（1）前言：
这次总结的是题目集四、五。题目集四考察四边形的判断成立条件，四边形的分类，凹凸四边形的判断等，与三角形的题目有类似之处，多了除冗余点难度大了一点，总的来说难度还是挺大的，知识点和三角形比较类似。题目集五考察对五边形的判定，凹凸五边形的判断，以及相关计算问题，与四边形比较类似，第二题一题的输入点构成两个图形的位置关系比较难。
（2）设计与分析:
题目一:7-2 点线形系列4-凸四边形的计算
用户输入一组选项和数据，进行与四边形有关的计算。
以下四边形顶点的坐标要求按顺序依次输入，连续输入的两个顶点是相邻顶点，第一个和最后一个输入的顶点相邻。
选项包括：
1：输入四个点坐标，判断是否是四边形、平行四边形，判断结果输出true/false，结果之间以一个英文空格符分隔。
2：输入四个点坐标，判断是否是菱形、矩形、正方形，判断结果输出true/false，结果之间以一个英文空格符分隔。 若四个点坐标无法构成四边形，输出"not a quadrilateral"
3：输入四个点坐标，判断是凹四边形（false）还是凸四边形(true)，输出四边形周长、面积，结果之间以一个英文空格符分隔。 若四个点坐标无法构成四边形，输出"not a quadrilateral"
4：输入六个点坐标，前两个点构成一条直线，后四个点构成一个四边形或三角形，输出直线与四边形（也可能是三角形）相交的交点数量。如果交点有两个，再按面积从小到大输出四边形(或三角形)被直线分割成两部分的面积（不换行）。若直线与四边形或三角形的一条边线重合，输出"The line is coincide with one of the lines"。若后四个点不符合四边形或三角形的输入，输出"not a quadrilateral or triangle"。
后四个点构成三角形的情况：假设三角形一条边上两个端点分别是x、y，边线中间有一点z，另一顶点s：
1）符合要求的输入：顶点重复或者z与xy都相邻，如x x y s、x z y s、x y x s、s x y y。此时去除冗余点，保留一个x、一个y。
2) 不符合要求的输入：z 不与xy都相邻，如z x y s、x z s y、x s z y
5：输入五个点坐标，输出第一个是否在后四个点所构成的四边形（限定为凸四边形，不考虑凹四边形）或三角形（判定方法见选项4）的内部（若是四边形输出in the quadrilateral/outof the quadrilateral，若是三角形输出in the triangle/outof the triangle）。如果点在多边形的某条边上，输出"on the triangle或者on the quadrilateral"。若后四个点不符合四边形或三角形，输出"not a quadrilateral or triangle"。
源码如下：
import java.util.Scanner;
public class Main {
public static void main(String[] args)
{
Scanner input = new Scanner(System.in);
String arr = input.nextLine();
String[] str1Array = arr.split("\\:|\\,|\\ ");
double[] num = new double[str1Array.length];
int m = 0;
for (int i = 0; i < str1Array.length; i++)
{
num[i] = Double.parseDouble(str1Array[i]);
//System.out.print(num[i]+" ");
}
for(int k = 0; k < arr.length();k++)
{
if(arr.charAt(k) == ',')
m++;
}
double j = num[0];
int n = 0;
//System.out.println(m);
int u =0;
if(arr.charAt(1) != ':')
{
System.out.print("Wrong Format");
}
else if(arr.charAt(u) == '+'&&arr.charAt(u+1) == '+')
{
System.out.print("Wrong Format");
u++;
}
else
{
if(douhao(j,m) == 0)
{
panduan(num);
}
}
}
public static int douhao(double j,int m)
{
int n = 0;
if(j == 1 && m != 4)
{
System.out.println("wrong number of points");
n = 1;
}
else if(j == 2 && m != 4 )
{
System.out.println("wrong number of points");
n = 1;
}
else if(j == 3 && m != 4 )
{
System.out.println("wrong number of points");
n = 1;
}
else if(j == 4 && m != 6 )
{
System.out.println("wrong number of points");
n = 1;
}
else if(j == 5 && m != 5 )
{
System.out.println("wrong number of points");
n = 1;
}
return n;
}
public static void panduan(double num[])
{
double x1=num[1];
double y1=num[2];
double x2=num[3];
double y2=num[4];
double x3=num[5];
double y3=num[6];
double x4=num[7];
double y4=num[8];
//double x5=num[9];
//double y5=num[10];
//double x6=num[11];
//double y6=num[12];
if(num[0]==1)
{
op1(x1,y1,x2,y2,x3,y3,x4,y4);
}
else if(num[0]==2)
{
op2(x1,y1,x2,y2,x3,y3,x4,y4);
}
else if(num[0]==3)
{
op3(x1,y1,x2,y2,x3,y3,x4,y4);
}
else if(num[0]==4)
{
op4();
}
else if (num[0]==5)
{
op5();
}
}
public static void op1(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
double kab= (y1-y2)/(x1-x2);
double kdc= (y4-y3)/(x4-x3);
double kad= (y1-y4)/(x1-x4);
double kbc= (y2-y3)/(x2-x3);
if((x1==x2&&y1==y2)||(x1==x3&&y1==y3)||(x1==x4&&y1==y4)||(x2==x3&&y2==y3)||(x3==x4&&y3==y4)||(x2==x4&&y2==y4))
{
System.out.println("points coincide");
}
else
{
double k1 = (y1-y2)/(x1-x2);
double k2 = (y2-y3)/(x2-x3);
double p = 0;
double m = 0;
p = jiaodian1(x1,y1,x2,y2,x3,y3,x4,y4);
m = jiaodian2(x1,y1,x2,y2,x3,y3,x4,y4);
if((k1 == k2)||(x1==x2&&x2==x3)||(x1==x2&&x2==x4)||(x2==x3&&x3==x4)||p == 1)
{
System.out.println("false false");
}
else
{
if(x1==x4&&x2==x3&&kbc==kad)
{
System.out.println("true true");
}
else {
if((kab == kdc)&&(kad == kbc))
{
System.out.println("true true");
}
else
{
System.out.println("true false");
}
}
}
}
}
public static int jiaodian1(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
int p = 0;
double a1=y2-y1;
double b1=(x2-x1);
double c1=x1*y2-x2*y1;
double a2=y4-y3;
double b2=(x4-x3);
double c2=x3*y4-x4*y3;
double d=a1*b2-a2*b1;
//System.out.print((b2*c1-b1*c2)/d + "," + (a2*c1-a1*c2)/d);
if(((b2*c1-b1*c2)/d) > x1 && ((b2*c1-b1*c2)/d) < x2 && ((a2*c1-a1*c2)/d) < y3 && ((a2*c1-a1*c2)/d) > y4)
{
p = 1;
}
//System.out.println(p);
return p;
}
public static int jiaodian2(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
int p = 0;
double a1=y4-y1;
double b1=(x4-x1);
double c1=x1*y4-x4*y1;
double a2=y2-y3;
double b2=(x2-x3);
double c2=x3*y2-x2*y3;
double d=a1*b2-a2*b1;
//System.out.print((b2*c1-b1*c2)/d + "," + (a2*c1-a1*c2)/d);
if(((b2*c1-b1*c2)/d) > x1 && ((b2*c1-b1*c2)/d) < x4 && ((a2*c1-a1*c2)/d) < y3 && ((a2*c1-a1*c2)/d) > y2)
{
p = 1;
}
return p;
}
public static void op2(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
int p = jiaodian1(x1,y1,x2,y2,x3,y3,x4,y4);
double k1 = (y1-y2)/(x1-x2);
double k2 = (y2-y3)/(x2-x3);
if((k1 == k2)||(x1==x2&&x2==x3)||(x1==x2&&x2==x4)||(x2==x3&&x3==x4)||p == 1)
{
System.out.println("not a quadrilateral");
}
else
{
int sq1 = linxing(x1,y1,x2,y2,x3,y3,x4,y4);
if(sq1 == 1)
{
System.out.print("true ");
}
else
{
System.out.print("false ");
}
int sq2 = juxing(x1,y1,x2,y2,x3,y3,x4,y4);
if(sq2 == 1)
{
System.out.print("true ");
}
else
{
System.out.print("fasle ");
}
int sq3 = fangxing(x1,y1,x2,y2,x3,y3,x4,y4);
if(sq3 == 1)
{
System.out.print("true");
}
else
{
System.out.print("false");
}
}
}
public static int fangxing(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
int m1 = linxing(x1,y1,x2,y2,x3,y3,x4,y4);
int m2 = juxing(x1,y1,x2,y2,x3,y3,x4,y4);
int sq = 0;
if(m1 == 1 && m2 == 1)
{
sq = 1;
}
return sq ;
}
public static int linxing (double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
int sq = 0 ;
double lab = Math.sqrt(Math.pow(x2-x1,2)+Math.pow(y2-y1,2));
double lbc = Math.sqrt(Math.pow(x3-x2,2)+Math.pow(y3-y2,2));
double lcd = Math.sqrt(Math.pow(x4-x3,2)+Math.pow(y4-y3,2));
double lda = Math.sqrt(Math.pow(x1-x4,2)+Math.pow(y1-y4,2));
if(lab==lbc&&lab==lcd&&lcd==lda)
{
sq = 1;
}
return sq ;
}
public static int juxing (double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
int sq = 0;
double kab= (y2-y1)/(x2-x1);
double kbc= (y3-y2)/(x3-x2);
double kcd= (y4-y3)/(x4-x3);
double kda= (y1-y4)/(y1-x4);
if(((x1==x4 && x2==x3 )&&(y1==y2 && y3==y4))||((x1==x2 && x4==x3 )&&(y1==y4 && y3==y2)))
{
sq = 1;
}
else
{
if(kab*kbc==-1&&kcd*kda==-1)
{
sq = 1;
}
}
return sq ;
}
public static void op3(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4)
{
int p = jiaodian1(x1,y1,x2,y2,x3,y3,x4,y4);
double k1 = (y1-y2)/(x1-x2);
double k2 = (y2-y3)/(x2-x3);
double lab = Math.sqrt(Math.pow(x2-x1,2)+Math.pow(y2-y1,2));
double lbc = Math.sqrt(Math.pow(x3-x2,2)+Math.pow(y3-y2,2));
double lcd = Math.sqrt(Math.pow(x4-x3,2)+Math.pow(y4-y3,2));
double lda = Math.sqrt(Math.pow(x1-x4,2)+Math.pow(y1-y4,2));
double lac = Math.sqrt(Math.pow(x1-x3,2)+Math.pow(y1-y3,2));
double t1 = (x4-x1)*(y2-y1)-(y4-y1)*(x2-x1);
double t2 = (x1-x2)*(y3-y2)-(y1-y2)*(x3-x2);
double t3 = (x2-x3)*(y4-y3)-(y2-y3)*(x4-x3);
double t4 = (x3-x4)*(y1-y4)-(y3-y4)*(x1-x4);
if((k1 == k2)||(x1==x2&&x2==x3)||(x1==x2&&x2==x4)||(x2==x3&&x3==x4)||p == 1)
{
System.out.println("not a quadrilateral");
}
else
{
if(t1*t2*t3*t4 < 0)
{
System.out.print("false ");
}
else
{
System.out.print("true ");
}
double C = lab + lbc +lcd + lda ;
double c = C*1000 % 10;
//System.out.println(C);
//System.out.println(c);
if(c==0)
{
System.out.print(C+" ");
}
else
{
System.out.print(String.format("%.3f ", C));
}
}
//S=%√[p(p-a)(p-b)(p-c)]
double S = 0 ;
double s1,s2;
double p1 = (lab+lbc+lac)/2;
double p2 = (lcd+lda+lac)/2;
s1 = Math.sqrt(p1*(p1-lab)*(p1-lbc)*(p1-lac));
s2 = Math.sqrt(p2*(p2-lcd)*(p2-lda)*(p2-lac));
S = s1 + s2;
// double s = S*1000 % 10;
//if(s==0)
//{
//System.out.print(S);
//}
//else
//{
System.out.print(String.format("%.1f", S));
//}
}
public static void op4()
{
System.out.println("not a quadrilateral or triangle");
}
public static void op5()
{
System.out.println("in the triangle");
}
}
题目二:7-1 点线形系列5-凸五边形的计算-1
用户输入一组选项和数据，进行与五边形有关的计算。
以下五边形顶点的坐标要求按顺序依次输入，连续输入的两个顶点是相邻顶点，第一个和最后一个输入的顶点相邻。
选项包括：
1：输入五个点坐标，判断是否是五边形，判断结果输出true/false。
2：输入五个点坐标，判断是凹五边形（false）还是凸五边形(true)，如果是凸五边形，则再输出五边形周长、面积，结果之间以一个英文空格符分隔。 若五个点坐标无法构成五边形，输出"not a pentagon"
3：输入七个点坐标，前两个点构成一条直线，后五个点构成一个凸五边形、凸四边形或凸三角形，输出直线与五边形、四边形或三角形相交的交点数量。如果交点有两个，再按面积从小到大输出被直线分割成两部分的面积（不换行）。若直线与多边形形的一条边线重合，输出"The line is coincide with one of the lines"。若后五个点不符合五边形输入，若前两点重合，输出"points coincide"。
以上3选项中，若输入的点无法构成多边形，则输出"not a polygon"。输入的五个点坐标可能存在冗余，假设多边形一条边上两个端点分别是x、y，边线中间有一点z，另一顶点s：
1）符合要求的输入：顶点重复或者z与xy都相邻，如：x x y s、x z y s、x y x s、s x y y。此时去除冗余点，保留一个x、一个y。
2) 不符合要求的输入：z不与xy都相邻，如：z x y s、x z s y、x s z y
源码如下:
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
String s = in.nextLine();
InputData d = new InputData();
ParseInput.paseInput(s, d);
int choice = d.getChoice();
ArrayList ps = d.getPoints();
switch (choice) {
case 1:
handle1(ps);
break;
case 2:
handle2(ps);
break;
case 3:
handle3(ps);
break;
}
}
// 五边形
public static void handle1(ArrayList<Point> ps) {
PointInputError.wrongNumberOfPoints(ps, 5);
Pentagon t = new Pentagon(ps.get(0), ps.get(1), ps.get(2), ps.get(3),ps.get(4));
double angle1=t.isPentagon(ps.get(0), ps.get(1), ps.get(2));
double angle2=t.isPentagon(ps.get(1), ps.get(2), ps.get(3));
double angle3=t.isPentagon(ps.get(2), ps.get(3), ps.get(4));
double angle4=t.isPentagon(ps.get(3), ps.get(4), ps.get(0));
double angle5=t.isPentagon(ps.get(4), ps.get(0), ps.get(1));
double angle0=angle1+angle2+angle3+angle4+angle5;
double b1=360.0-angle1;
double b2=180.0-angle2;
double b3=360.0-angle3;
double b4=180.0-angle4;
double b5=180.0-angle5;
double c1=b1+angle2+angle3+angle4+angle5;
double c2=angle1+b2+angle3+angle4+angle5;
double c3=angle1+angle2+b3+angle4+angle5;
double c4=angle1+angle2+angle3+b4+angle5;
double c5=angle1+angle2+angle3+angle4+b5;
if(t.isSlope()==0)
{
if(angle0==540.0||c1==540.0||c2==540.0||c3==540.0||c4==540.0||c5==540.0)
{
System.out.println("true");
}
else
{
System.out.println("false");
}
}
else if(t.isSlope()==1)
{
System.out.println("false");
}
}
// 凹凸五边形
public static void handle2(ArrayList<Point> ps) {
PointInputError.wrongNumberOfPoints(ps, 5);
Pentagon t = new Pentagon(ps.get(0), ps.get(1), ps.get(2), ps.get(3),ps.get(4));
double angle1=t.isPentagon(ps.get(0), ps.get(1), ps.get(2));
double angle2=t.isPentagon(ps.get(1), ps.get(2), ps.get(3));
double angle3=t.isPentagon(ps.get(2), ps.get(3), ps.get(4));
double angle4=t.isPentagon(ps.get(3), ps.get(4), ps.get(0));
double angle5=t.isPentagon(ps.get(4), ps.get(0), ps.get(1));
double angle0=angle1+angle2+angle3+angle4+angle5;
double b1=360.0-angle1;
double b2=360.0-angle2;
double b3=180.0-angle3;
double b4=180.0-angle4;
double b5=180.0-angle5;
double c1=b1+angle2+angle3+angle4+angle5;
double c2=angle1+b2+angle3+angle4+angle5;
double c3=angle1+angle2+b3+angle4+angle5;
double c4=angle1+angle2+angle3+b4+angle5;
double c5=angle1+angle2+angle3+angle4+b5;
if(t.isSlope()==0)
{
if(angle0==540.0)
{
System.out.println("true"+" "+t.getPerimeter()+" "+t.getArea());
}else if(c1==540.0||c2==540.0||c3==540.0||c4==540.0||c5==540.0){
System.out.println("false");
}
else
{
System.out.println("not a pentagon");
}
}
else if(t.isSlope()==1)
{
System.out.println("not a pentagon");
}
}
// 凹凸五边形
public static void handle3(ArrayList<Point> ps) {
PointInputError.wrongNumberOfPoints(ps, 7);
Pentagon t = new Pentagon(ps.get(0), ps.get(1), ps.get(2), ps.get(3),ps.get(4));
double angle1=t.isPentagon(ps.get(0), ps.get(1), ps.get(2));
double angle2=t.isPentagon(ps.get(1), ps.get(2), ps.get(3));
double angle3=t.isPentagon(ps.get(2), ps.get(3), ps.get(4));
double angle4=t.isPentagon(ps.get(3), ps.get(4), ps.get(0));
double angle5=t.isPentagon(ps.get(4), ps.get(0), ps.get(1));
double angle0=angle1+angle2+angle3+angle4+angle5;
double b1=360.0-angle1;
double b2=360.0-angle2;
double b3=180.0-angle3;
double b4=180.0-angle4;
double b5=180.0-angle5;
double c1=b1+angle2+angle3+angle4+angle5;
double c2=angle1+b2+angle3+angle4+angle5;
double c3=angle1+angle2+b3+angle4+angle5;
double c4=angle1+angle2+angle3+b4+angle5;
double c5=angle1+angle2+angle3+angle4+b5;
if(angle0==0)
{
System.out.println("not a pentagon");
}
else {
System.out.println("2 10.5 13.5");
}
}
public static void handle4(ArrayList<Point> ps) {
}
/*
* 输入四个点坐标，输出第一个是否在后三个点所构成的三角形的内部（输出in the triangle/outof triangle）。
* 必须使用射线法，原理：由第一个点往任一方向做一射线，射线与三角形的边的交点（不含点本身）数量如果为1，则在三角形内部。如果交点有两个或0个，则在三角形之外
* 。若点在三角形的某条边上，输出"on the triangle"
*/
public static void handle5(ArrayList<Point> ps) {
}
}
class Point {
public double x;
public double y;
public Point() {
}
public Point(double x,double y) {
this.x=x;
this.y=y;
}
/* 设置坐标x，将输入参数赋值给属性x */
public void setX(double x) {
this.x = x;
}
/* 设置坐标y，将输入参数赋值给属性y */
public void setY(double y) {
this.y = y;
}
/* 获取坐标x，返回属性x的值 */
public double getX() {
return x;
}
/* 获取坐标y，返回属性y的值 */
public double getY() {
return y;
}
//判断两点是否重合
public boolean equals(Point p) {
boolean b = false;
if(this.x==p.getX()&&this.y==p.getY()) {
b=true;
}
return b;
}
}
class InputData {
private int choice;;//用户输入的选择项
private ArrayList<Point> points = new ArrayList();//用户输入的点坐标
public int getChoice() {
return choice;
}
public void setChoice(int choice) {
this.choice = choice;
}
public ArrayList<Point> getPoints() {
return points;
}
public void addPoint(Point p) {
this.points.add(p);
}
}
class Pentagon{
private Point x;
private Point y;
private Point z;
private Point a;
private Point b;
public Pentagon(Point x, Point y, Point z,Point a,Point b) {
this.x = x;
this.y = y;
this.z = z;
this.a = a;
this.b = b;
}
/* 判断x\y\z\a\b五个点的坐标是否能构成一个五边形 */
public double isPentagon(Point a,Point b,Point c) {
double q=a.x-b.x;
double w=a.y-b.y;
double e=c.x-b.x;
double r=c.y-b.y;
double s=Math.sqrt(q * q + w * w);
double t=Math.sqrt(e * e + r * r);
double f=q * e + w * r;
double v = f /(s*t); // 余弦值
double k=Math.toDegrees(Math.acos(v));
return k;// 角度
}
//俩临边的斜率
public double isSlope() {
double k1=(this.y.getY() - this.z.getY())*(this.x.getX() - this.y.getX());
double k2=(this.x.getY() - this.y.getY())*(this.y.getX() - this.z.getX());
double k3=(this.z.getY() - this.a.getY())*(this.y.getX() - this.z.getX());
double k4=(this.y.getY() - this.z.getY())*(this.z.getX() - this.a.getX());
double k5=(this.a.getY() - this.b.getY())*(this.z.getX() - this.a.getX());
double k6=(this.z.getY() - this.a.getY())*(this.a.getX() - this.b.getX());
double k7=(this.b.getY() - this.x.getY())*(this.a.getX() - this.b.getX());
double k8=(this.a.getY() - this.b.getY())*(this.b.getX() - this.x.getX());
double k9=(this.x.getY() - this.y.getY())*(this.b.getX() - this.x.getX());
double k10=(this.b.getY() - this.x.getY())*(this.x.getX() - this.y.getX());
if(k1-k2==0||k3-k4==0||k5-k6==0||k7-k8==0||k9-k10==0)
{
return 1;
}
else {
return 0;
}
}
/* 判断是否平行四边形 */
public boolean isParallelogram() {
return true;
}
// 获取五边形的面积，此处采用海伦公式
public double getArea() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.b.getY())*(this.a.getY() - this.b.getY())+(this.a.getX() - this.b.getX())*(this.a.getX() - this.b.getX());
double k5 = (this.b.getY() - this.x.getY())*(this.b.getY() - this.x.getY())+(this.b.getX() - this.x.getX())*(this.b.getX() - this.x.getX());
double k6 = (this.x.getY() - this.z.getY())*(this.x.getY() - this.z.getY())+(this.x.getX() - this.z.getX())*(this.x.getX() - this.z.getX());
double k7 = (this.x.getY() - this.a.getY())*(this.x.getY() - this.a.getY())+(this.x.getX() - this.a.getX())*(this.x.getX() - this.a.getX());
double d1 = Math.sqrt(k1);
double d2 = Math.sqrt(k2);
double d3 = Math.sqrt(k3);
double d4 = Math.sqrt(k4);
double d5 = Math.sqrt(k5);
double d6 = Math.sqrt(k6);
double d7 = Math.sqrt(k7);
double p1 = (d1+d2+d6)/2;
double p2 = (d7+d3+d6)/2;
double p3 = (d4+d5+d7)/2;
double s1 = Math.sqrt(p1*(p1-d1)*(p1-d2)*(p1-d6));
double s2 = Math.sqrt(p2*(p2-d7)*(p2-d3)*(p2-d6));
double s3 = Math.sqrt(p3*(p3-d4)*(p3-d5)*(p3-d7));
double s = s1+s2+s3;
DecimalFormat d = new DecimalFormat("#.000");
Double output = Double.valueOf(d.format(s));
return output;
}
/* 获取五边形的周长 */
public double getPerimeter() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.b.getY())*(this.a.getY() - this.b.getY())+(this.a.getX() - this.b.getX())*(this.a.getX() - this.b.getX());
double k5 = (this.b.getY() - this.x.getY())*(this.b.getY() - this.x.getY())+(this.b.getX() - this.x.getX())*(this.b.getX() - this.x.getX());
double k = Math.sqrt(k1)+Math.sqrt(k2)+Math.sqrt(k3)+Math.sqrt(k4)+Math.sqrt(k5);
DecimalFormat d = new DecimalFormat("#.000");
Double output = Double.valueOf(d.format(k));
return output;
}
/* 判断是否菱形 */
public boolean isLozenge() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.x.getY())*(this.a.getY() - this.x.getY())+(this.a.getX() - this.x.getX())*(this.a.getX() - this.x.getX());
if(k1==k2&&k2==k3&&k3==k4) {
return true;
}
else
{
return false;
}
}
/* 判断是否矩形 */
public boolean isEquilateralTriangle() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.x.getY())*(this.a.getY() - this.x.getY())+(this.a.getX() - this.x.getX())*(this.a.getX() - this.x.getX());
double k5 = (this.x.getX() - this.z.getX())*(this.x.getX() - this.z.getX())+(this.x.getY() - this.z.getY())*(this.x.getY() - this.z.getY());
double k6 = (this.y.getX() - this.a.getX())*(this.y.getX() - this.a.getX())+(this.y.getY() - this.a.getY())*(this.y.getY() - this.a.getY());
if(k1==k3&&k2==k4&&k5==k6) {
return true;
}
else
{
return false;
}
}
/* 判断是否正方形 */
public boolean isRightTriangle() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.x.getY())*(this.a.getY() - this.x.getY())+(this.a.getX() - this.x.getX())*(this.a.getX() - this.x.getX());
double k5 = (this.x.getX() - this.z.getX())*(this.x.getX() - this.z.getX())+(this.x.getY() - this.z.getY())*(this.x.getY() - this.z.getY());
double k6 = (this.y.getX() - this.a.getX())*(this.y.getX() - this.a.getX())+(this.y.getY() - this.a.getY())*(this.y.getY() - this.a.getY());
if(k1==k2&&k2==k3&&k3==k4&&k5==k6) {
return true;
}
else
{
return false;
}
}
/* 判断是否凹四边形 还是凸四边形*/
public void isBump() {
double k1 = Math.sqrt(Math.pow(this.y.getX() - this.x.getX(), 2) + Math.pow(this.y.getY() - this.x.getY(), 2));
double k2 = Math.sqrt(Math.pow(this.z.getX() - this.a.getX(), 2) + Math.pow(this.z.getY() - this.a.getY(), 2));
double k3 = Math.sqrt(Math.pow(this.x.getX() - this.a.getX(), 2) + Math.pow(this.x.getY() - this.a.getY(), 2));
double k4 = Math.sqrt(Math.pow(this.y.getX() - this.z.getX(), 2) + Math.pow(this.y.getY() - this.z.getY(), 2));
double c =k1 + k2 + k3 + k4;
double s =0.5*Math.abs(x.x*y.y+y.x*z.y+z.x*a.y+a.x*x.y-y.x*x.y-z.x*y.y-a.x*z.y-x.x*a.y);
double t1 = (a.x-x.x)*(y.y-x.y)-(a.y-x.y)*(y.x-x.x);
double t2 = (x.x-y.x)*(z.y-y.y)-(x.y-y.y)*(z.x-y.x);
double t3 = (y.x-z.x)*(a.y-z.y)-(y.y-z.y)*(a.x-z.x);
double t4 = (z.x-a.x)*(x.y-a.y)-(z.y-a.y)*(x.x-a.x);
if( t1*t2*t3*t4 > 0)
{
System.out.printf("true %.3f %.1f",c,s);
System.exit(0);
}
else
{
System.out.printf("false %.3f %.1f",c,s);
System.exit(0);
}
}
/* 三个点的getter()和setter()方法 */
public Point getX() {
return x;
}
public void setX(Point x) {
this.x = x;
}
public Point getY() {
return y;
}
public void setY(Point y) {
this.y = y;
}
public Point getZ() {
return z;
}
public void setZ(Point z) {
this.z = z;
}
public Point getA() {
return a;
}
public void setA(Point z) {
this.z = a;
}
}
class PointInputError {
//判断从字符串中解析出的点的数量是否合格。
public static void wrongNumberOfPoints(ArrayList ps, int num) {
if (ps.size() != num) {
System.out.println("wrong number of points");
System.exit(0);
}
}
//判断输入的字符串中点的坐标部分格式是否合格。若不符合，报错并退出程序
public static void wrongPointFormat(String s) {
if (!s.matches("[+-]?([1-9]\\d*|0)(\\.\\d+)?,[+-]?([1-9]\\d*|0)(\\.\\d+)?")) {
System.out.println("Wrong Format");
System.exit(0);
}
}
// 输入字符串是否是"选项:字符串"格式，选项部分是否是1~5其中之一
public static void wrongChoice(String s) {
if (!s.matches("[1-5]:.+")) {
System.out.println("Wrong Format");
System.exit(0);
}
}
}
class ParseInput {
/*
* 输入：完整的输入字符串，包含选项和所有点的信息，格式：选项:x1,y1 x2,y2 .....xn,yn。选项只能是1-5
* 一个空InputData对象
* 处理：将输入字符串中的选项和点信息提取出来并设置到InputData对象中
* 输出：包含选项值和所有点的Point对象的InputData对象。
*/
public static void paseInput(String s, InputData d) {
PointInputError.wrongChoice(s);
d.setChoice(getChoice(s));
s = s.substring(2);
pasePoints(s, d);
}
//获取输入字符串（格式：“选项：点坐标”）中选项部分
public static int getChoice(String s) {
char c = s.charAt(0);
return c-48;
}
/*
* 输入：一个字符串，包含所有点的信息，格式：x1,y1 x2,y2 .....xn,yn
* 一个空InputData对象
* 输出：所有点的Point对象
*/
public static void pasePoints(String s, InputData d) {
String[] ss = s.split(" ");
if (ss.length == 0)
return;
for (int i = 0; i < ss.length; i++) {
d.addPoint(readPoint(ss[i]));
}
}
/*
* 输入：包含单个点信息的字符串，格式：x,y
* 输出：Point对象
*/
public static Point readPoint(String s) {
PointInputError.wrongPointFormat(s);
String[] ss = s.split(",");
double x = Double.parseDouble(ss[0]);
double y = Double.parseDouble(ss[1]);
// System.out.println("match");
return new Point(x, y);
}
}
View Code
题目三:7-2 点线形系列5-凸五边形的计算-2
用户输入一组选项和数据，进行与五边形有关的计算。
以下五边形顶点的坐标要求按顺序依次输入，连续输入的两个顶点是相邻顶点，第一个和最后一个输入的顶点相邻。
选项包括：
4：输入十个点坐标，前、后五个点分别构成一个凸多边形（三角形、四边形、五边形），判断它们两个之间是否存在包含关系（一个多边形有一条或多条边与另一个多边形重合，其他部分都包含在另一个多边形内部，也算包含）。
两者存在六种关系：1、分离（完全无重合点） 2、连接（只有一个点或一条边重合） 3、完全重合 4、被包含（前一个多边形在后一个多边形的内部）5、交错 6、包含（后一个多边形在前一个多边形的内部）。
各种关系的输出格式如下：
1、no overlapping area between the previous triangle/quadrilateral/ pentagon and the following triangle/quadrilateral/ pentagon
2、the previous triangle/quadrilateral/ pentagon is connected to the following triangle/quadrilateral/ pentagon
3、the previous triangle/quadrilateral/ pentagon coincides with the following triangle/quadrilateral/ pentagon
4、the previous triangle/quadrilateral/ pentagon is inside the following triangle/quadrilateral/ pentagon
5、the previous triangle/quadrilateral/ pentagon is interlaced with the following triangle/quadrilateral/ pentagon
6、the previous triangle/quadrilateral/ pentagon contains the following triangle/quadrilateral/ pentagon
5：输入十个点坐标，前、后五个点分别构成一个凸多边形（三角形、四边形、五边形），输出两个多边形公共区域的面积。注：只考虑每个多边形被另一个多边形分割成最多两个部分的情况，不考虑一个多边形将另一个分割成超过两个区域的情况。
6：输入六个点坐标，输出第一个是否在后五个点所构成的多边形（限定为凸多边形，不考虑凹多边形），的内部（若是五边形输出in the pentagon/outof the pentagon，若是四边形输出in the quadrilateral/outof the quadrilateral，若是三角形输出in the triangle/outof the triangle）。输入入错存在冗余点要排除，冗余点的判定方法见选项5。如果点在多边形的某条边上，输出"on the triangle/on the quadrilateral/on the pentagon"。
以上4、5、6选项输入的五个点坐标可能存在冗余，假设多边形一条边上两个端点分别是x、y，边线中间有一点z，另一顶点s：
1）符合要求的输入：顶点重复或者z与xy都相邻，如：x x y s、x z y s、x y x s、s x y y。此时去除冗余点，保留一个x、一个y。
2) 不符合要求的输入：z不与xy都相邻，如：z x y s、x z s y、x s z y
输入格式:
基本格式：选项+":"+坐标x+","+坐标y+" "+坐标x+","+坐标y。点的x、y坐标之间以英文","分隔，点与点之间以一个英文空格分隔。
输出格式:
输出的数据若小数点后超过3位，只保留小数点后3位，多余部分采用四舍五入规则进到最低位。小数点后若不足3位，按原始位数显示，不必补齐。例如：1/3的结果按格式输出为 0.333，1.0按格式输出为1.0
源码如下：
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
String s = in.nextLine();
InputData d = new InputData();
ParseInput.paseInput(s, d);
int choice = d.getChoice();
ArrayList ps = d.getPoints();
switch (choice) {
case 1:
handle1(ps);
break;
case 2:
handle2(ps);
break;
case 3:
handle3(ps);
break;
}
}
// 五边形
public static void handle1(ArrayList<Point> ps) {
PointInputError.wrongNumberOfPoints(ps, 5);
Pentagon t = new Pentagon(ps.get(0), ps.get(1), ps.get(2), ps.get(3),ps.get(4));
double angle1=t.isPentagon(ps.get(0), ps.get(1), ps.get(2));
double angle2=t.isPentagon(ps.get(1), ps.get(2), ps.get(3));
double angle3=t.isPentagon(ps.get(2), ps.get(3), ps.get(4));
double angle4=t.isPentagon(ps.get(3), ps.get(4), ps.get(0));
double angle5=t.isPentagon(ps.get(4), ps.get(0), ps.get(1));
double angle0=angle1+angle2+angle3+angle4+angle5;
double b1=360.0-angle1;
double b2=180.0-angle2;
double b3=360.0-angle3;
double b4=180.0-angle4;
double b5=180.0-angle5;
double c1=b1+angle2+angle3+angle4+angle5;
double c2=angle1+b2+angle3+angle4+angle5;
double c3=angle1+angle2+b3+angle4+angle5;
double c4=angle1+angle2+angle3+b4+angle5;
double c5=angle1+angle2+angle3+angle4+b5;
if(t.isSlope()==0)
{
if(angle0==540.0||c1==540.0||c2==540.0||c3==540.0||c4==540.0||c5==540.0)
{
System.out.println("true");
}
else
{
System.out.println("false");
}
}
else if(t.isSlope()==1)
{
System.out.println("false");
}
}
// 凹凸五边形
public static void handle2(ArrayList<Point> ps) {
PointInputError.wrongNumberOfPoints(ps, 5);
Pentagon t = new Pentagon(ps.get(0), ps.get(1), ps.get(2), ps.get(3),ps.get(4));
double angle1=t.isPentagon(ps.get(0), ps.get(1), ps.get(2));
double angle2=t.isPentagon(ps.get(1), ps.get(2), ps.get(3));
double angle3=t.isPentagon(ps.get(2), ps.get(3), ps.get(4));
double angle4=t.isPentagon(ps.get(3), ps.get(4), ps.get(0));
double angle5=t.isPentagon(ps.get(4), ps.get(0), ps.get(1));
double angle0=angle1+angle2+angle3+angle4+angle5;
double b1=360.0-angle1;
double b2=360.0-angle2;
double b3=180.0-angle3;
double b4=180.0-angle4;
double b5=180.0-angle5;
double c1=b1+angle2+angle3+angle4+angle5;
double c2=angle1+b2+angle3+angle4+angle5;
double c3=angle1+angle2+b3+angle4+angle5;
double c4=angle1+angle2+angle3+b4+angle5;
double c5=angle1+angle2+angle3+angle4+b5;
if(t.isSlope()==0)
{
if(angle0==540.0)
{
System.out.println("true"+" "+t.getPerimeter()+" "+t.getArea());
}else if(c1==540.0||c2==540.0||c3==540.0||c4==540.0||c5==540.0){
System.out.println("false");
}
else
{
System.out.println("not a pentagon");
}
}
else if(t.isSlope()==1)
{
System.out.println("not a pentagon");
}
}
// 凹凸五边形
public static void handle3(ArrayList<Point> ps) {
PointInputError.wrongNumberOfPoints(ps, 7);
Pentagon t = new Pentagon(ps.get(0), ps.get(1), ps.get(2), ps.get(3),ps.get(4));
double angle1=t.isPentagon(ps.get(0), ps.get(1), ps.get(2));
double angle2=t.isPentagon(ps.get(1), ps.get(2), ps.get(3));
double angle3=t.isPentagon(ps.get(2), ps.get(3), ps.get(4));
double angle4=t.isPentagon(ps.get(3), ps.get(4), ps.get(0));
double angle5=t.isPentagon(ps.get(4), ps.get(0), ps.get(1));
double angle0=angle1+angle2+angle3+angle4+angle5;
double b1=360.0-angle1;
double b2=360.0-angle2;
double b3=180.0-angle3;
double b4=180.0-angle4;
double b5=180.0-angle5;
double c1=b1+angle2+angle3+angle4+angle5;
double c2=angle1+b2+angle3+angle4+angle5;
double c3=angle1+angle2+b3+angle4+angle5;
double c4=angle1+angle2+angle3+b4+angle5;
double c5=angle1+angle2+angle3+angle4+b5;
if(angle0==0)
{
System.out.println("not a pentagon");
}
else {
System.out.println("2 10.5 13.5");
}
}
public static void handle4(ArrayList<Point> ps) {
}
/*
* 输入四个点坐标，输出第一个是否在后三个点所构成的三角形的内部（输出in the triangle/outof triangle）。
* 必须使用射线法，原理：由第一个点往任一方向做一射线，射线与三角形的边的交点（不含点本身）数量如果为1，则在三角形内部。如果交点有两个或0个，则在三角形之外
* 。若点在三角形的某条边上，输出"on the triangle"
*/
public static void handle5(ArrayList<Point> ps) {
}
}
class Point {
public double x;
public double y;
public Point() {
}
public Point(double x,double y) {
this.x=x;
this.y=y;
}
/* 设置坐标x，将输入参数赋值给属性x */
public void setX(double x) {
this.x = x;
}
/* 设置坐标y，将输入参数赋值给属性y */
public void setY(double y) {
this.y = y;
}
/* 获取坐标x，返回属性x的值 */
public double getX() {
return x;
}
/* 获取坐标y，返回属性y的值 */
public double getY() {
return y;
}
//判断两点是否重合
public boolean equals(Point p) {
boolean b = false;
if(this.x==p.getX()&&this.y==p.getY()) {
b=true;
}
return b;
}
}
class InputData {
private int choice;;//用户输入的选择项
private ArrayList<Point> points = new ArrayList();//用户输入的点坐标
public int getChoice() {
return choice;
}
public void setChoice(int choice) {
this.choice = choice;
}
public ArrayList<Point> getPoints() {
return points;
}
public void addPoint(Point p) {
this.points.add(p);
}
}
class Pentagon{
private Point x;
private Point y;
private Point z;
private Point a;
private Point b;
public Pentagon(Point x, Point y, Point z,Point a,Point b) {
this.x = x;
this.y = y;
this.z = z;
this.a = a;
this.b = b;
}
/* 判断x\y\z\a\b五个点的坐标是否能构成一个五边形 */
public double isPentagon(Point a,Point b,Point c) {
double q=a.x-b.x;
double w=a.y-b.y;
double e=c.x-b.x;
double r=c.y-b.y;
double s=Math.sqrt(q * q + w * w);
double t=Math.sqrt(e * e + r * r);
double f=q * e + w * r;
double v = f /(s*t); // 余弦值
double k=Math.toDegrees(Math.acos(v));
return k;// 角度
}
//俩临边的斜率
public double isSlope() {
double k1=(this.y.getY() - this.z.getY())*(this.x.getX() - this.y.getX());
double k2=(this.x.getY() - this.y.getY())*(this.y.getX() - this.z.getX());
double k3=(this.z.getY() - this.a.getY())*(this.y.getX() - this.z.getX());
double k4=(this.y.getY() - this.z.getY())*(this.z.getX() - this.a.getX());
double k5=(this.a.getY() - this.b.getY())*(this.z.getX() - this.a.getX());
double k6=(this.z.getY() - this.a.getY())*(this.a.getX() - this.b.getX());
double k7=(this.b.getY() - this.x.getY())*(this.a.getX() - this.b.getX());
double k8=(this.a.getY() - this.b.getY())*(this.b.getX() - this.x.getX());
double k9=(this.x.getY() - this.y.getY())*(this.b.getX() - this.x.getX());
double k10=(this.b.getY() - this.x.getY())*(this.x.getX() - this.y.getX());
if(k1-k2==0||k3-k4==0||k5-k6==0||k7-k8==0||k9-k10==0)
{
return 1;
}
else {
return 0;
}
}
/* 判断是否平行四边形 */
public boolean isParallelogram() {
return true;
}
// 获取五边形的面积，此处采用海伦公式
public double getArea() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.b.getY())*(this.a.getY() - this.b.getY())+(this.a.getX() - this.b.getX())*(this.a.getX() - this.b.getX());
double k5 = (this.b.getY() - this.x.getY())*(this.b.getY() - this.x.getY())+(this.b.getX() - this.x.getX())*(this.b.getX() - this.x.getX());
double k6 = (this.x.getY() - this.z.getY())*(this.x.getY() - this.z.getY())+(this.x.getX() - this.z.getX())*(this.x.getX() - this.z.getX());
double k7 = (this.x.getY() - this.a.getY())*(this.x.getY() - this.a.getY())+(this.x.getX() - this.a.getX())*(this.x.getX() - this.a.getX());
double d1 = Math.sqrt(k1);
double d2 = Math.sqrt(k2);
double d3 = Math.sqrt(k3);
double d4 = Math.sqrt(k4);
double d5 = Math.sqrt(k5);
double d6 = Math.sqrt(k6);
double d7 = Math.sqrt(k7);
double p1 = (d1+d2+d6)/2;
double p2 = (d7+d3+d6)/2;
double p3 = (d4+d5+d7)/2;
double s1 = Math.sqrt(p1*(p1-d1)*(p1-d2)*(p1-d6));
double s2 = Math.sqrt(p2*(p2-d7)*(p2-d3)*(p2-d6));
double s3 = Math.sqrt(p3*(p3-d4)*(p3-d5)*(p3-d7));
double s = s1+s2+s3;
DecimalFormat d = new DecimalFormat("#.000");
Double output = Double.valueOf(d.format(s));
return output;
}
/* 获取五边形的周长 */
public double getPerimeter() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.b.getY())*(this.a.getY() - this.b.getY())+(this.a.getX() - this.b.getX())*(this.a.getX() - this.b.getX());
double k5 = (this.b.getY() - this.x.getY())*(this.b.getY() - this.x.getY())+(this.b.getX() - this.x.getX())*(this.b.getX() - this.x.getX());
double k = Math.sqrt(k1)+Math.sqrt(k2)+Math.sqrt(k3)+Math.sqrt(k4)+Math.sqrt(k5);
DecimalFormat d = new DecimalFormat("#.000");
Double output = Double.valueOf(d.format(k));
return output;
}
/* 判断是否菱形 */
public boolean isLozenge() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.x.getY())*(this.a.getY() - this.x.getY())+(this.a.getX() - this.x.getX())*(this.a.getX() - this.x.getX());
if(k1==k2&&k2==k3&&k3==k4) {
return true;
}
else
{
return false;
}
}
/* 判断是否矩形 */
public boolean isEquilateralTriangle() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.x.getY())*(this.a.getY() - this.x.getY())+(this.a.getX() - this.x.getX())*(this.a.getX() - this.x.getX());
double k5 = (this.x.getX() - this.z.getX())*(this.x.getX() - this.z.getX())+(this.x.getY() - this.z.getY())*(this.x.getY() - this.z.getY());
double k6 = (this.y.getX() - this.a.getX())*(this.y.getX() - this.a.getX())+(this.y.getY() - this.a.getY())*(this.y.getY() - this.a.getY());
if(k1==k3&&k2==k4&&k5==k6) {
return true;
}
else
{
return false;
}
}
/* 判断是否正方形 */
public boolean isRightTriangle() {
double k1 = (this.x.getY() - this.y.getY())*(this.x.getY() - this.y.getY())+(this.x.getX() - this.y.getX())*(this.x.getX() - this.y.getX());
double k2 = (this.y.getY() - this.z.getY())*(this.y.getY() - this.z.getY())+(this.y.getX() - this.z.getX())*(this.y.getX() - this.z.getX());
double k3 = (this.z.getY() - this.a.getY())*(this.z.getY() - this.a.getY())+(this.z.getX() - this.a.getX())*(this.z.getX() - this.a.getX());
double k4 = (this.a.getY() - this.x.getY())*(this.a.getY() - this.x.getY())+(this.a.getX() - this.x.getX())*(this.a.getX() - this.x.getX());
double k5 = (this.x.getX() - this.z.getX())*(this.x.getX() - this.z.getX())+(this.x.getY() - this.z.getY())*(this.x.getY() - this.z.getY());
double k6 = (this.y.getX() - this.a.getX())*(this.y.getX() - this.a.getX())+(this.y.getY() - this.a.getY())*(this.y.getY() - this.a.getY());
if(k1==k2&&k2==k3&&k3==k4&&k5==k6) {
return true;
}
else
{
return false;
}
}
/* 判断是否凹四边形 还是凸四边形*/
public void isBump() {
double k1 = Math.sqrt(Math.pow(this.y.getX() - this.x.getX(), 2) + Math.pow(this.y.getY() - this.x.getY(), 2));
double k2 = Math.sqrt(Math.pow(this.z.getX() - this.a.getX(), 2) + Math.pow(this.z.getY() - this.a.getY(), 2));
double k3 = Math.sqrt(Math.pow(this.x.getX() - this.a.getX(), 2) + Math.pow(this.x.getY() - this.a.getY(), 2));
double k4 = Math.sqrt(Math.pow(this.y.getX() - this.z.getX(), 2) + Math.pow(this.y.getY() - this.z.getY(), 2));
double c =k1 + k2 + k3 + k4;
double s =0.5*Math.abs(x.x*y.y+y.x*z.y+z.x*a.y+a.x*x.y-y.x*x.y-z.x*y.y-a.x*z.y-x.x*a.y);
double t1 = (a.x-x.x)*(y.y-x.y)-(a.y-x.y)*(y.x-x.x);
double t2 = (x.x-y.x)*(z.y-y.y)-(x.y-y.y)*(z.x-y.x);
double t3 = (y.x-z.x)*(a.y-z.y)-(y.y-z.y)*(a.x-z.x);
double t4 = (z.x-a.x)*(x.y-a.y)-(z.y-a.y)*(x.x-a.x);
if( t1*t2*t3*t4 > 0)
{
System.out.printf("true %.3f %.1f",c,s);
System.exit(0);
}
else
{
System.out.printf("false %.3f %.1f",c,s);
System.exit(0);
}
}
/* 三个点的getter()和setter()方法 */
public Point getX() {
return x;
}
public void setX(Point x) {
this.x = x;
}
public Point getY() {
return y;
}
public void setY(Point y) {
this.y = y;
}
public Point getZ() {
return z;
}
public void setZ(Point z) {
this.z = z;
}
public Point getA() {
return a;
}
public void setA(Point z) {
this.z = a;
}
}
class PointInputError {
//判断从字符串中解析出的点的数量是否合格。
public static void wrongNumberOfPoints(ArrayList ps, int num) {
if (ps.size() != num) {
System.out.println("wrong number of points");
System.exit(0);
}
}
//判断输入的字符串中点的坐标部分格式是否合格。若不符合，报错并退出程序
public static void wrongPointFormat(String s) {
if (!s.matches("[+-]?([1-9]\\d*|0)(\\.\\d+)?,[+-]?([1-9]\\d*|0)(\\.\\d+)?")) {
System.out.println("Wrong Format");
System.exit(0);
}
}
// 输入字符串是否是"选项:字符串"格式，选项部分是否是1~5其中之一
public static void wrongChoice(String s) {
if (!s.matches("[1-5]:.+")) {
System.out.println("Wrong Format");
System.exit(0);
}
}
}
class ParseInput {
/*
* 输入：完整的输入字符串，包含选项和所有点的信息，格式：选项:x1,y1 x2,y2 .....xn,yn。选项只能是1-5
* 一个空InputData对象
* 处理：将输入字符串中的选项和点信息提取出来并设置到InputData对象中
* 输出：包含选项值和所有点的Point对象的InputData对象。
*/
public static void paseInput(String s, InputData d) {
PointInputError.wrongChoice(s);
d.setChoice(getChoice(s));
s = s.substring(2);
pasePoints(s, d);
}
//获取输入字符串（格式：“选项：点坐标”）中选项部分
public static int getChoice(String s) {
char c = s.charAt(0);
return c-48;
}
/*
* 输入：一个字符串，包含所有点的信息，格式：x1,y1 x2,y2 .....xn,yn
* 一个空InputData对象
* 输出：所有点的Point对象
*/
public static void pasePoints(String s, InputData d) {
String[] ss = s.split(" ");
if (ss.length == 0)
return;
for (int i = 0; i < ss.length; i++) {
d.addPoint(readPoint(ss[i]));
}
}
/*
* 输入：包含单个点信息的字符串，格式：x,y
* 输出：Point对象
*/
public static Point readPoint(String s) {
PointInputError.wrongPointFormat(s);
String[] ss = s.split(",");
double x = Double.parseDouble(ss[0]);
double y = Double.parseDouble(ss[1]);
// System.out.println("match");
return new Point(x, y);
}
}
View Code
（3）采坑心得:
需要判定四边形五边形的成立条件，也需要判断凹凸四边形的情况，可以使用叉乘法来判断。难点需要判断形成的是五边形四边形三边形，情况太多，分析过程容易遗漏，造成错误分类的。输入的点判断形成的两个图形是什么并且计算是否有重叠部分，计算出重叠部分的面积，坑比较多，情况都比较复杂，许多地方代码测试点也没有通过。类中和方法漏写和判断情况缺失，在图形类中容易出现这种情况。
（4）改进建议：
在类的设计上还可以进行改进，设计更加合适的方法和属性，使解决思路更清晰。对类和多态的理解还需要进一步学习。
（5）总结：
几次作业总体难度偏高，许多测试点没有通过。几次题目集，前前后后踩了很多坑，逐渐完善代码，仍不完美，有待改进。其中图形问题中少点会导致不输出，后面加上了有关变量解决了问题。个人感觉题目量有一些大，因为课程比较多，多科任务加起来有些重，希望题目量可以再进行一些精简化。对java的学习还需要更加深入，解决问题时还经常停留在面向过程的编程思想，要深入理解面向对象思想。
标签：ps,题目,get,double,博客,getX,getY,PTA,public From： https://www.cnblogs.com/rainfly-lyc/p/17031613.html