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);
    }
}