（高精度/Java）HDU 6206 Apple

Apple

Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 488    Accepted Submission(s): 160

Problem Description

Apple is Taotao's favourite fruit. In his backyard, there are three apple trees with coordinates (x1,y1), (x2,y2), and (x3,y3). Now Taotao is planning to plant a new one, but he is not willing to take these trees too close. He believes that the new apple tree should be outside the circle which the three apple trees that already exist is on. Taotao picked a potential position (x,y) of the new tree. Could you tell him if it is outside the circle or not?

 

Input

The first line contains an integer T, indicating that there are T(T≤30) cases.
In the first line of each case, there are eight integers x1,y1,x2,y2,x3,y3,x,y, as described above.
The absolute values of integers in input are less than or equal to 1,000,000,000,000.
It is guaranteed that, any three of the four positions do not lie on a straight line.

 

Output

For each case, output "Accepted" if the position is outside the circle, or "Rejected" if the position is on or inside the circle.

 

Sample Input

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

 

Sample Output

Accepted Rejected Rejected

 

Source

2017 ACM/ICPC Asia Regional Qingdao Online

 

利用同弧所对圆周角相等，不妨设需要判断的D点与B点在AC同侧，则只需要比较∠ABC与∠ADC的大小，利用余弦定理可以很轻松表示起来，只有cosD比cosB大时，D比B小，点D在△ABC外接圆外。为避免开方运算，同时平方（其中一些正负的判断细节需要注意）再比较。

判断是否在同侧只需要算一下叉积，D、B关于AC叉积如果具有相同正负性即在同侧。

//package com.company;

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
    public static BigInteger lo(BigInteger x,BigInteger y,BigInteger sx,BigInteger sy,BigInteger ex,BigInteger ey)
    {
        return x.subtract(sx).multiply(ey.subtract(sy)).subtract(ex.subtract(sx).multiply(y.subtract(sy)));
        //return ey.multiply(x).subtract(sy.multiply(x)).add(sy.multiply(ex)).subtract(sx.multiply(ey)).subtract(y.multiply(ex)).add(sx.multiply(y));
    }
    public static boolean check(BigInteger sx,BigInteger sy,BigInteger ex,BigInteger ey,BigInteger tx,BigInteger ty,BigInteger tx2,BigInteger ty2)
    {
        if(lo(tx2,ty2,sx,sy,ex,ey).multiply(lo(tx,ty,sx,sy,ex,ey)).compareTo(BigInteger.ZERO)>0)
            return true;
        else return false;
    }
    public static void main(String[] args) {
    // write your code here
        Scanner sc=new Scanner(System.in);
        BigInteger x1,y1,x2,y2,x3,y3,x4,y4;
        BigInteger ab,ac,bc,ad,cd,bd,lin1,lin2;
        BigInteger tem1,tem2,an;
        int t=sc.nextInt();
        for(int k=0;k<t;k++)
        {
            x1=sc.nextBigInteger();
            y1=sc.nextBigInteger();
            x2=sc.nextBigInteger();
            y2=sc.nextBigInteger();
            x3=sc.nextBigInteger();
            y3=sc.nextBigInteger();
            x4=sc.nextBigInteger();
            y4=sc.nextBigInteger();
            ab=x1.subtract(x2).pow(2).add(y1.subtract(y2).pow(2));
            ac=x1.subtract(x3).pow(2).add(y1.subtract(y3).pow(2));
            bc=x2.subtract(x3).pow(2).add(y2.subtract(y3).pow(2));
            bd=x2.subtract(x4).pow(2).add(y2.subtract(y4).pow(2));
            ad=x1.subtract(x4).pow(2).add(y1.subtract(y4).pow(2));
            cd=x3.subtract(x4).pow(2).add(y3.subtract(y4).pow(2));
            if(check(x1,y1,x3,y3,x2,y2,x4,y4))//compare with ABC
            {
                lin1=ab.add(bc).subtract(ac);//numerator of B
                lin2=ad.add(cd).subtract(ac);//numerator of D
                if(lin1.compareTo(BigInteger.ZERO)>0 && lin2.compareTo(BigInteger.ZERO)<=0)
                {
                    System.out.println("Rejected");
                    continue;
                }
                else if(lin1.compareTo(BigInteger.ZERO)<=0 && lin2.compareTo(BigInteger.ZERO)>0)
                {
                    System.out.println("Accepted");
                    continue;
                }
                tem1=lin1.pow(2).multiply(ad).multiply(cd);
                tem2=lin2.pow(2).multiply(ab).multiply(bc);
                an=tem1.subtract(tem2);
                if(lin1.compareTo(BigInteger.ZERO)<0 && lin2.compareTo(BigInteger.ZERO)<0)
                {
                    if(an.compareTo(BigInteger.ZERO)>0)
                    {
                        System.out.println("Accepted");
                        continue;
                    }
                    else
                    {
                        System.out.println("Rejected");
                        continue;
                    }
                }
                else if(an.compareTo(BigInteger.ZERO)<0)
                {
                    System.out.println("Accepted");
                    continue;
                }
                else
                {
                    System.out.println("Rejected");
                    continue;
                }
            }
            else if(check(x1,y1,x2,y2,x3,y3,x4,y4))
            {
                lin1=ac.add(bc).subtract(ab);
                lin2=ad.add(bd).subtract(ab);
                if(lin1.compareTo(BigInteger.ZERO)>0 && lin2.compareTo(BigInteger.ZERO)<=0)
                {
                    System.out.println("Rejected");
                    continue;
                }
                else if(lin1.compareTo(BigInteger.ZERO)<=0 && lin2.compareTo(BigInteger.ZERO)>0)
                {
                    System.out.println("Accepted");
                    continue;
                }
                tem1=lin1.pow(2).multiply(ad).multiply(bd);
                tem2=lin2.pow(2).multiply(ac).multiply(bc);
                an=tem1.subtract(tem2);
                if(lin1.compareTo(BigInteger.ZERO)<0 && lin2.compareTo(BigInteger.ZERO)<0)
                {
                    if(an.compareTo(BigInteger.ZERO)>0)
                    {
                        System.out.println("Accepted");
                        continue;
                    }
                    else
                    {
                        System.out.println("Rejected");
                        continue;
                    }
                }
                else if(an.compareTo(BigInteger.ZERO)<0)
                {
                    System.out.println("Accepted");
                    continue;
                }
                else
                {
                    System.out.println("Rejected");
                    continue;
                }
            }
            else if(check(x2,y2,x3,y3,x1,y1,x4,y4))
            {
                lin1=ab.add(ac).subtract(bc);
                lin2=bd.add(cd).subtract(bc);
                if(lin1.compareTo(BigInteger.ZERO)>0 && lin2.compareTo(BigInteger.ZERO)<=0)
                {
                    System.out.println("Rejected");
                    continue;
                }
                else if(lin1.compareTo(BigInteger.ZERO)<=0 && lin2.compareTo(BigInteger.ZERO)>0)
                {
                    System.out.println("Accepted");
                    continue;
                }
                tem1=lin1.pow(2).multiply(bd).multiply(cd);
                tem2=lin2.pow(2).multiply(ab).multiply(ac);
                an=tem1.subtract(tem2);
                if(lin1.compareTo(BigInteger.ZERO)<0 && lin2.compareTo(BigInteger.ZERO)<0)
                {
                    if(an.compareTo(BigInteger.ZERO)>0)
                    {
                        System.out.println("Accepted");
                        continue;
                    }
                    else
                    {
                        System.out.println("Rejected");
                        continue;
                    }
                }
                else if(an.compareTo(BigInteger.ZERO)<0)
                {
                    System.out.println("Accepted");
                    continue;
                }
                else
                {
                    System.out.println("Rejected");
                    continue;
                }
            }
            else
            {
                System.out.println("Rejected");
                continue;
            }
        }
    }
}