Problem:
Diameter of a Convex Polygon

Find the diameter of a convex polygon g. In other words, find a pair of points that have maximum distance between them.

Input

n
x1 y1
x2 y2
:
xn yn

The first integer n is the number of points in g.

In the following lines, the coordinate of the i-th point pi is given by two real numbers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them. Each value is a real number with at most 6 digits after the decimal point.

Output

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

Constraints

3 ≤ n ≤ 80000

-100 ≤ xi, yi ≤ 100

No point in the g will occur more than once.

Sample Input 1

3
0.0 0.0
4.0 0.0
2.0 2.0

Sample Output 1

4.00

Sample Input 2

4
0.0 0.0
1.0 0.0
1.0 1.0
0.0 1.0

Sample Output 2

1.414213562373

Solution in C# (judge verdict: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Collections.Generic;
using System.Diagnostics;
//using System.Numerics;
using Enu = System.Linq.Enumerable;

public class Program
{
    public void Solve()
    {
        int N = Reader.Int();
        var P = new Point[N];
        for (int i = 0; i < N; i++)
            P[i] = new Point(Reader.Double(), Reader.Double());
        var poly = new Polygon(P);
        Console.WriteLine(ConvexPolygonDiameter(poly));
        Console.ReadLine();
    }

    public double ConvexPolygonDiameter(Polygon poly)
    {
        int N = poly.N;
        if (N == 2) return poly[0].Distance(poly[1]);
        int a = 0, b = 0;
        for (int i = 0; i < N; i++)
        {
            if (poly[i].X < poly[a].X) a = i;
            if (poly[i].X > poly[b].X) b = i;
        }
        double maxLen = 0;
        int sa = a, sb = b;
        while (a != sb || b != sa)
        {
            maxLen = Math.Max(maxLen, poly[a].Distance(poly[b]));
            if ((poly[a + 1] - poly[a]).Det(poly[b + 1] - poly[b]) < 0)
                a = (a + 1) % N;
            else
                b = (b + 1) % N;
        }
        return maxLen;
    }

    public class Polygon
    {
        public readonly Point[] P;
        public Polygon(Point[] points) { P = points; }
        public Polygon(IEnumerable<Point> points) { P = points.ToArray(); }
        public int N { get { return P.Length; } }
        public Point this[int i] { get { return P[(i % N + N) % N]; } }

        public double Area() { return Math.Abs(SignedArea()); }
        public double SignedArea()
        {
            double area = 0;
            for (int i = 0; i < P.Length; i++)
                area += P[i].Det(P[(i + 1) % P.Length]);
            return area / 2;
        }
        public bool IsConvex()
        {
            for (int i = 1; i < P.Length; i++)
                if ((P[i] - P[i - 1]).Det(P[(i + 1) % P.Length] - P[i]) < 0)
                    return false;
            return true;
        }
    }

    public struct Point : IEquatable<Point>, IComparable<Point>
    {
        public static readonly double Eps = 1e-10;
        public double X, Y;
        public Point(double x, double y) { X = x; Y = y; }
        public static Point operator +(Point a, Point b)
        {
            return new Point(Add(a.X, b.X), Add(a.Y, b.Y));
        }
        public static Point operator -(Point a, Point b)
        {
            return new Point(Add(a.X, -b.X), Add(a.Y, -b.Y));
        }
        public static Point operator *(Point p, double d)
        {
            return new Point(p.X * d, p.Y * d);
        }
        public double Distance(Point b) { return Math.Sqrt((b - this).Dot(b - this)); }
        public double Dot(Point b) { return Add(X * b.X, Y * b.Y); }
        public double Det(Point b) { return Add(X * b.Y, -Y * b.X); }
        public bool Equals(Point b) { return X == b.X && Y == b.Y; }
        public int CompareTo(Point b) { return X != b.X ? Math.Sign(X - b.X) : Math.Sign(Y - b.Y); }
        public override int GetHashCode() { return (int)(X * 100000 + Y); }
        public override string ToString() { return X + ", " + Y; }

        private static double Add(double a, double b)
        {
            if (Math.Abs(a + b) < Eps * (Math.Abs(a) + Math.Abs(b))) return 0;
            return a + b;
        }
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    private static TextReader reader = Console.In;
    private static readonly char[] separator = { ' ' };
    private static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    private static string[] A = new string[0];
    private static int i;
    private static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Enu.Range(0, N).Select(i => Int()).ToArray(); }
    public static int[][] IntTable(int H) { return Enu.Range(0, H).Select(i => IntLine()).ToArray(); }
    public static string[] StringArray(int N) { return Enu.Range(0, N).Select(i => Next()).ToArray(); }
    public static string Line() { return reader.ReadLine().Trim(); }
    private static string[] Split(string s) { return s.Split(separator, op); }
    private static string Next() { CheckNext(); return A[i++]; }
    private static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}