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: Accepted)

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, new ComparerX());

            Console.WriteLine("{0:f10}", ClosestPair(P, 0, n));
        }

        static double ClosestPair(Point[] points, int begin, int end)
        {
            double minDist = double.MaxValue;

            if (end - begin < 4)
            {
                for (int i = begin; i < end; i++)
                {
                    for (int j = i + 1; j < end; j++)
                    {
                        minDist = Math.Min(minDist, points[i].Distance(points[j]));
                    }
                }
                return minDist;
            }

            int middle = (begin + end) / 2;
            double middleX = points[middle].x;

            minDist = Math.Min(ClosestPair(points, begin, middle), ClosestPair(points, middle, end));

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

            for (int i = begin; i < end; i++)
            {
                if (Math.Abs(middleX - points[i].x) < minDist)
                {
                    candidates.Add(points[i]);
                }
            }

            int k = candidates.Count;

            if (k <= 1) return minDist;

            candidates.Sort(new ComparerY());

            for (int i = 0; i < k; i++)
            {
                for (int j = i + 1; j < k && (candidates[j].y - candidates[i].y < minDist); j++)
                {
                    minDist = Math.Min(minDist, candidates[j].Distance(candidates[i]));
                }
            }
            return minDist;
        }
    }

    class Point : IComparable
    {
        static readonly double EPS = 1E-16;
        static int _counter;

        internal int Id;
        internal double x, y;

        public Point(double x, double y)
        {
            Id = ++_counter;
            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 double Distance(Point p) { return (this - p).Abs; }

        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(object obj)
        {
            var other = obj as Point;
            if (other == null) return -1;

            ComparerX compX = new ComparerX();
            return compX.Compare(this, other);
        }

        public override bool Equals(object obj)
        {
            var other = obj as Point;

            return Id == other.Id;
        }

        public override int GetHashCode()
        {
            return Id.GetHashCode();
        }

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

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

        public int Compare(Point a, Point b)
        {
            if (a.x - b.x < -EPS) return -1;
            if (a.x - b.x > EPS) return 1;
            if (a.y - b.y < -EPS) return -1;
            if (a.y - b.y > EPS) return 1;
            return 0;
        }
    }

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

        public int Compare(Point a, Point b)
        {
            if (a.y - b.y < -EPS) return -1;
            if (a.y - b.y > EPS) return 1;
            if (a.x - b.x < -EPS) return -1;
            if (a.x - b.x > EPS) return 1;
            return 0;
        }
    }

    class Segment
    {
        internal Point p1, p2;

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

    class Circle
    {
        internal Point p;
        internal double r;

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