int dy[] = {0, 1, 0, -1};

const ll oo = 1e18;
int T(1);

ll cross(ll x1, ll y1, ll x2, ll y2) {
  return x1 * y2 - x2 * y1;
}

ll polygonArea(vector<pll>& pts) {
  ll ats = 0;
  for (int i = 2; i < len(pts); i++)
    ats += cross(pts[i].first - pts[0].first,
                 pts[i].second - pts[0].second,
                 pts[i - 1].first - pts[0].first,
                 pts[i - 1].second - pts[0].second);
  return abs(ats / 2ll);
}

ll boundary(vector<pll>& pts) {
  ll ats = pts.size();
  for (int i = 0; i < len(pts); i++) {
    ll deltax =
      (pts[i].first - pts[(i + 1) % pts.size()].first);
    ll deltay =
      (pts[i].second - pts[(i + 1) % pts.size()].second);
    ats += abs(__gcd(deltax, deltay)) - 1;
  }
  return ats;
}

ll pickPoints(vector<pll>& pts, bool includeBorder = true) {
  ll bounds = boundary(pts);
  ll area = polygonArea(pts);
  ll inside = area + 1ll - bounds / 2ll;
  dbg(bounds);
  dbg(inside);
  if (includeBorder)
    return inside + bounds;
  else
    return inside;
}

auto solve() {
  vector<pll> pts(3);

  for (auto& [x, y] : pts) {
    cin >> x >> y;
  }

  ll pickpts = pickPoints(pts, false);

  cout << pickpts << endl;
}

int32_t main(void) {
#ifndef LOCAL
  fastio;
#endif

  // cin >> T;

  for (int i = 1; i <= T; i++) {
    solve();
  }
}

// AC, geometry, pick's theorem