hihoCoder 1040 矩阵判断 最详细的解题报告

题目来源：矩阵判断

解题思路：

1、判断矩阵的4个点是否相连，一共输入8个点，只要判断是否4个点是否都经过2遍；

2、判断矩阵中任意一条边与其他边之间要么平行，要么垂直。设A（x1，y1），B（x2，y2），C（x3，y3），D（x4，y4），则线段AB的向量为A’（x2-x1，y2-y1），线段CD的向量C'（x4-x3，y4-y3），另x2-x1=a1，y2-y1=a2，x4-x3=c1，y4-y3=c2，判断A’是否平行C'的方法是a1*c2-a2*c1=0；判断A’是否垂直C'的方法是a1*c1+a2*c2=0.

具体算法（java版，可以直接AC）

 import java.util.ArrayList;
 import java.util.List;
 import java.util.Scanner;

 public class Main {

     public static boolean isCycled(List<Line> list) {
         List<Point> temp = new ArrayList<Point>();
         for (Line line : list) {
             if (line.getDistance() == 0)// 保证面积大于0
                 return false;
             if (temp.contains(line.start)) {
                 temp.remove(line.start);
             } else {
                 temp.add(line.start);
             }
             if (temp.contains(line.end)) {
                 temp.remove(line.end);
             } else {
                 temp.add(line.end);
             }
         }
         return temp.size() == 0;
     }

     public static void main(String[] args) {
         Scanner scanner = new Scanner(System.in);
         int n = scanner.nextInt();
         List<Line> list = new ArrayList<Line>();
         for (int i = 0; i < n; i++) {
             list.clear();
             for (int j = 0; j < 4; j++) {
                 list.add(new Line(scanner.nextInt(), scanner.nextInt(), scanner
                         .nextInt(), scanner.nextInt()));
             }
             boolean ans = true;
             if (isCycled(list)) {
                 for (int j = 0; j < 4; j++) {
                     for (int k = j + 1; k < 4; k++) {
                         if (!list.get(j).isVerticalOrParallel(list.get(k))) {
                             ans = false;
                             break;
                         }
                     }
                     if (!ans)
                         break;
                 }
             } else {
                 ans = false;
             }
             if (ans) {
                 System.out.println("YES");
             } else {
                 System.out.println("NO");
             }
         }
     }

 }

 class Point {
     public int x;
     public int y;

     public Point(int x, int y) {
         this.x = x;
         this.y = y;
     }

     public boolean equals(Object o) {
         if (this == o)
             return true;
         if (o instanceof Point) {
             Point p = (Point) o;
             return this.x == p.x && this.y == p.y;
         }
         return false;
     }

     public int hashCode() {
         return this.x * 10 + this.y;
     }
 }

 class Line {
     public Point start;
     public Point end;

     public Line(int x1, int y1, int x2, int y2) {
         this.start = new Point(x1, y1);
         this.end = new Point(x2, y2);
     }

     private Point getVector() {
         return new Point(this.end.x - this.start.x, this.end.y - this.start.y);
     }

     private boolean isVertical(Line line) {
         Point p1 = this.getVector();
         Point p2 = line.getVector();
         return p1.x * p2.x + p1.y * p2.y == 0;
     }

     private boolean isParallel(Line line) {
         Point p1 = this.getVector();
         Point p2 = line.getVector();
         return p1.x * p2.y - p1.y * p2.x == 0;
     }

     public int getDistance() {
         return (int) ((this.start.x - this.end.x) * (this.start.x - this.end.x) + (this.start.y - this.end.y)
                 * (this.start.y - this.end.y));
     }

     public boolean isVerticalOrParallel(Line line) {
         return this.isParallel(line) || this.isVertical(line);
     }
 }