程序员代码面试指南刷题--23.判断一个点是否在矩形内部

题目描述

在二维坐标系中，所有的值是double类型，那么一个矩形可以由四个点来代表，(x1, y1)为最左的点，(x2, y2)为最上的点，(x3, y3)为最下的点，(x4, y4)为最右的点。给定4个点代表的矩形，再给定一个点(x, y)，判断(x, y)是否在矩形中

输入描述:

输入有五行，每行两个整数。
对于前四行，第i行的浮点数表示(xi,yix_i, y_ixi​,yi​)
最后一行两个浮点数表示(x, y)

输出描述:

若(x, y)在矩形中，输出"Yes"

否则输出"No"

示例1
输入
2.00 2.50
3.00 5.00
3.00 1.50
4.00 4.00
3.21 3.78

输出
Yes

示例2
输入
2.00 2.50
3.00 5.00
3.00 1.50
4.00 4.00
2333.33 2333333.33

输出
No

解法一：报错（只有那一个例子出错我佛了）

思路： 哪个好心人帮忙看看

import java.io.*;
public class Main{
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] ss = br.readLine().trim().split(" ");
        Double x1 = Double.parseDouble(ss[0]);
        Double y1 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x2 = Double.parseDouble(ss[0]);
        Double y2 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x3 = Double.parseDouble(ss[0]);
        Double y3 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x4 = Double.parseDouble(ss[0]);
        Double y4 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x = Double.parseDouble(ss[0]);
        Double y = Double.parseDouble(ss[1]);
        boolean flag = judge(x1,y1,x2,y2,x3,y3,x4,y4,x,y);
        if(flag==true) System.out.print("Yes");
        else System.out.print("No");
    }
    public static boolean judge(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4,double x,double y){
        int flag = uporDown(x1,y1,x2,y2,x,y);
        if(flag==1||flag==0) return false;
        flag = uporDown(x1,y1,x3,y3,x,y);
        if(flag==-1||flag==0) return false;
        flag = uporDown(x4,y4,x3,y3,x,y);
        if(flag==-1||flag==0) return false;
        flag = uporDown(x4,y4,x2,y2,x,y);
        if(flag==1||flag==0) return false;
        return true;
        
    }
    public static int uporDown(double x1,double y1,double x2,double y2,double x,double y){
        double k = (y2-y1)/(x2-x1);
        double b = y1-k*x1;
        if(y>(k*x+b)) return 1;
        else if(y==(k*x+b)) return 0;
        else return -1;
    }
}

解法二：调整方向

import java.io.*;
public class Main{
    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] ss = br.readLine().trim().split(" ");
        Double x1 = Double.parseDouble(ss[0]);
        Double y1 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x2 = Double.parseDouble(ss[0]);
        Double y2 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x3 = Double.parseDouble(ss[0]);
        Double y3 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x4 = Double.parseDouble(ss[0]);
        Double y4 = Double.parseDouble(ss[1]);
        ss = br.readLine().trim().split(" ");
        Double x = Double.parseDouble(ss[0]);
        Double y = Double.parseDouble(ss[1]);
        boolean flag = judge(x1,y1,x2,y2,x3,y3,x4,y4,x,y);
        if(flag==true) System.out.print("Yes");
        else System.out.print("No");
    }
    public static boolean judge(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4,double x,double y){
        if(y1==y2){
            return isInside(x1,y1,x4,y4,x,y);
        }
        double l=Math.abs(y4-y3);
        double k=Math.abs(x4-x3);
        double s=Math.sqrt(k*k+l*l);
        double sin=l/s;
        double cos=k/s;
        double x1r=x1*cos+y1*sin;
        double y1r=-x1*sin+y1*cos;
        double x4r=x4*cos+y4*sin;
        double y4r=-x4*sin+y4*cos;
        double xr=x*cos+y*sin;
        double yr=-x*sin+y*cos;
        return isInside(x1r,y1r,x4r,y4r,xr,yr);
    }
         
    public static boolean isInside(double x1,double y1,double x4,double y4,double x,double y){
        if(x<=x1){
            return false;
        }else if(x>=x4){
            return false;
        }else if(y>=y1){
            return false;
        }else if(y<=y4){
            return false;
        }else{
            return true;
        }
    }
    public static int uporDown(double x1,double y1,double x2,double y2,double x,double y){
        double k = (y2-y1)/(x2-x1);
        double b = y1-k*x1;
        if(y>(k*x+b)) return 1;
        else if(y==(k*x+b)) return 0;
        else return -1;
    }
}