Problem:
Distance

For given two segments s1 and s2, print the distance between them.

s1 is formed by end points p0 and p1, and
s2 is formed by end points p2 and p3.

Input

The entire input looks like:

q (the number of queries)
1st query
2nd query
...
qth query

Each query consists of integer coordinates of end points of s1 and s2 in the following format:

xp0 yp0 xp1 yp1 xp2 yp2 xp3 yp3

Output

For each query, print the distance. The output values should be in a decimal fraction with an error less than 0.00000001.

Constraints

1 ≤ q ≤ 1000

-10000 ≤ xpi, ypi ≤ 10000

p0 ≠ p1 and
p2 ≠ p3.

Sample Input

3
0 0 1 0 0 1 1 1
0 0 1 0 2 1 1 2
-1 0 1 0 0 1 0 -1

Sample Output

1.0000000000
1.4142135624
0.0000000000

Solution in C# (judge verdict: Accepted)

using System;
//using System.Collections.Generic;
//using System.Linq;
//using Vector = CGL.Point;
//using Line = CGL.Segment;
//using Polygon = System.Collections.Generic.List<CGL.Point>;

namespace CGL
{
    class Program
    {
        static void Main(string[] args)
        {
            var q = scan[0];
            for (int i = 0; i < q; i++)
            {
                var t = scan;
                var P = new Point[4];
                for (int j = 0; j < 4; j++)
                {
                    P[j] = new Point(t[j * 2], t[j * 2 + 1]);
                }
                var s1 = new Segment(P[0], P[1]);
                var s2 = new Segment(P[2], P[3]);
                Console.WriteLine(s1.GetDistance(s2));
            }
        }
        static int[] scan { get { return Array.ConvertAll(Console.ReadLine().Split(), int.Parse); } }
    }
    
    struct Point
    {
        static readonly double EPS = 1E-10;
        public double x, y;
        public Point(double x, double y)
        {
            this.x = x;
            this.y = 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 a, Point b) { return new Point(a.x - b.x, a.y - b.y); }
        public static Point operator *(double k, Point a) { return new Point(k * a.x, k * a.y); }
        public static Point operator /(double k, Point a) { return new Point(a.x / k, a.y / k); }
        
        public double Abs { get { return Math.Sqrt(Norm); } }  
        public double Norm { get { return x * x + y * 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 ? 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 override bool Equals(object p){  return Math.Abs(x - ((Point)p).x) < EPS && Math.Abs(y - ((Point)p).y) < EPS; }
        public override int GetHashCode(){ return x.GetHashCode() ^ y.GetHashCode(); }

        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 GetDistance(Point p) { return (this - p).Abs; }

        public int CCW(Point b)
        {
            if (Cross(b) > EPS) return 1;
            if (Cross(b) < -EPS) return -1;
            if (Dot(b) < -EPS) return 2;
            if (Norm < b.Norm) return -2;
            return 0;
        }
    }
    struct Segment
    {
        public Point p1, p2;
        public Segment(Point p1, Point p2)
        {
            this.p1 = p1;
            this.p2 = p2;
        }
        public Point Projection(Point p)
        {
            Point b = p2 - p1;
            double r = b.Dot(p - p1) / b.Norm;
            return p1 + r * b;
        }
        public Point Reflection(Point p)
        {
            return p + 2 * (Projection(p) - p);
        }
        public double GetD_LP(Point p)
        {
            return Math.Abs((p - p1).Cross(p2 - p1) / (p2 - p1).Abs);
        }
        public double GetD_SP(Point p)
        {
            if ((p - p1).Dot(p2 - p1) < 0) return (p - p1).Abs;
            if ((p - p2).Dot(p1 - p2) < 0) return (p - p2).Abs;
            return GetD_LP(p);
        }
        public bool Intersect(Segment s)
        {
            return (p2 - p1).CCW(s.p1 - p1) * (p2 - p1).CCW(s.p2 - p1) <= 0 &&
                (s.p2 - s.p1).CCW(p1 - s.p1) * (s.p2 - s.p1).CCW(p2 - s.p1) <= 0;
        }
        public double GetDistance(Segment s)
        {
            if (this.Intersect(s)) return 0;
            return Math.Min(Math.Min(GetD_SP(s.p1), GetD_SP(s.p2)), Math.Min(s.GetD_SP(p1), s.GetD_SP(p2)));
        }
    }
    /*struct Circle
    {
        public Point c; double r;
        public Circle(Point c, double r)
        {
            this.c = c;
            this.r = r;
        }

    }*/
}