Closest Pair of Points in 2D

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

#define int long long
#define OO 0x3f3f3f3f3f3f3f3f

#define point pair<double, double>
#define X first
#define Y second

double mindist;

void upd_ans(const point & a, const point & b) {
    double dist = sqrt((a.X - b.X) * (a.X - b.X) + (a.Y - b.Y) * (a.Y - b.Y));
    if(dist < mindist) mindist = dist;
}

void closest_points(vector<point> &p) {
   int n = p.size();

   if(n <= 3) {
      for(int i = 0; i < n; i++)
         for(int j = i + 1; j < n; j++)
            upd_ans(p[i], p[j]);

      sort(p.begin(), p.end(),
         [](point p1, point p2) {
            return p1.Y < p2.Y;
         }
      );

      return;
   }

   int mid = n / 2;
   point m = p[mid];
   vector<point> a, b;
   for(int i = 0; i < mid; i++) a.push_back(p[i]);
   for(int i = mid; i < n; i++) b.push_back(p[i]);

   closest_points(a);
   closest_points(b);

   int l = 0, r = 0;
   a.push_back({OO, OO});
   b.push_back({OO, OO});

   vector<point> aux;

   for(int i = 0; i < n; i++) {
      if(a[l].Y < b[r].Y)
         p[i] = a[l++];
      else
         p[i] = b[r++];

      if(abs(m.X - p[i].X) < mindist)
         aux.push_back(p[i]);
   }

   a.pop_back();
   b.pop_back();

   n = aux.size();
   for(int i = 0; i < n; ++i)
      for(int j = i + 1; j < n and (aux[j].Y - aux[i].Y) < mindist; j++)
         upd_ans(aux[i], aux[j]);
}

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

    int n;
    while(cin >> n and n) {
        vector<point> arr;
        for(int i = 0; i < n; i++) {
            double x, y;
            cin >> x >> y;
            arr.push_back({x, y});
        }
        sort(arr.begin(), arr.end(),
            [](point a, point b) {
                return a.X < b.X;
            }
        );

        mindist = OO;
        closest_points(arr);
        if(mindist >= 10000) cout << "INFINITY\n";
        else cout << fixed << setprecision(4) << mindist << '\n';
    }

    return 0;
}