第二次博客作业
前言：
由之前的三角形到现在的四边形，五边形，后面又在java课程中学习了面向对象的三个基本特征中的封装、继承和多态。以及Exception的处理等等。然后便是期中考试，由于基础不牢固导致最后面一道题没有写完，如果再给一些时间的话应该可以完成。接下来对面向对象的三个基本特征给出我自己的理解以及对PTA和期中考试进行分析与总结。
封装：
对成员变量实行更准确的控制。
封装可以隐藏内部程序实现的细节。
良好的封装能够减少代码之间的耦合度。
外部成员无法修改已封装好的程序代码。
方便数据检查，有利于保护对象信息的完整性，同时也提高程序的安全性。
便于修改，体高代码的可维护性。
继承：
只支持单继承，即一个子类只允许有一个父类，但是可以实现多级继承，及子类拥有唯一的父类，而父类还可以再继承。
子类可以拥有父类的属性和方法。
子类可以拥有自己的属性和方法。
子类可以重写覆盖父类的方法。
多态：
消除类型之间的耦合关系，实现低耦合。
灵活性。
可扩充性。
可替换性。
7-2 点线形系列4-凸四边形的计算
题目： 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"。
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:
基本输出格式见每种选项的描述。
异常情况输出：
如果不符合基本格式，输出"Wrong Format"。
如果符合基本格式，但输入点的数量不符合要求，输出"wrong number of points"。
注意：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
选项1、2、3中，若四边形四个点中有重合点，输出"points coincide"。
选项4中，若前两个输入线的点重合，输出"points coincide"。
输入样例1:
选项1，点重合。例如：
1:-1,-1 -1,-1 1,2 1,-2
输出样例:
在这里给出相应的输出。例如：
points coincide
输入样例2:
不符合基本格式。例如：
1:-1,-1 1,2 -1,1 ++1,0
输出样例:
在这里给出相应的输出。例如：
Wrong Format
输入样例3:
选项1，输入点数量不对。例如：
1:-1,-1 -1,2
输出样例:
在这里给出相应的输出。例如：
wrong number of points
输入样例4:
选项1，正确输入判断。例如：
1:-1,-1 -1,1 1,2 1,-2
输出样例:
在这里给出相应的输出。例如：
true false
输入样例5:
选项2，输入点不构成四边形。例如：
2:10,10 1,1 0,0 1,20
输出样例:
在这里给出相应的输出。例如：
not a quadrilateral
输入样例6:
选项2，正方形。例如：
2:0,0 0,80 80,80 80,0
输出样例:
在这里给出相应的输出。例如：
true true true
输入样例7:
选项2。例如：
2:0,0 -10,80 0,160 -10,80
输出样例:
在这里给出相应的输出。例如：
not a quadrilateral
输入样例8:
选项3，凸四边形。例如：
3:-1,-1 -1,1 1,2 1,-2
输出样例:
在这里给出相应的输出。例如：
true 10.472 6.0
输入样例9:
选项3，。例如：
3:0,0 -10,100 0,99 10,100
输出样例:
在这里给出相应的输出。例如：
false 221.097 990.0
试题分析： 首先case1要求判断是否是四边形，判断是否是多边形其实都差不多，只要做到相邻边不平行（共线），第i条边与第i+2条边不线段相交即可，这两个条件只要用循环判断即可（利用取余）。判断平行四边形在四边形的基础上对是否两对边都平行即可。case2判断三种特殊的四边形，首先菱形最简单，只要是平行四边形且邻边相等即可，矩形可用线段垂直判断是否有邻边垂直确定。前两个写好了，正方形只要是菱形且是矩形就可以确定是正方形。case3判断四边形的凹凸性，我利用的是凸多边形的每一条边，其他的所有点都在同一侧的特性，通过循环判断点是否在边的同侧，若不则为凹四边形，反之为凸，此方法可以沿用到五边形，求四边形面积可以把四边形拆成三角形来求，注意凹凸不同即可，不多赘述。case4是直线和四边形的问题，主要要理清有两个交点的有多少种情况。首先需要对传进来的点去重去余，去重简单，去余就是循环对第i和第i+2个点构成的直线判断第i+1个点是否在之上，在则去除即可，然后若剩三个点就是三角形。求交点个数的办法就是拿四边形的每一条边（直线形式）先与线L求得一个交点，然后再去掉不在边（线段）和线L（线段）上的点与重复的点，所得的就是交点，0个交点和1个交点不多讨论，主要说2个交点的情况。其实就是C42，6种情况，2个交点，所以从4条边中任选两条边（无需考虑顶点情况，顶点其实也是在边上）一共6种情况。如落在1，2上，落在2，3上...知道落在哪条边上有什么用呢？其实就是确定直线和哪个顶点那组成三角形（或是四边形），由此可求得已知三角形（四边形）的面积，再用总四边形面积一减即可求得剩余部分面积。case6判断一个点是否在四边形内用面积法即可，同三角形。
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import static java.lang.Double.POSITIVE_INFINITY;
public class Main {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
String input = in.nextLine();
String s = input.substring(2);
//if(!check.CheckFormat()) return;
if (input.charAt(0) == '1' && input.charAt(1) == ':') {
Case1(s);
} else if (input.charAt(0) == '2' && input.charAt(1) == ':') {
Case2(s);
} else if (input.charAt(0) == '3' && input.charAt(1) == ':') {
Case3(s);
} else if (input.charAt(0) == '4' && input.charAt(1) == ':') {
Case4(s);
} else if (input.charAt(0) == '5' && input.charAt(1) == ':') {
Case5(s);
} else {
System.out.println("Wrong Format");
}
}
public static void Case1(String s) {//判断是不是四边形，平行四边形
Check check = new Check();
check.setInput(s);
if (!check.CheckFormat(4)) return;//判断格式
List<Points> PointsList = check.GetStingPointsList();
List<Points> pointsList = PointsList.subList(0, 4);
if (Check.IsRepeatPoints(pointsList)) {//有重复点
System.out.println("points coincide");
return;
}
Quadrilateral quadrilateral = new Quadrilateral(pointsList);
System.out.println(quadrilateral.IsQuadrilateral() + " " + quadrilateral.IsParallelogram());
}
public static void Case2(String s) {
Check check = new Check();
check.setInput(s);
if (!check.CheckFormat(4)) return;//判断格式
List<Points> PointsList = check.GetStingPointsList();
List<Points> pointsList = PointsList.subList(0, 4);
Quadrilateral quadrilateral = new Quadrilateral(pointsList);
if (!quadrilateral.IsQuadrilateral()) {//判断是否能构成四边形
System.out.println("not a quadrilateral");
return;
}
System.out.println(quadrilateral.IsDiamond() + " " + quadrilateral.IsRectangle() + " " + quadrilateral.IsSquare());
}
public static void Case3(String s) {
Check check = new Check();
check.setInput(s);
if (!check.CheckFormat(4)) return;//判断格式
List<Points> PointsList = check.GetStingPointsList();
List<Points> pointsList = PointsList.subList(0, 4);
Quadrilateral quadrilateral = new Quadrilateral(pointsList);
if (!quadrilateral.IsQuadrilateral()) {//判断是否能构成四边形
System.out.println("not a quadrilateral");
return;
}
System.out.println(quadrilateral.IsConvexQuadrilateral() + " " + Check.sswr(quadrilateral.getPerimeter(), 3) + " " + Check.sswr(quadrilateral.getArea(), 3));
}
public static void Case4(String s) {
Check check = new Check();
check.setInput(s);
if (!check.CheckFormat(6)) return;//判断格式
List<Points> PointsList = check.GetStingPointsList();
List<Points> pointsList = PointsList.subList(2, 6);
Line line = new Line(PointsList.get(0), PointsList.get(1));
pointsList = Check.DelRepeatPoints(pointsList);//去重复点
if (Quadrilateral.IsQuadrilateral(pointsList) != null) {
Quadrilateral quadrilateral = new Quadrilateral(pointsList);
//System.out.println(quadrilateral.getArea());
if (quadrilateral.IsLineCoincide(line)) {
System.out.println("The line is coincide with one of the lines");
return;
}
double area = quadrilateral.getArea();
//System.out.println(area);
quadrilateral.twoPointsOneQuadrilateral(line);
} else if (Triangle.IsTriangle(pointsList) != null) {
pointsList = Triangle.IsTriangle(pointsList);
Triangle triangle = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2));
if (triangle.IsLineCoincide(line)) {
System.out.println("The line is coincide with one of the lines");
return;
}
triangle.twoPointsOneTriangle(line);
} else {
System.out.println("not a quadrilateral or triangle");
}
}
public static void Case5(String s) {
Check check = new Check();
check.setInput(s);
if (!check.CheckFormat(5)) return;//判断格式
List<Points> PointsList = check.GetStingPointsList();
List<Points> pointsList = PointsList.subList(1, 5);
Points p = new Points(PointsList.get(0));
pointsList = Check.DelRepeatPoints(pointsList);
//System.out.println((Quadrilateral.IsQuadrilateral(pointsList)!=null));
if (Quadrilateral.IsQuadrilateral(pointsList) != null) {
pointsList = Quadrilateral.IsQuadrilateral(pointsList);
Quadrilateral quadrilateral = new Quadrilateral(pointsList);
quadrilateral.IsInQuadrilateral(p);
} else if (Triangle.IsTriangle(pointsList) != null) {
//for (Points po : pointsList){
// System.out.println(po.getX()+","+po.getY());
//}
pointsList = Triangle.IsTriangle(pointsList);
Triangle triangle = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2));
//System.out.println(triangle.getArea());
//System.out.println(triangle.getLab().getM().getX()+","+triangle.getLab().getM().getY()+" "+triangle.getLab().getN().getX()+","+triangle.getLab().getN().getY());
//System.out.println(triangle.getLac().getM().getX()+","+triangle.getLac().getM().getY()+" "+triangle.getLac().getN().getX()+","+triangle.getLac().getN().getY());
//System.out.println(triangle.getLbc().getM().getX()+","+triangle.getLbc().getM().getY()+" "+triangle.getLbc().getN().getX()+","+triangle.getLbc().getN().getY());
triangle.IsInTriangle(p);
} else {
System.out.println("not a quadrilateral or triangle");
}
}
}
class Check {
private String input;
public static boolean IsRepeatPoints(List<Points> pointsList) {
for (Points p : pointsList) {
for (Points points : pointsList) {
if (p.CheckPoints(points) && points != p) {
return true;
}
}
}
return false;
}
public static List<Points> DelRepeatPoints(List<Points> pointsList) {//去除重复顶点
List<Points> points = new ArrayList<>();
for (Points p1 : pointsList) {
boolean flag = true;
for (Points p2 : points) {
if (p1.CheckPoints(p2))
flag = false;
}
if (flag)
points.add(p1);
}
//for(Points p : points)
//System.out.println(p.getX()+","+p.getY());
return points;
}
public static double sswr(double s, int index) {
String str = String.valueOf(s);
String substring = str.substring(str.indexOf(".") + 1);
int str_len;
if (substring.length() > index) {
str_len = index;
} else {
str_len = substring.length();
}
String formats = "%." + str_len + "f";
String out = String.format(formats, s);
return Double.parseDouble(out);
}
public String getInput() {
return input;
}
public void setInput(String input) {
this.input = input;
}
public boolean CheckFormat(int index) {
boolean flag = true;
int cnt = 0;
String p[] = input.split(" ");
for (String x : p) {
String num[] = x.split(",");
if (num.length != 2) {
System.out.println("Wrong Format");
return false;
}
for (String y : num) {
if (!y.matches("^[+-]?(0|(0\\.\\d+)?|[1-9][0-9]*(\\.\\d+)?)$"))
flag = false;
}
cnt++;
}
//System.out.println(input);
if (!flag) {
System.out.println("Wrong Format");
return false;
}
if (cnt > index || cnt < index) {
System.out.println("wrong number of points");
return false;
}
return true;
}
public Points GetStingPoints(int index) {
Points a = new Points();
String p[] = input.split(" ");
String num[] = p[index].split(",");
a.setX(Double.valueOf(num[0]));
a.setY(Double.valueOf(num[1]));
return a;
}
public List GetStingPointsList() {
List<Points> pointsList = new ArrayList<>();
String[] p = input.split(" ");
for (int i = 0; i < p.length; i++) {
String[] num = p[i].split(",");
Points a = new Points(Double.valueOf(num[0]), Double.valueOf(num[1]));
pointsList.add(a);
}
return pointsList;
}
}
class Quadrilateral {
private List<Points> pointsList = new ArrayList<>();
private List<Line> lineList = new ArrayList<>();
public Quadrilateral() {
}
public Quadrilateral(List pointsList) {
this.pointsList = pointsList;
setPolygon();
}
public Quadrilateral(Points a, Points b, Points c, Points d) {
pointsList.add(a);
pointsList.add(b);
pointsList.add(c);
pointsList.add(c);
setPolygon();
}
public static List<Points> IsQuadrilateral(List<Points> pointsList) {//判断点是否能构成四边形
if (pointsList.size() < 4)//不足4个点
return null;
else if (pointsList.size() == 4) {//4个点情况
Quadrilateral quadrilateral = new Quadrilateral(pointsList);
if (quadrilateral.IsQuadrilateral()) {
return pointsList;
} else
return null;
}
return null;
}
public void setPolygon() {
for (int i = 0; i < pointsList.size(); i++) {
if (i == pointsList.size() - 1) {
Line line = new Line(pointsList.get(i), pointsList.get(0));
lineList.add(line);
} else {
Line line = new Line(pointsList.get(i), pointsList.get(i + 1));
lineList.add(line);
}
}
}
public List<Line> getLineList() {
return lineList;
}
public void setLineList(List<Line> lineList) {
this.lineList = lineList;
}
public List<Points> getPointsList() {
return pointsList;
}
public void setPointsList(List<Points> pointsList) {
this.pointsList = pointsList;
}
public double getPerimeter() {
double perimeter = 0;
for (Line l : lineList) {
perimeter += l.getLength();
}
return perimeter;
}
public double getArea() {
if (IsConvexQuadrilateral()) {
Triangle triangle1 = new Triangle(pointsList.get(0),pointsList.get(1),pointsList.get(2));
Triangle triangle2 = new Triangle(pointsList.get(0),pointsList.get(3),pointsList.get(2));
return triangle1.getArea()+triangle2.getArea();
}
else {
Line l1 = new Line(pointsList.get(0), pointsList.get(2));
if (l1.whichSide(pointsList.get(1)) != l1.whichSide(pointsList.get(3))) {
Triangle triangle1 = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2));
Triangle triangle2 = new Triangle(pointsList.get(0), pointsList.get(2), pointsList.get(3));
return triangle1.getArea() + triangle2.getArea();
} else {
Triangle triangle1 = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(3));
Triangle triangle2 = new Triangle(pointsList.get(1), pointsList.get(2), pointsList.get(3));
return triangle1.getArea() + triangle2.getArea();
}
}
}
public boolean IsQuadrilateral() {//判断是不是四边形
for (int i = 0; i < lineList.size(); i++) {//邻边不能平行
Line line1 = lineList.get(i);
if (i == lineList.size() - 1) {
Line line2 = lineList.get(0);
if (line1.IsParallel(line2))
return false;
} else {
Line line2 = lineList.get(i + 1);
if (line1.IsParallel(line2))
return false;
}
}
for (int i = 0; i < lineList.size() / 2; i++) {//对边（线段）不能相交
if (lineList.get(i).IsReallyCrossover(lineList.get(i + 2)))
return false;
}
return true;
}
public boolean IsParallelogram() {//判断是不是平行四边形
if (IsQuadrilateral() && lineList.get(0).IsParallel(lineList.get(2)) && lineList.get(1).IsParallel(lineList.get(3)))
return true;
else
return false;
}
public boolean IsDiamond() {//判断是否是菱形
if (IsParallelogram() && lineList.get(0).getLength() == lineList.get(1).getLength())//相邻边相等
return true;
return false;
}
public boolean IsRectangle() {//判断是否是矩形
if (IsParallelogram() && lineList.get(0).IsPerpendicular(lineList.get(1)))//相邻边垂直
return true;
return false;
}
public boolean IsSquare() {//判断是否是正方形
if (IsDiamond() && IsRectangle())//既是矩形又是菱形
return true;
return false;
}
public boolean IsConvexQuadrilateral() {//判断凹凸性
int flag = 0;
for (Line l : lineList) {
for (Points p : pointsList) {
if (l.getM().CheckPoints(p) || l.getN().CheckPoints(p))
continue;
if (flag == 0) {
flag = l.whichSide(p);
} else if (flag != l.whichSide(p))
return false;
}
}
return true;
}
public boolean IsLineCoincide(Line line) {//判断直线与四边形是否重合
for (Line l : lineList) {
if (line.IsCoincide(l))
return true;
}
return false;
}
public void IsInQuadrilateral(Points u) {//判断点与四边形的关系
double area = getArea();
double s = 0;
for (Points p : pointsList) {
if (p.CheckPoints(u)) {
System.out.println("on the quadrilateral");
return;
}
}
for (Line l : lineList) {
if (l.IsReallyCollinear(u) && l.IsCollinear(u)) {
System.out.println("on the quadrilateral");
return;
}
}
for (int i = 0; i < lineList.size(); i++) {
Triangle triangle = new Triangle(u, lineList.get(i).getM(), lineList.get(i).getN());
s += triangle.getArea();
}
if ( Math.abs(s - area)<0.0001 ) {
System.out.println("in the quadrilateral");
return;
}
System.out.println("outof the quadrilateral");
}
public void twoPointsOneQuadrilateral(Line line) {//直线与四边形相交问题
List<Points> list = new ArrayList<>();
Points u;
for (Line l : lineList) {
u = l.CrossoverPoint(line);
boolean flag = false;
if (u != null) {
for (Line line1 : lineList) {
if (line1.IsReallyCollinearInclude(u)) {
flag = true;
}
}
for (Points p : list) {
if (p.CheckPoints(u)) {
flag = false;
break;
}
}
if (flag) {
list.add(u);
}
}
}
if (list.size() != 2) {
System.out.println(list.size());
} else {
Points m = list.get(0);
Points n = list.get(1);
//System.out.println(m.getX()+","+m.getY()+" "+n.getX()+","+n.getY());
Line line1 = lineList.get(0);
Line line2 = lineList.get(1);
Line line3 = lineList.get(2);
Line line4 = lineList.get(3);
//System.out.println(line1.IsCollinear(m) && line3.IsCollinear(n));
Points k = null, v = null;
double s1 = 0, s2 = 0;
// System.out.println( );
//System.out.println((line4.IsCollinear(m) && line1.IsCollinear(n)));
if ((line1.IsCollinear(m) && line2.IsCollinear(n)) )
k = pointsList.get(1);
else if ((line2.IsCollinear(m) && line3.IsCollinear(n)) )
k = pointsList.get(2);
else if ((line3.IsCollinear(m) && line4.IsCollinear(n)) )
k = pointsList.get(3);
else if ((line1.IsCollinear(m) && line4.IsCollinear(n)) )
k = pointsList.get(0);
else if ((line1.IsCollinear(m) && line3.IsCollinear(n)) ) {
k = pointsList.get(0);
v = pointsList.get(3);
} else if ((line2.IsCollinear(m) && line4.IsCollinear(n)) ) {
k = pointsList.get(0);
v = pointsList.get(1);
}
if (v == null) {
Triangle triangle = new Triangle(m, n, k);
s1 = triangle.getArea();
} else {
Triangle triangle1 = new Triangle(k, v, m);
Triangle triangle2 = new Triangle(m, v, n);
s1 = triangle1.getArea() + triangle2.getArea();
}
double area = getArea();
s1 = Check.sswr(s1, 3);
area = Check.sswr(area, 3);
s2 = area - s1;
s2 = Check.sswr(s2, 3);
//System.out.println("s1 = " + s1 + " s2 = " + s2 + " area = " + area);
System.out.println("2 " + Math.min(s1, s2) + " " + Math.max(s1, s2));
}
}
}
class Triangle {
private Points a;
private Points b;
private Points c;
private Line lab;
private Line lbc;
private Line lac;
public Triangle() {
}
public Triangle(Points a, Points b, Points c) {
this.a = a;
this.b = b;
this.c = c;
Line l1 = new Line(a, b);
Line l2 = new Line(a, c);
Line l3 = new Line(b, c);
lab = l1;
lac = l2;
lbc = l3;
SetTriangle();
}
public static List<Points> IsTriangle(List<Points> pointsList) {//判断点是否能构成三角形
//pointsList = Check.DelRepeatPoints(pointsList);
if (pointsList.size() > 3) {//4个点情况，去除冗余
for (int i = 0; i < pointsList.size(); i++) {
Line l = new Line(pointsList.get(i), pointsList.get((i + 2) % pointsList.size()));
if (l.IsReallyCollinear(pointsList.get((i + 1) % pointsList.size()))) {
//System.out.println((i+1)%pointsList.size());
pointsList.remove((i+1)%pointsList.size());
break;
}
}
}
if (pointsList.size() == 3) {//去除重复有3个点情况
//System.out.println(pointsList.get(2).getX()+","+pointsList.get(2).getY());
Triangle triangle = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2));
if (triangle.IsTriangle())
return pointsList;
else
return null;
}
return null;
}
public Points getA() {
return a;
}
public void setA(Points a) {
this.a = a;
}
public Points getB() {
return b;
}
public void setB(Points b) {
this.b = b;
}
public Points getC() {
return c;
}
public void setC(Points c) {
this.c = c;
}
public Line getLac() {
return lac;
}
public void setLac(Line lac) {
this.lac = lac;
}
public Line getLbc() {
return lbc;
}
public void setLbc(Line lbc) {
this.lbc = lbc;
}
public Line getLab() {
return lab;
}
public void setLab(Line lab) {
this.lab = lab;
}
public void SetTriangle() {
lab.SetLine();
lbc.SetLine();
lac.SetLine();
}
/*public double getArea(){
double p = (getPerimeter()/ 2.0) ;
//System.out.println("p = " + p + " lab = "+lab.getLength()+ " lac = "+lac.getLength()+ " lbc = "+lbc.getLength());
return Math.sqrt( p * (p - lab.getLength()) * (p - lac.getLength()) * (p - lbc.getLength()) );
}*/
public double getPerimeter() {
return lab.getLength() + lbc.getLength() + lac.getLength();
}
public double getArea() {
return lac.distance(b) * lac.getLength() / 2.0;
}
/*
public double getArea(){
double cos = (lab.getLength() * lab.getLength() + lac.getLength() * lac.getLength() - lbc.getLength() * lbc.getLength()) / (2.0 * lac.getLength() * lab.getLength() );
return Math.sqrt(1 - Math.pow(cos, 2)) * lab.getLength() * lac.getLength() * 0.5;
}*/
public Points getCentrePoint() {
Points CentrePoint = new Points();
double x1 = (a.getX() + b.getX() + c.getX()) / 3;
double y1 = (a.getY() + b.getY() + c.getY()) / 3;
CentrePoint.setX(x1);
CentrePoint.setY(y1);
return CentrePoint;
}
public void whichTriangle() {
double l1 = -1, l2 = -1, l3 = -1;
l1 = Math.min(lab.getLength(), Math.min(lbc.getLength(), lac.getLength()));
l3 = Math.max(lab.getLength(), Math.max(lbc.getLength(), lac.getLength()));
if (lab.getLength() == lbc.getLength() || lac.getLength() == lbc.getLength() || lab.getLength() == lac.getLength())
l2 = l1;
else {
if (lab.getLength() != l1 && lab.getLength() != l3)
l2 = lab.getLength();
else if (lac.getLength() != l1 && lac.getLength() != l3)
l2 = lac.getLength();
else
l3 = lbc.getLength();
}
int type = -1;
if (Math.abs(l1 * l1 + l2 * l2 - l3 * l3) < 2)
type = 2;
else if (l1 * l1 + l2 * l2 > l3 * l3)
type = 3;
else
type = 1;
if (type == 1)
System.out.println("true false false");
else if (type == 2)
System.out.println("false true false");
else
System.out.println("false false true");
}
public boolean IsTriangle() {
if (lab.IsCollinear(c) || lac.IsCollinear(b) || lbc.IsCollinear(a)) {
return false;
}
if (lab.IsParallel(lac) || lab.IsParallel(lbc) || lbc.IsParallel(lac)) {
return false;
}
return true;
}
public void IsSPTriangle() {
SetTriangle();
if (lab.getLength() == lbc.getLength() || lac.getLength() == lbc.getLength() || lab.getLength() == lac.getLength()) {
System.out.print("true" + " ");
} else
System.out.print("false" + " ");
if (lab.getLength() == lbc.getLength() && lab.getLength() == lac.getLength()) {
System.out.println("true");
} else
System.out.println("false");
}
public boolean IsLineCoincide(Line line) {//判断直线与三角形是否重合
if (line.IsCoincide(lab) || line.IsCoincide(lac) || line.IsCoincide(lbc))
return true;
return false;
}
public void IsInTriangle(Points u) {
double s1, s2, s3, s = 0;
Triangle triangle1 = new Triangle(a, b, u);
Triangle triangle2 = new Triangle(a, c, u);
Triangle triangle3 = new Triangle(c, b, u);
s1 = triangle1.getArea();
//System.out.println(s1);
s2 = triangle2.getArea();
//System.out.println(s2);
s3 = triangle3.getArea();
//System.out.println(s3);
s = getArea();
//System.out.println(s);
if ((s1 + s2 + s3) - s > 0.01) {
System.out.println("outof the triangle");
return;
}
List<Points> pointsList = new ArrayList<>();
pointsList.add(a);
pointsList.add(b);
pointsList.add(c);
List<Line> lineList = new ArrayList<>();
lineList.add(lac);
lineList.add(lab);
lineList.add(lbc);
for (Points p : pointsList) {
if (p.CheckPoints(u)) {
System.out.println("on the triangle");
return;
}
}
for (Line l : lineList) {
if (l.IsReallyCollinear(u) && l.IsCollinear(u)) {
System.out.println("on the triangle");
return;
}
}
System.out.println("in the triangle");
}
public void twoPointsOneTriangle(Line line) {
List<Line> lineList = new ArrayList<>();
lineList.add(lac);
lineList.add(lab);
lineList.add(lbc);
List<Points> pointsList = new ArrayList<>();
pointsList.add(a);
pointsList.add(b);
pointsList.add(c);
List<Points> list = new ArrayList<>();
int cnt = 0;
Points u;
for (Line l : lineList) {
u = l.CrossoverPoint(line);
boolean flag = false;
if (u != null) {
for (Line line1 : lineList) {
if (line1.IsReallyCollinearInclude(u)) {
flag = true;
}
}
for (Points p : list) {
if (p.CheckPoints(u)) {
flag = false;
break;
}
}
if (flag) {
list.add(u);
cnt++;
}
}
}
if (cnt != 2) {
System.out.println(cnt);
} else {
double s1, s2, s;
System.out.print("2 ");
Points p1 = list.get(0), p2 = list.get(1);
Points m;
if (lac.IsCollinear(p1) && lab.IsCollinear(p2) || lac.IsCollinear(p2) && lab.IsCollinear(p1))
m = a;
else if (lac.IsCollinear(p1) && lbc.IsCollinear(p2) || lac.IsCollinear(p2) && lbc.IsCollinear(p1))
m = c;
else
m = b;
Triangle triangle1 = new Triangle(m, list.get(0), list.get(1));
s1 = triangle1.getArea();
s1 = Check.sswr(s1, 3);
s = this.getArea();
s = Check.sswr(s, 3);
s2 = s - s1;
s2 = Check.sswr(s2, 3);
System.out.println(Math.min(s1, s2) + " " + Math.max(s1, s2));
}
}
}
class Line {
private Points m;
private Points n;
private double k;
private double b;
private double A;
private double B2;
private double C;
private double length;
public Line() {
}
public Line(Points m, Points n) {
this.m = m;
this.n = n;
SetLine();
}
public void setLength() {
length = m.PointsDistance(n.getX(), n.getY());
}
public double getA() {
return A;
}
public void setA(double a) {
A = a;
}
public double getB2() {
return B2;
}
public void setB2(double b2) {
B2 = b2;
}
public double getC() {
return C;
}
public void setC(double c) {
C = c;
}
public double getB() {
return b;
}
public void setB(double b) {
this.b = b;
}
public double getK() {
return k;
}
public void setK(double k) {
this.k = k;
}
public Points getN() {
return n;
}
public void setN(Points n) {
this.n = n;
// System.out.println("n :"+this.n.getX()+" "+this.n.getY());
}
public Points getM() {
return m;
}
public void setM(Points m) {
this.m = m;
// System.out.println("m :"+this.m.getX()+" "+this.m.getY());
}
public double getLength() {
return length;
}
public boolean CheckLine() {
if (m.getX() == n.getX() && m.getY() == n.getY()) {
System.out.println("points coincide");
return false;
}
return true;
}
public double slope() {
if (m.getX() == n.getX())
return POSITIVE_INFINITY;
else
return (m.getY() - n.getY()) / (m.getX() - n.getX());
}
public void SetLine() {
setK(Check.sswr(slope(), 6));
setB(Check.sswr(m.getY() - m.getX() * getK(), 6));
setA(m.getY() - n.getY());
setB2(n.getX() - m.getX());
setC(m.getX() * n.getY() - n.getX() * m.getY());
setLength();
}
public double distance(Points a) {
return Math.abs(getA() * a.getX() + getB2() * a.getY() + getC()) / Math.sqrt(getA() * getA() + getB2() * getB2());
}
public Points CrossoverPoint(Line l) {
Points CroPoint = new Points();
if (!IsParallel(l)) {
double x1 = (getB2() * l.getC() - l.getB2() * getC()) / (getA() * l.getB2() - l.getA() * getB2());
double y1 = (l.getA() * getC() - getA() * l.getC()) / (getA() * l.getB2() - l.getA() * getB2());
//System.out.println( "crp "+CroPoint.getX()+","+CroPoint.getY() );
CroPoint.setX(x1);
CroPoint.setY(y1);
return CroPoint;
}
// else
return null;
}
public boolean IsCoincide(Line l) {//判断两直线是否重合
if (slope() == l.slope() && IsCollinear(l.getM()) && IsCollinear(l.getN()))
return true;
return false;
}
public boolean IsPerpendicular(Line l) {//判断直线是否垂直
if (slope() == POSITIVE_INFINITY && l.slope() == 0 || slope() == 0 && l.slope() == POSITIVE_INFINITY)//斜率不存在的情况
return true;
if (slope() * l.slope() == -1)//斜率相乘等于-1垂直
return true;
return false;
}
public boolean IsReallyCrossover(Line l) {//判断两线段是否相交
Points m = CrossoverPoint(l);
// System.out.println( (m!=null&&l.IsReallyCollinearInclude(m)));
if (m != null && l.IsReallyCollinearInclude(m) && IsReallyCollinearInclude(m))
return true;
return false;
}
public boolean IsCollinear(Points a) {//判断点是否在直线上
if (m.getX() == n.getX()) {
if (m.getX() == a.getX())
return true;
else
return false;
}
if (Math.abs(getA() * a.getX() + getB2() * a.getY() + getC()) < 0.01)
return true;
return false;
}
public boolean IsReallyCollinear(Points a) {
if(m.getX() == 0 && n.getX() == 0 && a.getX() == 0){
if(a.getY() > Math.min(m.getY(),n.getY() ) && a.getY() < Math.max(m.getY(),n.getY()))
return true;
else
return false;
}
else if(m.getY() == 0 && n.getY() == 0 && a.getY() == 0){
if(a.getX() > Math.min(m.getX(),n.getX() ) && a.getX() < Math.max(m.getX(),n.getX()))
return true;
else
return false;
}
else if (a.getX() > Math.min(m.getX(), n.getX()) && a.getX() < Math.max(m.getX(), n.getX()) && a.getY() > Math.min(m.getY(), n.getY()) && a.getY() < Math.max(m.getY(), n.getY()))
return true;
else
return false;
}
public boolean IsReallyCollinearInclude(Points a) {
if (a.getX() >= Math.min(m.getX(), n.getX()) && a.getX() <= Math.max(m.getX(), n.getX()) && a.getY() >= Math.min(m.getY(), n.getY()) && a.getY() <= Math.max(m.getY(), n.getY()))
return true;
else
return false;
}
public boolean IsParallel(Line l) {
if (this.slope() == l.slope()) {
return true;
} else
return false;
}
public int whichSide(Points p) {//判断点在直线哪一侧，返回0在直线上，小于0右侧，大于0左侧
if (getA() * p.getX() + getB2() * p.getY() + getC() == 0)
return 0;
else if (getA() * p.getX() + getB2() * p.getY() + getC() < 0)
return -1;
else
return 1;
}
}
class Points {
private double x;
private double y;
public Points() {
}
public Points(double x, double y) {
this.x = x;
this.y = y;
}
public Points(Points a) {
this.x = a.getX();
this.y = a.getY();
}
public double getX() {
return this.x;
}
public void setX(double x) {
this.x = x;
}
public double getY() {
return this.y;
}
public void setY(double y) {
this.y = y;
}
public boolean CheckPoints(Points p) {
if (Math.abs(getX() - p.getX()) < 0.001 && Math.abs(getY() - p.getY()) < 0.001) {
//System.out.println("points coincide");
return true;
} else
return false;
}
public double PointsDistance(double x, double y) {
return Math.sqrt(Math.pow((x - this.x), 2) + Math.pow((y - this.y), 2));
}
}
第五次作业
7-1and 7-2 点线形系列5-凸五边形的计算
第五次作业是两道题目，但实际是一道题拆成了两道，在此我放一起来说明。
题目： 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"。
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
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
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:
基本输出格式见每种选项的描述。
异常情况输出：
如果不符合基本格式，输出"Wrong Format"。
如果符合基本格式，但输入点的数量不符合要求，输出"wrong number of points"。
注意：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
输入样例1:
选项1，点重合。例如：
1:-1,-1 1,2 -1,1 1,0
输出样例:
在这里给出相应的输出。例如：
wrong number of points
输入样例:
在这里给出一组输入。例如：
4:0,0 6,0 7,1 8,3 6,6 0,0 6,0 7,1 8,3 6,6
输出样例:
在这里给出相应的输出。例如：
the previous pentagon coincides with the following pentagon
试题分析： case1，case2判断是否是五边形以及凹凸性，方法同四边形，不多赘述。case3同四边形也是直线与五边形问题（求交点个数同四，这里只讨论两个交点情况，其余个数交点输出结束即可）。首先传进来的五个点要去重去冗余，方法同四边形，若还剩五个点则有C52,10种情况，循环遍历即可（暴力写10个if,else也行），通过直线与五边形交点落在哪两点边上可以确定构成三角形（四边形）的顶点从而求得一个已知面积，再拿总面积减去已知面积即可。（构成四边形，三角形直接调用之前的四边形类的方法和三角形类的方法即可）case4判断两多边形关系主要以点判断为主，重合即双重循环判断是否有找不到的点，想离即判断是否有在多边形内的点（a对b判断一次，b对a判断一次，防止包含），包含判断是否有在外的点即可,被包含换一下调用顺序即可。连接的话稍复杂一点，需判断只能有一个或两个交点且其他点都在外部，以此法判断两次即可，至于交错直接else即可。csae5是求相交面积，我的方法是按顺序（第一个点，第一条边，第二个点...）对多边形求点是否在内部，边是否相交，将内部点和交点存起来，这就是相交的多边形的点集（有序），然后用多边形求面积即可（分割成若干个三角形）。case6仍然同之前一样，使用面积法判断是否在五边形内即可。
import java.util.ArrayList; import java.util.List; import java.util.Scanner; import static java.lang.Double.POSITIVE_INFINITY; public class Main { public static void main(String[] args) { Scanner in = new Scanner(System.in); String input = in.nextLine(); String s = input.substring(2); //if(!check.CheckFormat()) return; if (input.charAt(0) == '1' && input.charAt(1) == ':') { Case1(s); } else if (input.charAt(0) == '2' && input.charAt(1) == ':') { Case2(s); } else if (input.charAt(0) == '3' && input.charAt(1) == ':') { Case3(s); } else if (input.charAt(0) == '4' && input.charAt(1) == ':') { Case4(s); } else if (input.charAt(0) == '5' && input.charAt(1) == ':') { Case5(s); } else if(input.charAt(0) == '6' && input.charAt(1) == ':'){ Case6(s); } else { System.out.println("Wrong Format"); } } public static void Case1(String s) {//判断是不是五边形 Check check = new Check(); check.setInput(s); if (!check.CheckFormat(5)) return;//判断格式,5坐标 List<Points> PointsList = check.GetStingPointsList(); List<Points> pointsList = PointsList.subList(0, 5); /* if (Check.IsRepeatPoints(pointsList)) {//有重复点 System.out.println("points coincide"); return; }*/ Pentagon pentagon = new Pentagon(pointsList); if(Pentagon.IsPentagon(pointsList) == null){ System.out.println(false); return; } System.out.println(pentagon.IsPentagon()); //System.out.println(false); } public static void Case2(String s) { Check check = new Check(); check.setInput(s); if (!check.CheckFormat(5)) return;//判断格式 List<Points> PointsList = check.GetStingPointsList(); List<Points> pointsList = PointsList.subList(0, 5); Pentagon pentagon = new Pentagon(pointsList); if (!pentagon.IsPentagon()) {//判断是否能构成五边形 System.out.println("not a pentagon"); return; } System.out.print(pentagon.IsConvexPentagon()); if(pentagon.IsConvexPentagon()) System.out.println(" "+Check.sswr(pentagon.getPerimeter(),3)+" "+Check.sswr(pentagon.getArea(),3)); } public static void Case3(String s) { Check check = new Check(); check.setInput(s); if (!check.CheckFormat(7)) return;//判断格式 List<Points> PointsList = check.GetStingPointsList(); List<Points> pointsList = PointsList.subList(2, 7); Line line = new Line(PointsList.get(0),PointsList.get(1)); pointsList = Check.DelRepeatPoints(pointsList); //System.out.println((Quadrilateral.IsQuadrilateral(pointsList) != null)); Quadrilateral.IsQuadrilateral(pointsList); if(Pentagon.IsPentagon(pointsList) != null){ Pentagon pentagon = new Pentagon(pointsList); if(pentagon.IsLineCoincide(line)) { System.out.println("The line is coincide with one of the lines"); return; } pentagon.twoPointsOnePentagon(line); } else if (Quadrilateral.IsQuadrilateral(pointsList) != null) { Quadrilateral quadrilateral = new Quadrilateral(pointsList); //System.out.println(quadrilateral.getArea()); if (quadrilateral.IsLineCoincide(line)) { System.out.println("The line is coincide with one of the lines"); return; } quadrilateral.twoPointsOneQuadrilateral(line); } //System.out.println((Triangle.IsTriangle(pointsList) != null)); else if (Triangle.IsTriangle(pointsList) != null) { pointsList = Triangle.IsTriangle(pointsList); Triangle triangle = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2)); if (triangle.IsLineCoincide(line)) { System.out.println("The line is coincide with one of the lines"); return; } triangle.twoPointsOneTriangle(line); } else System.out.println("not a polygon"); } public static void Case4(String s) { Check check = new Check(); check.setInput(s); if (!check.CheckFormat(10)) return;//判断格式 List<Points> PointsList = check.GetStingPointsList(); Polygon.PolygonAndPolygon(PointsList); } public static void Case5(String s) { Check check = new Check(); check.setInput(s); if (!check.CheckFormat(10)) return;//判断格式 List<Points> PointsList = check.GetStingPointsList(); System.out.println(Check.sswr(Polygon.PolygonCrossPolygon(PointsList),3)); } public static void Case6(String s) { Check check = new Check(); check.setInput(s); if (!check.CheckFormat(6)) return;//判断格式 List<Points> PointsList = check.GetStingPointsList(); List<Points> pointsList = PointsList.subList(1, 6); Points u = PointsList.get(0); pointsList = Check.DelRepeatPoints(pointsList); //System.out.println((Quadrilateral.IsQuadrilateral(pointsList) != null)); Quadrilateral.IsQuadrilateral(pointsList); if(Pentagon.IsPentagon(pointsList) != null){ Pentagon pentagon = new Pentagon(pointsList); //pentagon.IsInPentagon(u); if(Polygon.IsInPolygon(u,pointsList)==0) System.out.println("on the pentagon"); else if(Polygon.IsInPolygon(u,pointsList)==-1) System.out.println("in the pentagon"); else System.out.println("outof the pentagon"); } else if (Quadrilateral.IsQuadrilateral(pointsList) != null) { Quadrilateral quadrilateral = new Quadrilateral(pointsList); //System.out.println(quadrilateral.getArea()); //quadrilateral.IsInQuadrilateral(u); if(Polygon.IsInPolygon(u,pointsList)==0) System.out.println("on the quadrilateral"); else if(Polygon.IsInPolygon(u,pointsList)==-1) System.out.println("in the quadrilateral"); else System.out.println("outof the quadrilateral"); } else if (Triangle.IsTriangle(pointsList) != null) { pointsList = Triangle.IsTriangle(pointsList); Triangle triangle = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2)); //triangle.IsInTriangle(u); if(Polygon.IsInPolygon(u,pointsList)==0) System.out.println("on the triangle"); else if(Polygon.IsInPolygon(u,pointsList)==-1) System.out.println("in the triangle"); else System.out.println("outof the triangle"); } else System.out.println("not a polygon"); } } class Check { private String input; public static boolean IsRepeatPoints(List<Points> pointsList) { for (Points p : pointsList) { for (Points points : pointsList) { if (p.CheckPoints(points) && points != p) { return true; } } } return false; } public static void showPoints(List<Points> pointsList){ for (Points p : pointsList) System.out.println(p.getX()+","+p.getY()); } public static List<Points> DelRepeatPoints(List<Points> pointsList) {//去除重复顶点 List<Points> points = new ArrayList<>(); for (Points p1 : pointsList) { boolean flag = true; for (Points p2 : points) { if (p1.CheckPoints(p2)) flag = false; } if (flag) points.add(p1); } //for(Points p : points) //System.out.println(p.getX()+","+p.getY()); return points; } public static List<Points> delRedundantPoints(List<Points> pointsList){ for (int i = 0; i < pointsList.size();) { Line l = new Line(pointsList.get(i), pointsList.get((i + 2) % pointsList.size())); if (l.IsCollinear(pointsList.get((i + 1) % pointsList.size()))) { pointsList.remove( (i+1)%pointsList.size() ); i = 0; } else i++; } //Check.showPoints(pointsList); return pointsList; } public static double sswr(double s, int index) { String str = String.valueOf(s); String substring = str.substring(str.indexOf(".") + 1); int str_len; if (substring.length() > index) { str_len = index; } else { str_len = substring.length(); } String formats = "%." + str_len + "f"; String out = String.format(formats, s); return Double.parseDouble(out); } public String getInput() { return input; } public void setInput(String input) { this.input = input; } public boolean CheckFormat(int index) { boolean flag = true; int cnt = 0; String p[] = input.split(" "); for (String x : p) { String num[] = x.split(","); if (num.length != 2) { System.out.println("Wrong Format"); return false; } for (String y : num) { if (!y.matches("^[+-]?(0|(0\\.\\d+)?|[1-9][0-9]*(\\.\\d+)?)$")) flag = false; } cnt++; } //System.out.println(input); if (!flag) { System.out.println("Wrong Format"); return false; } if (cnt > index || cnt < index) { System.out.println("wrong number of points"); return false; } return true; } public Points GetStingPoints(int index) { Points a = new Points(); String p[] = input.split(" "); String num[] = p[index].split(","); a.setX(Double.valueOf(num[0])); a.setY(Double.valueOf(num[1])); return a; } public List GetStingPointsList() { List<Points> pointsList = new ArrayList<>(); String[] p = input.split(" "); for (int i = 0; i < p.length; i++) { String[] num = p[i].split(","); Points a = new Points(Double.valueOf(num[0]), Double.valueOf(num[1])); pointsList.add(a); } return pointsList; } } class Polygon { public static List<Line> getLineList(List<Points> pointsList){ List<Line> lineList = new ArrayList<>(); //System.out.println(pointsList.size()); for(int i = 0 ; i < pointsList.size() ; i++){ Line line = new Line(pointsList.get(i),pointsList.get((i+1)%pointsList.size())); lineList.add(line); } return lineList; } public static int IsInPolygon(Points u,List<Points> pointsList) {//判断点与多边形的关系 List<Line> lineList = getLineList(pointsList); double s = 0; for (Points p : pointsList) { if (p.CheckPoints(u)) {return 0;}} for (Line l : lineList) { if (l.IsReallyCollinear(u) && l.IsCollinear(u)) {return 0;}} for (int i = 0; i < lineList.size(); i++) { Triangle triangle = new Triangle(u, lineList.get(i).getM(), lineList.get(i).getN()); s += triangle.getArea();} if(pointsList.size() == 3){ Triangle polygon = new Triangle(pointsList.get(0),pointsList.get(1),pointsList.get(2)); double area = polygon.getArea(); if ( Math.abs(s - area)<0.0001 ) return -1; } else if(pointsList.size() == 4){ Quadrilateral polygon = new Quadrilateral(pointsList); double area = polygon.getArea(); if ( Math.abs(s - area)<0.0001 ) return -1; } else { Pentagon polygon = new Pentagon(pointsList); double area = polygon.getArea(); if ( Math.abs(s - area)<0.0001 ) return -1; } return 1; } public static void PolygonAndPolygon(List<Points> pointsList){ List<Points> pointsList1 = pointsList.subList(0, 5); List<Points> pointsList2 = pointsList.subList(5, 10); //System.out.println("p1");Check.showPoints(pointsList1); //System.out.println("p2");Check.showPoints(pointsList2); pointsList1 = Check.DelRepeatPoints(pointsList1); pointsList2 = Check.DelRepeatPoints(pointsList2); pointsList1 = Check.delRedundantPoints(pointsList1); pointsList2 = Check.delRedundantPoints(pointsList2); String[] polygonName = {"triangle","quadrilateral","pentagon"}; //double crossArea = PolygonCrossPolygon(pointsList); //double s1 = getPolygonArea(pointsList1); //double s2 = getPolygonArea(pointsList2); if(IsSeparate(pointsList1,pointsList2))//分离 //if(crossArea == 0) System.out.println("no overlapping area between the previous "+polygonName[getPolygonNameNum(pointsList1.size())]+" and the following "+polygonName[getPolygonNameNum(pointsList2.size())]); else if(IsCompleteCoincidence(pointsList1,pointsList2) )//重合 System.out.println("the previous "+polygonName[getPolygonNameNum(pointsList1.size())]+" coincides with the following "+polygonName[getPolygonNameNum(pointsList2.size())]); else if(IsInclude(pointsList1,pointsList2))//包含 System.out.println("the previous "+polygonName[getPolygonNameNum(pointsList1.size())]+" contains the following "+polygonName[getPolygonNameNum(pointsList2.size())]); else if(IsInclude(pointsList2,pointsList1))//被包含 System.out.println("the previous "+polygonName[getPolygonNameNum(pointsList1.size())]+" is inside the following "+polygonName[getPolygonNameNum(pointsList2.size())]); else if(IsConnect(pointsList1,pointsList2) || IsConnect(pointsList2,pointsList1) )//连接 System.out.println("the previous "+polygonName[getPolygonNameNum(pointsList1.size())]+" is connected to the following "+polygonName[getPolygonNameNum(pointsList2.size())]); else //交错 System.out.println("the previous "+polygonName[getPolygonNameNum(pointsList1.size())]+" is interlaced with the following "+polygonName[getPolygonNameNum(pointsList2.size())]); //System.out.println("the previous "+polygonName[getPolygonNameNum(pointsList1.size())]+" is interlaced with the following "+polygonName[getPolygonNameNum(pointsList2.size())]); } public static double getPolygonArea(List<Points> pointsList){ double s = 0; List<Line> lineList = getLineList(pointsList); for(int i = 1 ; i < lineList.size() - 1 ; i++){ Triangle triangle = new Triangle(pointsList.get(0),pointsList.get(i),pointsList.get(i+1)); s += triangle.getArea(); } return s; } public static Points IsLineCrossPolygon(Line l,List<Points> pointsList){ List<Line> lineList = getLineList(pointsList); for(Line line : lineList){ if(l.IsReallyCrossoverReturnPoint(line) != null) return l.IsReallyCrossoverReturnPoint(line); } return null; } public static double PolygonCrossPolygon(List<Points> pointsList){ List<Points> pointsList1 = pointsList.subList(0, 5); List<Points> pointsList2 = pointsList.subList(5, 10); List<Points> list = new ArrayList<>(); pointsList1 = Check.DelRepeatPoints(pointsList1); pointsList2 = Check.DelRepeatPoints(pointsList2); pointsList1 = Check.delRedundantPoints(pointsList1); pointsList2 = Check.delRedundantPoints(pointsList2); List<Line> lineList1 = new ArrayList<>(); List<Line> lineList2 = new ArrayList<>(); for (int i = 0 ; i < pointsList1.size(); i++ ){ if(Polygon.IsInPolygon(pointsList1.get(i),pointsList2) == -1){ list.add(pointsList1.get(i)); } Line l = new Line( pointsList1.get(i),pointsList1.get( (i+1) % pointsList1.size()) ); if(IsLineCrossPolygon(l,pointsList2) != null){ list.add(IsLineCrossPolygon(l,pointsList2)); } } for (int i = 0 ; i < pointsList2.size(); i++ ){ if(Polygon.IsInPolygon(pointsList2.get(i),pointsList1) == -1){ list.add(pointsList2.get(i)); } Line l = new Line( pointsList2.get(i),pointsList2.get( (i+1) % pointsList2.size()) ); if(IsLineCrossPolygon(l,pointsList1) != null){ list.add(IsLineCrossPolygon(l,pointsList1)); } } list = Check.DelRepeatPoints(list);list = Check.DelRepeatPoints(list); return getPolygonArea(list); } public static boolean IsSeparate(List<Points> pointsList1,List<Points> pointsList2){//判断是否分离 for (Points p : pointsList1){ if(IsInPolygon(p,pointsList2)!=1) return false; } for (Points p : pointsList2){ if(IsInPolygon(p,pointsList1)!=1) return false; } return true; } public static boolean IsCompleteCoincidence(List<Points> pointsList1,List<Points> pointsList2){//判断是否完全重合 if(pointsList1.size() != pointsList2.size()) return false; for (Points p : pointsList1){ boolean flag = false; for (Points u : pointsList2){ if(p.CheckPoints(u)){ flag = true; break; } } if(!flag) return false; } return true; } public static boolean IsInclude(List<Points> pointsList1,List<Points> pointsList2) {//判断是否包含 for(Points u : pointsList2){ if(IsInPolygon(u,pointsList1) == 1) return false; } return true; } public static boolean IsConnect(List<Points> pointsList1,List<Points> pointsList2) {//判断是否连接，需调用两次 int cntIn = 0, cntOn = 0, cntOut = 0; for (Points u : pointsList1){ if(IsInPolygon(u,pointsList2)==-1) return false; else if(IsInPolygon(u,pointsList1) == 0) cntOn++; } if(cntOn == 1 || cntOn == 2) return true; return false; } public static int getPolygonNameNum(int size){ if(size == 3) return 0; else if(size == 4) return 1; else return 2; } } class Pentagon { private List<Points> pointsList = new ArrayList<>(); //线集 private List<Line> lineList = new ArrayList<>(); public void setPointsList(List<Points> pointsList) { this.pointsList = pointsList; } public void setLineList(List<Line> lineList) { this.lineList = lineList; } public List<Points> getPointsList() { return pointsList; } public List<Line> getLineList() { return lineList; } public Pentagon(List<Points> pointsList){ this.pointsList = pointsList; setPentagon(); } public void setPentagon(){ for(int i = 0 ; i < pointsList.size() ; i++){ Line line = new Line(pointsList.get(i),pointsList.get((i+1)%pointsList.size())); lineList.add(line); } } public double getPerimeter() {//求周长 double perimeter = 0; for (Line l : lineList) { perimeter += l.getLength(); } return perimeter; } public boolean IsPentagon() {//判断是不是五边形 for (int i = 0; i < lineList.size(); i++) {//邻边不能平行 Line line1 = lineList.get(i); if (i == lineList.size() - 1) { Line line2 = lineList.get(0); if (line1.IsParallel(line2)) return false; } else { Line line2 = lineList.get(i + 1); if (line1.IsParallel(line2)) return false; } } for (int i = 0; i < lineList.size() ; i++) {//对边（线段）不能相交 if (lineList.get(i).IsReallyCrossover(lineList.get((i + 2)%lineList.size()))) return false; } return true; } public static List<Points> IsPentagon(List<Points> pointsList) {//判断点是否能构成五边形 if (pointsList.size() < 5)//不足5个点 return null; else if (pointsList.size() == 5) {//5个点情况 Pentagon pentagon = new Pentagon(pointsList); //System.out.println(pentagon.IsPentagon()+"1"); if (pentagon.IsPentagon()) { return pointsList; } else return null; } return null; } public boolean IsConvexPentagon() {//判断凹凸性 int flag = 0; for (Line l : lineList) { for (Points p : pointsList) { if (l.getM().CheckPoints(p) || l.getN().CheckPoints(p)) continue; if (flag == 0) { flag = l.whichSide(p); } else if (flag != l.whichSide(p)) return false; } } return true; } public double getArea() {//求面积 double s = 0; if (IsPentagon()) {//凸 for(int i = 1 ; i < lineList.size() - 1 ; i++){ Triangle triangle = new Triangle(pointsList.get(0),pointsList.get(i),pointsList.get(i+1)); //System.out.println(triangle.getArea()); s += triangle.getArea(); } } return s; } public boolean IsLineCoincide(Line line) {//判断直线与五边形是否重合 for (Line l : lineList) { if (line.IsCoincide(l)) return true; } return false; } public void IsInPentagon(Points u) {//判断点与五边形的关系 double area = getArea(); double s = 0; for (Points p : pointsList) { if (p.CheckPoints(u)) { System.out.println("on the pentagon"); return; } } for (Line l : lineList) { if (l.IsReallyCollinear(u) && l.IsCollinear(u)) { System.out.println("on the pentagon"); return; } } for (int i = 0; i < lineList.size(); i++) { Triangle triangle = new Triangle(u, lineList.get(i).getM(), lineList.get(i).getN()); s += triangle.getArea(); } if ( Math.abs(s - area)<0.0001 ) { System.out.println("in the pentagon"); return; } System.out.println("outof the pentagon"); } public void twoPointsOnePentagon(Line line) {//直线与五边形相交问题 List<Points> list = new ArrayList<>(); Points u; for (Line l : lineList) { u = l.CrossoverPoint(line); boolean flag = false; if (u != null) { for (Line line1 : lineList) { if (line1.IsReallyCollinearInclude(u)) { flag = true; } } for (Points p : list) { if (p.CheckPoints(u)) { flag = false; break; } } if (flag) { list.add(u); } } } if (list.size() != 2) { System.out.println(list.size()); } else { Points m = list.get(0); Points n = list.get(1); //System.out.println(m.getX()+","+m.getY()); //System.out.println(n.getX()+","+n.getY()); Points k = null, v = null; for(int i = 0 ; i < lineList.size() ; i++){ if(lineList.get(Math.min(i,(i+1)%lineList.size())).IsCollinear(m) && lineList.get(Math.max(i,(i+1)%lineList.size())).IsCollinear(n) ) k = pointsList.get((i+1)%lineList.size()); } for(int i = 0 ; i < lineList.size() ; i++){ if(k==null && lineList.get(Math.min(i,(i+2)%lineList.size())).IsCollinear(m) && lineList.get(Math.max(i,(i+2)%lineList.size())).IsCollinear(n) ){ k = pointsList.get((i+1)%lineList.size()); v = pointsList.get((i+2)%lineList.size()); } } //System.out.println(k.getX()+","+k.getY()); //System.out.println(v.getX()+","+v.getY()); double s1 = 0,s2 = 0,area = Check.sswr(getArea(),3); if(v == null){ Triangle triangle = new Triangle(k,m,n); s1 = Check.sswr(triangle.getArea(),3); } else { Triangle triangle1 = new Triangle(k, v, m); Triangle triangle2 = new Triangle(m, v, n); s1 = triangle1.getArea() + triangle2.getArea(); } s2 = Check.sswr(area - s1 , 3); System.out.println("2 " + Math.min(s1, s2) + " " + Math.max(s1, s2)); } } } class Quadrilateral { private List<Points> pointsList = new ArrayList<>(); private List<Line> lineList = new ArrayList<>(); public Quadrilateral() { } public Quadrilateral(List pointsList) { this.pointsList = pointsList; setQuadrilateral(); } public Quadrilateral(Points a, Points b, Points c, Points d) { pointsList.add(a); pointsList.add(b); pointsList.add(c); pointsList.add(c); setQuadrilateral(); } public static List<Points> IsQuadrilateral(List<Points> pointsList) {//判断点是否能构成四边形 if (pointsList.size() > 4) {//5个点情况，去除冗余 for (int i = 0; i < pointsList.size(); i++) { Line l = new Line(pointsList.get(i), pointsList.get((i + 2) % pointsList.size())); if (l.IsCollinear(pointsList.get((i + 1) % pointsList.size()))) { pointsList.remove((i+1)%pointsList.size()); i = 0; } } //Check.showPoints(pointsList); } else if (pointsList.size() < 4)//不足4个点 return null; else if (pointsList.size() == 4) {//4个点情况 Quadrilateral quadrilateral = new Quadrilateral(pointsList); if (quadrilateral.IsQuadrilateral()) { return pointsList; } else return null; } return null; } public void setQuadrilateral() { for (int i = 0; i < pointsList.size(); i++) { if (i == pointsList.size() - 1) { Line line = new Line(pointsList.get(i), pointsList.get(0)); lineList.add(line); } else { Line line = new Line(pointsList.get(i), pointsList.get(i + 1)); lineList.add(line); } } } public List<Line> getLineList() { return lineList; } public void setLineList(List<Line> lineList) { this.lineList = lineList; } public List<Points> getPointsList() { return pointsList; } public void setPointsList(List<Points> pointsList) { this.pointsList = pointsList; } public double getPerimeter() { double perimeter = 0; for (Line l : lineList) { perimeter += l.getLength(); } return perimeter; } public double getArea() { if (IsConvexQuadrilateral()) { Triangle triangle1 = new Triangle(pointsList.get(0),pointsList.get(1),pointsList.get(2)); Triangle triangle2 = new Triangle(pointsList.get(0),pointsList.get(3),pointsList.get(2)); return triangle1.getArea()+triangle2.getArea(); } else { Line l1 = new Line(pointsList.get(0), pointsList.get(2)); if (l1.whichSide(pointsList.get(1)) != l1.whichSide(pointsList.get(3))) { Triangle triangle1 = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2)); Triangle triangle2 = new Triangle(pointsList.get(0), pointsList.get(2), pointsList.get(3)); return triangle1.getArea() + triangle2.getArea(); } else { Triangle triangle1 = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(3)); Triangle triangle2 = new Triangle(pointsList.get(1), pointsList.get(2), pointsList.get(3)); return triangle1.getArea() + triangle2.getArea(); } } } public boolean IsQuadrilateral() {//判断是不是四边形 for (int i = 0; i < lineList.size(); i++) {//邻边不能平行 Line line1 = lineList.get(i); if (i == lineList.size() - 1) { Line line2 = lineList.get(0); if (line1.IsParallel(line2)) return false; } else { Line line2 = lineList.get(i + 1); if (line1.IsParallel(line2)) return false; } } for (int i = 0; i < lineList.size() / 2; i++) {//对边（线段）不能相交 if (lineList.get(i).IsReallyCrossover(lineList.get(i + 2))) return false; } return true; } public boolean IsParallelogram() {//判断是不是平行四边形 if (IsQuadrilateral() && lineList.get(0).IsParallel(lineList.get(2)) && lineList.get(1).IsParallel(lineList.get(3))) return true; else return false; } public boolean IsDiamond() {//判断是否是菱形 if (IsParallelogram() && lineList.get(0).getLength() == lineList.get(1).getLength())//相邻边相等 return true; return false; } public boolean IsRectangle() {//判断是否是矩形 if (IsParallelogram() && lineList.get(0).IsPerpendicular(lineList.get(1)))//相邻边垂直 return true; return false; } public boolean IsSquare() {//判断是否是正方形 if (IsDiamond() && IsRectangle())//既是矩形又是菱形 return true; return false; } public boolean IsConvexQuadrilateral() {//判断凹凸性 int flag = 0; for (Line l : lineList) { for (Points p : pointsList) { if (l.getM().CheckPoints(p) || l.getN().CheckPoints(p)) continue; if (flag == 0) { flag = l.whichSide(p); } else if (flag != l.whichSide(p)) return false; } } return true; } public boolean IsLineCoincide(Line line) {//判断直线与四边形是否重合 for (Line l : lineList) { if (line.IsCoincide(l)) return true; } return false; } public void IsInQuadrilateral(Points u) {//判断点与四边形的关系 double area = getArea(); double s = 0; for (Points p : pointsList) { if (p.CheckPoints(u)) { System.out.println("on the quadrilateral"); return; } } for (Line l : lineList) { if (l.IsReallyCollinear(u) && l.IsCollinear(u)) { System.out.println("on the quadrilateral"); return; } } for (int i = 0; i < lineList.size(); i++) { Triangle triangle = new Triangle(u, lineList.get(i).getM(), lineList.get(i).getN()); s += triangle.getArea(); } if ( Math.abs(s - area)<0.0001 ) { System.out.println("in the quadrilateral"); return; } System.out.println("outof the quadrilateral"); } public void twoPointsOneQuadrilateral(Line line) {//直线与四边形相交问题 List<Points> list = new ArrayList<>(); Points u; for (Line l : lineList) { u = l.CrossoverPoint(line); boolean flag = false; if (u != null) { for (Line line1 : lineList) { if (line1.IsReallyCollinearInclude(u)) { flag = true; } } for (Points p : list) { if (p.CheckPoints(u)) { flag = false; break; } } if (flag) { list.add(u); } } } if (list.size() != 2) { System.out.println(list.size()); } else { Points m = list.get(0); Points n = list.get(1); //System.out.println(m.getX()+","+m.getY()+" "+n.getX()+","+n.getY()); Line line1 = lineList.get(0); Line line2 = lineList.get(1); Line line3 = lineList.get(2); Line line4 = lineList.get(3); //System.out.println(line1.IsCollinear(m) && line3.IsCollinear(n)); Points k = null, v = null; double s1 = 0, s2 = 0; // System.out.println( ); //System.out.println((line4.IsCollinear(m) && line1.IsCollinear(n))); if ((line1.IsCollinear(m) && line2.IsCollinear(n)) ) k = pointsList.get(1); else if ((line2.IsCollinear(m) && line3.IsCollinear(n)) ) k = pointsList.get(2); else if ((line3.IsCollinear(m) && line4.IsCollinear(n)) ) k = pointsList.get(3); else if ((line1.IsCollinear(m) && line4.IsCollinear(n)) ) k = pointsList.get(0); else if ((line1.IsCollinear(m) && line3.IsCollinear(n)) ) { k = pointsList.get(0); v = pointsList.get(3); } else if ((line2.IsCollinear(m) && line4.IsCollinear(n)) ) { k = pointsList.get(0); v = pointsList.get(1); } if (v == null) { Triangle triangle = new Triangle(m, n, k); s1 = triangle.getArea(); } else { Triangle triangle1 = new Triangle(k, v, m); Triangle triangle2 = new Triangle(m, v, n); s1 = triangle1.getArea() + triangle2.getArea(); } double area = getArea(); s1 = Check.sswr(s1, 3); area = Check.sswr(area, 3); s2 = area - s1; s2 = Check.sswr(s2, 3); //System.out.println("s1 = " + s1 + " s2 = " + s2 + " area = " + area); System.out.println("2 " + Math.min(s1, s2) + " " + Math.max(s1, s2)); } } } class Triangle { private Points a; private Points b; private Points c; private Line lab; private Line lbc; private Line lac; public Triangle() { } public Triangle(Points a, Points b, Points c) { this.a = a; this.b = b; this.c = c; Line l1 = new Line(a, b); Line l2 = new Line(a, c); Line l3 = new Line(b, c); lab = l1; lac = l2; lbc = l3; SetTriangle(); } public static List<Points> IsTriangle(List<Points> pointsList) {//判断点是否能构成三角形 //pointsList = Check.DelRepeatPoints(pointsList); if (pointsList.size() > 3) {//4个点情况，去除冗余 for (int i = 0; i < pointsList.size(); i++) { Line l = new Line(pointsList.get(i), pointsList.get((i + 2) % pointsList.size())); if (l.IsCollinear(pointsList.get((i + 1) % pointsList.size()))) { //System.out.println((i+1)%pointsList.size()); pointsList.remove((i+1)%pointsList.size()); i = 0; } } } if (pointsList.size() == 3) {//去除重复有3个点情况 //System.out.println(pointsList.get(2).getX()+","+pointsList.get(2).getY()); Triangle triangle = new Triangle(pointsList.get(0), pointsList.get(1), pointsList.get(2)); if (triangle.IsTriangle()) return pointsList; else return null; } return null; } public Points getA() { return a; } public void setA(Points a) { this.a = a; } public Points getB() { return b; } public void setB(Points b) { this.b = b; } public Points getC() { return c; } public void setC(Points c) { this.c = c; } public Line getLac() { return lac; } public void setLac(Line lac) { this.lac = lac; } public Line getLbc() { return lbc; } public void setLbc(Line lbc) { this.lbc = lbc; } public Line getLab() { return lab; } public void setLab(Line lab) { this.lab = lab; } public void SetTriangle() { lab.SetLine(); lbc.SetLine(); lac.SetLine(); } /*public double getArea(){ double p = (getPerimeter()/ 2.0) ; //System.out.println("p = " + p + " lab = "+lab.getLength()+ " lac = "+lac.getLength()+ " lbc = "+lbc.getLength()); return Math.sqrt( p * (p - lab.getLength()) * (p - lac.getLength()) * (p - lbc.getLength()) ); }*/ public double getPerimeter() { return lab.getLength() + lbc.getLength() + lac.getLength(); } public double getArea() { return lac.distance(b) * lac.getLength() / 2.0; } /* public double getArea(){ double cos = (lab.getLength() * lab.getLength() + lac.getLength() * lac.getLength() - lbc.getLength() * lbc.getLength()) / (2.0 * lac.getLength() * lab.getLength() ); return Math.sqrt(1 - Math.pow(cos, 2)) * lab.getLength() * lac.getLength() * 0.5; }*/ public Points getCentrePoint() { Points CentrePoint = new Points(); double x1 = (a.getX() + b.getX() + c.getX()) / 3; double y1 = (a.getY() + b.getY() + c.getY()) / 3; CentrePoint.setX(x1); CentrePoint.setY(y1); return CentrePoint; } public void whichTriangle() { double l1 = -1, l2 = -1, l3 = -1; l1 = Math.min(lab.getLength(), Math.min(lbc.getLength(), lac.getLength())); l3 = Math.max(lab.getLength(), Math.max(lbc.getLength(), lac.getLength())); if (lab.getLength() == lbc.getLength() || lac.getLength() == lbc.getLength() || lab.getLength() == lac.getLength()) l2 = l1; else { if (lab.getLength() != l1 && lab.getLength() != l3) l2 = lab.getLength(); else if (lac.getLength() != l1 && lac.getLength() != l3) l2 = lac.getLength(); else l3 = lbc.getLength(); } int type = -1; if (Math.abs(l1 * l1 + l2 * l2 - l3 * l3) < 2) type = 2; else if (l1 * l1 + l2 * l2 > l3 * l3) type = 3; else type = 1; if (type == 1) System.out.println("true false false"); else if (type == 2) System.out.println("false true false"); else System.out.println("false false true"); } public boolean IsTriangle() { if (lab.IsCollinear(c) || lac.IsCollinear(b) || lbc.IsCollinear(a)) { return false; } if (lab.IsParallel(lac) || lab.IsParallel(lbc) || lbc.IsParallel(lac)) { return false; } return true; } public void IsSPTriangle() { SetTriangle(); if (lab.getLength() == lbc.getLength() || lac.getLength() == lbc.getLength() || lab.getLength() == lac.getLength()) { System.out.print("true" + " "); } else System.out.print("false" + " "); if (lab.getLength() == lbc.getLength() && lab.getLength() == lac.getLength()) { System.out.println("true"); } else System.out.println("false"); } public boolean IsLineCoincide(Line line) {//判断直线与三角形是否重合 if (line.IsCoincide(lab) || line.IsCoincide(lac) || line.IsCoincide(lbc)) return true; return false; } public void IsInTriangle(Points u) { double s1, s2, s3, s = 0; Triangle triangle1 = new Triangle(a, b, u); Triangle triangle2 = new Triangle(a, c, u); Triangle triangle3 = new Triangle(c, b, u); s1 = triangle1.getArea(); //System.out.println(s1); s2 = triangle2.getArea(); //System.out.println(s2); s3 = triangle3.getArea(); //System.out.println(s3); s = getArea(); //System.out.println(s); if ((s1 + s2 + s3) - s > 0.01) { System.out.println("outof the triangle"); return; } List<Points> pointsList = new ArrayList<>(); pointsList.add(a); pointsList.add(b); pointsList.add(c); List<Line> lineList = new ArrayList<>(); lineList.add(lac); lineList.add(lab); lineList.add(lbc); for (Points p : pointsList) { if (p.CheckPoints(u)) { System.out.println("on the triangle"); return; } } for (Line l : lineList) { if (l.IsReallyCollinear(u) && l.IsCollinear(u)) { System.out.println("on the triangle"); return; } } System.out.println("in the triangle"); } public void twoPointsOneTriangle(Line line) { List<Line> lineList = new ArrayList<>(); lineList.add(lac); lineList.add(lab); lineList.add(lbc); List<Points> pointsList = new ArrayList<>(); pointsList.add(a); pointsList.add(b); pointsList.add(c); List<Points> list = new ArrayList<>(); int cnt = 0; Points u; for (Line l : lineList) { u = l.CrossoverPoint(line); boolean flag = false; if (u != null) { for (Line line1 : lineList) { if (line1.IsReallyCollinearInclude(u)) { flag = true; } } for (Points p : list) { if (p.CheckPoints(u)) { flag = false; break; } } if (flag) { list.add(u); cnt++; } } } if (cnt != 2) { System.out.println(cnt); } else { double s1, s2, s; System.out.print("2 "); Points p1 = list.get(0), p2 = list.get(1); Points m; if (lac.IsCollinear(p1) && lab.IsCollinear(p2) || lac.IsCollinear(p2) && lab.IsCollinear(p1)) m = a; else if (lac.IsCollinear(p1) && lbc.IsCollinear(p2) || lac.IsCollinear(p2) && lbc.IsCollinear(p1)) m = c; else m = b; Triangle triangle1 = new Triangle(m, list.get(0), list.get(1)); s1 = triangle1.getArea(); s1 = Check.sswr(s1, 3); s = this.getArea(); s = Check.sswr(s, 3); s2 = s - s1; s2 = Check.sswr(s2, 3); System.out.println(Math.min(s1, s2) + " " + Math.max(s1, s2)); } } } class Line { private Points m; private Points n; private double k; private double b; private double A; private double B2; private double C; private double length; public Line() { } public Line(Points m, Points n) { this.m = m; this.n = n; SetLine(); } public void setLength() { length = m.PointsDistance(n.getX(), n.getY()); } public double getA() { return A; } public void setA(double a) { A = a; } public double getB2() { return B2; } public void setB2(double b2) { B2 = b2; } public double getC() { return C; } public void setC(double c) { C = c; } public double getB() { return b; } public void setB(double b) { this.b = b; } public double getK() { return k; } public void setK(double k) { this.k = k; } public Points getN() { return n; } public void setN(Points n) { this.n = n; // System.out.println("n :"+this.n.getX()+" "+this.n.getY()); } public Points getM() { return m; } public void setM(Points m) { this.m = m; // System.out.println("m :"+this.m.getX()+" "+this.m.getY()); } public double getLength() { return length; } public boolean CheckLine() { if (m.getX() == n.getX() && m.getY() == n.getY()) { System.out.println("points coincide"); return false; } return true; } public double slope() { if (m.getX() == n.getX()) return POSITIVE_INFINITY; else return (m.getY() - n.getY()) / (m.getX() - n.getX()); } public void SetLine() { setK(Check.sswr(slope(), 6)); setB(Check.sswr(m.getY() - m.getX() * getK(), 6)); setA(m.getY() - n.getY()); setB2(n.getX() - m.getX()); setC(m.getX() * n.getY() - n.getX() * m.getY()); setLength(); } public double distance(Points a) { return Math.abs(getA() * a.getX() + getB2() * a.getY() + getC()) / Math.sqrt(getA() * getA() + getB2() * getB2()); } public Points CrossoverPoint(Line l) { Points CroPoint = new Points(); if (!IsParallel(l)) { double x1 = (getB2() * l.getC() - l.getB2() * getC()) / (getA() * l.getB2() - l.getA() * getB2()); double y1 = (l.getA() * getC() - getA() * l.getC()) / (getA() * l.getB2() - l.getA() * getB2()); //System.out.println( "crp "+CroPoint.getX()+","+CroPoint.getY() ); CroPoint.setX(x1); CroPoint.setY(y1); return CroPoint; } // else return null; } public boolean IsCoincide(Line l) {//判断两直线是否重合 if (slope() == l.slope() && IsCollinear(l.getM()) && IsCollinear(l.getN())) return true; return false; } public boolean IsPerpendicular(Line l) {//判断直线是否垂直 if (slope() == POSITIVE_INFINITY && l.slope() == 0 || slope() == 0 && l.slope() == POSITIVE_INFINITY)//斜率不存在的情况 return true; if (slope() * l.slope() == -1)//斜率相乘等于-1垂直 return true; return false; } public boolean IsReallyCrossover(Line l) {//判断两线段是否相交 Points m = CrossoverPoint(l); // System.out.println( (m!=null&&l.IsReallyCollinearInclude(m))); if (m != null && l.IsReallyCollinearInclude(m) && IsReallyCollinearInclude(m)) return true; return false; } public Points IsReallyCrossoverReturnPoint(Line l) {//判断两线段是否相交 Points m = CrossoverPoint(l); // System.out.println( (m!=null&&l.IsReallyCollinearInclude(m))); if (m != null && l.IsReallyCollinearInclude(m) && IsReallyCollinearInclude(m)) return m; return null; } public boolean IsCollinear(Points a) {//判断点是否在直线上 if (m.getX() == n.getX()) { if (m.getX() == a.getX()) return true; else return false; } if (Math.abs(getA() * a.getX() + getB2() * a.getY() + getC()) < 0.01) return true; return false; } public boolean IsReallyCollinear(Points a) { if(m.getX() == n.getX() && m.getX() == a.getX() ){ if(a.getY() > Math.min(m.getY(),n.getY() ) && a.getY() < Math.max(m.getY(),n.getY())) return true; else return false; } else if(m.getY() == n.getY() && m.getY() == a.getY() ){ if(a.getX() > Math.min(m.getX(),n.getX() ) && a.getX() < Math.max(m.getX(),n.getX())) return true; else return false; } else if (a.getX() > Math.min(m.getX(), n.getX()) && a.getX() < Math.max(m.getX(), n.getX()) && a.getY() > Math.min(m.getY(), n.getY()) && a.getY() < Math.max(m.getY(), n.getY())) return true; else return false; } /* public boolean IsReallyCollinearInclude(Points a) { if (!IsCollinear(a)) return false; if (a.getX() >= Math.min(m.getX(), n.getX()) && a.getX() <= Math.max(m.getX(), n.getX()) && a.getY() >= Math.min(m.getY(), n.getY()) && a.getY() <= Math.max(m.getY(), n.getY())) return true; else return false; }*/ public boolean IsReallyCollinearInclude(Points a){ if(!IsCollinear(a)) return false; if(getM().CheckPoints(a) || getN().CheckPoints(a)) return true; if( ( a.getX()-getM().getX() ) * (a.getX() - getN().getX()) < 0 || ( a.getY()-getM().getY() ) * (a.getY() - getN().getY()) <0 ) return true; return false; } public boolean IsParallel(Line l) { if (this.slope() == l.slope()) { return true; } else return false; } public int whichSide(Points p) {//判断点在直线哪一侧，返回0在直线上，小于0右侧，大于0左侧 if (getA() * p.getX() + getB2() * p.getY() + getC() == 0) return 0; else if (getA() * p.getX() + getB2() * p.getY() + getC() < 0) return -1; else return 1; } } class Points { private double x; private double y; public Points() { } public Points(double x, double y) { this.x = x; this.y = y; } public Points(Points a) { this.x = a.getX(); this.y = a.getY(); } public double getX() { return this.x; } public void setX(double x) { this.x = x; } public double getY() { return this.y; } public void setY(double y) { this.y = y; } public boolean CheckPoints(Points p) { if (Math.abs(getX() - p.getX()) < 0.001 && Math.abs(getY() - p.getY()) < 0.001) { //System.out.println("points coincide"); return true; } else return false; } public double PointsDistance(double x, double y) { return Math.sqrt(Math.pow((x - this.x), 2) + Math.pow((y - this.y), 2)); } }
这里对期中考试的三道期中考试题目分析：
但是好在最后成功写了本次就是对之前所学知识的一个阶段性测验，重构造一个类，到新增父类来继承再到多态的一个使用。对方法的重构，最后一题考试中没有写出来，后经同学指导代码如下
import java.util.ArrayList; import java.util.Scanner; public class Main { public static void main(String[] args) { Scanner in = new Scanner(System.in); GeometryObject geometryObject = new GeometryObject(); int choice = in.nextInt(); while(choice != 0) { switch(choice) { case 1://insert Point object into list double x = in.nextDouble(); double y = in.nextDouble(); geometryObject.add(new Point(x, y)); break; case 2://insert Line object into list double x1 = in.nextDouble(); double y1 = in.nextDouble(); double x2 = in.nextDouble(); double y2 = in.nextDouble(); String color = in.next(); geometryObject.add(new Line(new Point(x1, y1),new Point(x2, y2), color)); break; case 3://insert Plane object into list String color1 = in.next(); geometryObject.add(new Plane(color1)); break; case 4://delete index - 1 object from list int index = in.nextInt(); geometryObject.remove(index); break; } choice = in.nextInt(); } for( Element element : geometryObject.getList() ) { element.display(); } } public static String xiaoshu_2(double a) { String result = String.format("%.2f",a); return result; } } class Point extends Element { double x,y; public Point() { // TODO 自动生成的构造函数存根 } public Point(double x,double y) { if(x<0 || x>=200) { System.out.println("Wrong Format"); System.exit(0); } if(y<0 || y>=200) { System.out.println("Wrong Format"); System.exit(0); } this.x = x; this.y = y; } double getX() { return x; } void setX(double x) { this.x = x; } double getY() { return y; } void setY(double y) { this.y = y; } @Override public void display() { System.out.println("(" + Main.xiaoshu_2(x) + "," + Main.xiaoshu_2(y) + ")"); } } class Line extends Element { Point point1,point2; String color; public Line() { // TODO 自动生成的构造函数存根 } public Line(Point point1,Point point2,String color) { this.point1 = point1; this.point2 = point2; this.color = color; } public Point getPoint1() { return point1; } public void setPoint1(Point point1) { this.point1 = point1; } public Point getPoint2() { return point2; } public void setPoint2(Point point2) { this.point2 = point2; } public String getColor() { return color; } public void setColor(String color) { this.color = color; } public double getDistance() { return Math.sqrt((point2.x-point1.x)*(point2.x-point1.x)+(point2.y-point1.y)*(point2.y-point1.y)); } @Override public void display() { System.out.println("The line's color is:"+color); System.out.println("The line's begin point's Coordinate is:"); point1.display(); System.out.println("The line's end point's Coordinate is:"); point2.display(); System.out.println("The line's length is:"+Main.xiaoshu_2(getDistance()) ); } } abstract class Element { public abstract void display(); } class Plane extends Element { private String color; public Plane() { // TODO 自动生成的构造函数存根 } public Plane(String color) { this.color = color; } public String getColor() { return color; } public void setColor(String color) { this.color = color; } @Override public void display() { System.out.println("The Plane's color is:"+color); } } class GeometryObject { ArrayList<Element> elements = new ArrayList<>(); public void add(Element e) { elements.add(e); } public void remove(int index) { if(index - 1 < 0 || index - 1 >= elements.size()) { } else elements.remove(index - 1); } public ArrayList<Element> getList() { return elements; } }
采坑心得:
由于四边形和五边形类似三角形，有了前面的经验，坑不算多，只要分析清楚了其实就是照着思路走罢了。主要可能踩的坑有可能一下几个：求四边形面积没考虑凹四边形的特殊性，处理直线与多边形关系的case中没去除冗余点，求面积时点的顺序不对，五边形连接问题考虑不全面等，这几个点容易出错，别的点应该不容易出错。
总结
通过这几次作业，我对java有了进一步的了解，也体会到了在大工程下，面向对象的优势，同时通过对java进一步深入的学习，了解了继承与多态后更体会到了java的灵活与便利，如果再写类似的作业时一点可以写得更完善更清晰。
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