Problem:
Closest Pair

For given n points in metric space, find the distance of the closest points.

Input

n
x0 y0
x1 y1
:
xn-1 yn-1

The first integer n is the number of points.

In the following n lines, the coordinate of the i-th point is given by two real numbers xi and yi. Each value is a real number with at most 6 digits after the decimal point.

Output

Print the distance in a line. The output values should be in a decimal fraction with an error less than 0.000001.

Constraints

2 ≤ n ≤ 100,000

-100 ≤ x, y ≤ 100

Sample Input 1

2
0.0 0.0
1.0 0.0

Sample Output 1

1.000000

Sample Input 2

3
0.0 0.0
2.0 0.0
1.0 1.0

Sample Output 2

1.41421356237

Solution in C# (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            Point[] P = new Point[n];

            for (int i = 0; i < n; i++)
            {
                double[] input = Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);
                P[i] = new Point(input[0], input[1]);
            }

            Array.Sort(P);
            Console.WriteLine(ClosestPair(P, 0, n));
        }

        static double ClosestPair(Point[] P, int begin, int end)
        {
            int n = P.Length;

            if (end - begin <= 1) return double.MaxValue;

            int middle = begin + (end - begin) / 2;

            double x = P[middle].x;
            double d = Math.Min(ClosestPair(P, begin, middle), ClosestPair(P, middle, end));

            Array.Sort(P, (a, b) => (int)(a.y - b.y));

            List<Point> temp = new List<Point>();

            for (int i = 0; i < n; i++)
            {
                if (Math.Abs(P[i].x - x) >= d) continue;

                for (int j = 0; j < temp.Count; j++)
                {
                    double dx = P[i].x - temp[temp.Count - j - 1].x;
                    double dy = P[i].y - temp[temp.Count - j - 1].y;

                    if (dy >= d) break;

                    d = Math.Min(d, Math.Sqrt(dx * dx + dy * dy));
                }
                temp.Add(P[i]);
            }

            return d;
        }
    }

    class Point : IComparable<Point>
    {
        static readonly double EPS = 1E-10;

        internal double x, y;

        public Point() { }

        public Point(double x, double y)
        {
            this.x = x;
            this.y = y;
        }

        public double Abs { get { return Math.Sqrt(Norm); } }
        public double Norm { get { return x * x + y * y; } }

        public double Dot(Point p) { return x * p.x + y * p.y; }
        public double Cross(Point p) { return x * p.y - y * p.x; }

        public static Point operator +(Point a, Point b) { return new Point(a.x + b.x, a.y + b.y); }
        public static Point operator -(Point a, Point b) { return new Point(a.x - b.x, a.y - b.y); }
        public static Point operator *(Point p, double d) { return new Point(p.x * d, p.y * d); }
        public static Point operator /(Point p, double d) { return new Point(p.x / d, p.y / d); }
        public static bool operator <(Point a, Point b) { return Math.Abs(a.x - b.x) > EPS ? a.x < b.x : a.y < b.y; }
        public static bool operator >(Point a, Point b) { return Math.Abs(a.x - b.x) > EPS ? a.x > b.x : a.y > b.y; }
        public static bool operator ==(Point a, Point b) { return Math.Abs(a.x - b.x) < EPS && Math.Abs(a.y - b.y) < EPS; }
        public static bool operator !=(Point a, Point b) { return Math.Abs(a.x - b.x) >= EPS || Math.Abs(a.y - b.y) >= EPS; }

        public int CompareTo(Point other)
        {
            return Math.Abs(x - other.x) < EPS ? (int)(x - other.x) : (int)(y - other.y);
        }

        public override bool Equals(object obj)
        {
            Point other = obj as Point;
            return Math.Abs(x - other.x) < EPS && Math.Abs(y - other.y) < EPS;
        }

        public override int GetHashCode()
        {
            return x.GetHashCode() ^ y.GetHashCode();
        }

        public override string ToString()
        {
            return string.Format("{0} {1}", x, y);
        }
    }

    class Segment
    {
        internal Point p1, p2;

        public Segment(Point p1, Point p2)
        {
            this.p1 = p1;
            this.p2 = p2;
        }

        public Segment(double ax, double ay, double bx, double by)
        {
            p1 = new Point(ax, ay);
            p2 = new Point(bx, by);
        }
    }

    class Circle
    {
        internal Point p;
        internal double r;

        public Circle(Point p, double r)
        {
            this.p = p;
            this.r = r;
        }
    }
}