Problem:
Cross Point

For given two segments s1 and s2, print the coordinate of the cross point of 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 coordinate of the cross point. 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.

The given segments have a cross point and are not in parallel.

Sample Input

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

Sample Output

1.0000000000 0.0000000000
0.5000000000 0.5000000000
0.5000000000 0.5000000000

Solution in Scala (judge verdict: Accepted)

import scala.io.StdIn

object Main {

  case class Point(x: Double = 0, y: Double = 0) {

    def +(p: Point): Point = Point(this.x + p.x, this.y + p.y)

    def -(p: Point): Point = Point(this.x - p.x, this.y - p.y)

    def *(a: Double): Point = Point(this.x * a, this.y * a)

    def /(a: Double): Point = {
      assert(a == 0)
      Point(this.x / a, this.y / a)
    }

    def norm(): Double = this.x * this.x + this.y * this.y

    def abs(): Double = scala.math.sqrt(norm())

    def <(p: Point): Boolean = this.x < p.x && this.y < p.y


    def ==(p: Point): Boolean = scala.math.abs(this.x - p.x) < Cgl0A.EPS &&
      scala.math.abs(this.y - p.y) < Cgl0A.EPS


  }

  case class Segment(p1: Point, p2: Point)

  case class Line(p1: Point, p2: Point)

  type GeoVector = Point

  object Cgl0A {
    val EPS: Double = scala.math.pow(10, -10)

    // 内積
    def dot(a: Point, b: Point): Double = a.x * b.x + a.y * b.y

    def isOrthogonal(a: GeoVector, b: GeoVector): Boolean = dot(a, b) == 0.0

    def isOrthogonal(a1: Point, a2: Point, b1: Point, b2: Point): Boolean = {
      isOrthogonal(a1 - a2, b1 - b2)
    }

    def isOrthogonal(s1: Segment, s2: Segment): Boolean = {
      dot(s1.p2 - s1.p1, s2.p2 - s2.p1) == 0.0
    }

    // 外積
    def cross(a: Point, b: Point): Double = a.x * b.y - a.y * b.x

    def isParallel(a: GeoVector, b: GeoVector): Boolean = cross(a, b) == 0.0

    def isParallel(a1: Point, a2: Point, b1: Point, b2: Point): Boolean = {
      isParallel(a1 - a2, b1 - b2)
    }

    def isParallel(s1: Segment, s2: Segment): Boolean = {
      cross(s1.p2 - s1.p1, s2.p2 - s2.p1) == 0.0
    }

    def project(s: Segment, p: Point): Point = {
      val base: GeoVector = s.p2 - s.p1
      val r: Double = Cgl0A.dot(p - s.p1, base) / base.norm()
      s.p1 + base * r
    }

    def reflect(s: Segment, p: Point): Point = {
      p + (project(s, p) - p) * 2.0
    }

    def getDistance(a: Point, b: Point): Double = (a - b).abs()

    def getDistanceLP(l: Line, a: Point): Double = {
      scala.math.abs(cross(l.p2 - l.p1, a - l.p1) / (l.p2 - l.p1).abs())
    }

    def getDistanceSP(s: Segment, a: Point): Double = {
      if (dot(s.p2 - s.p1, a - s.p1) < 0.0) (a - s.p1).abs()
      else if (dot(s.p1 - s.p2, a - s.p2) < 0.0) (a - s.p2).abs()
      else getDistanceLP(Line(s.p1, s.p2), a)
    }

    def getDistance(s1: Segment, s2: Segment): Double = {
      if (intersect(s1, s2)) {
        0.0
      }
      else {
        math.min(math.min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)),
          math.min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)))
      }
    }

    val COUNTER_CLOCKWISE: Int = 1
    val CLOCKWISE: Int = -1
    val ONLINE_BACK: Int = 2
    val ONLINE_FRONT: Int = -2
    val ON_SEGMENT: Int = 0

    def ccw(p0: Point, p1: Point, p2: Point): Int = {
      val a: GeoVector = p1 - p0
      val b: GeoVector = p2 - p0

      if (cross(a, b) > EPS) COUNTER_CLOCKWISE
      else if (cross(a, b) < -1 * EPS) CLOCKWISE
      else if (dot(a, b) < -1 * EPS) ONLINE_BACK
      else if (a.norm() < b.norm()) ONLINE_FRONT
      else ON_SEGMENT

    }

    def intersect(p1: Point, p2: Point, p3: Point, p4: Point): Boolean = {
      Cgl0A.ccw(p1, p2, p3) * Cgl0A.ccw(p1, p2, p4) <= 0 &&
        Cgl0A.ccw(p3, p4, p1) * Cgl0A.ccw(p3, p4, p2) <= 0
    }

    def intersect(s1: Segment, s2: Segment): Boolean = {
      Cgl0A.intersect(s1.p1, s1.p2, s2.p1, s2.p2)
    }
    
    def getCrossPoint(s1: Segment, s2: Segment): Point = {
      val base: GeoVector = s2.p2 - s2.p1
      val d1 = scala.math.abs(cross(base, s1.p1 - s2.p2))
      val d2 = scala.math.abs(cross(base, s1.p2 - s2.p1))
      val t = d1 / (d1 + d2)
      s1.p1 + (s1.p2 - s1.p1) * t
    }

  }


  def main(args: Array[String]): Unit = {
    val q = StdIn.readLine().toInt
    (0 until q).foreach { i =>
      val a = StdIn.readLine().split(' ').map(_.toDouble)
      val s1 = Segment(Point(a(0), a(1)),Point(a(2), a(3)))
      val s2 = Segment(Point(a(4), a(5)),Point(a(6), a(7)))

      val r = Cgl0A.getCrossPoint(s1, s2)
      println(f"${r.x}%.10f ${r.y}%.10f")      
    }

  }

}