正方形
Time Limit: 1000 ms Memory Limit: 65536 KiB
Problem Description
给出四个点,判断这四个点能否构成一个正方形。
Input
输入的第一行包含一个整数T(T≤30)表示数据组数,每组数据只有一行,包括8个整数x1, y1, x2, y2,x3,y3,x4,y4(数据均在-1000,1000 之间)以逆时针顺序给出四个点的坐标。
Output
每组数据输出一行,如果是正方形,则输出: YES, 否则,输出:NO。
Sample Input
2
0 0 1 0 1 1 0 1
-1 0 0 -2 1 0 2 0
Sample Output
YES
NO
Hint
构建一个与点有关的类,由一些定理我们可以知道,有一个角是直角的菱形就是正方形,所以就可以将问题完全转化为求两点之间距离的问题
package hello; import java.util.*; class Point{ int x, y; public Point (int x, int y) { this.x = x; this.y = y; } public double dist(Point p) { return (p.x-x)*(p.x-x) + (p.y-y)*(p.y-y); } } public class Main { public static void main(String[] args) { Scanner cin = new Scanner(System.in); int t; int x1, y1, x2, y2, x3, y3, x4, y4; double d1, d2, d3, d4; t = cin.nextInt(); while(t-- != 0) { x1 = cin.nextInt(); y1 = cin.nextInt(); x2 = cin.nextInt(); y2 = cin.nextInt(); x3 = cin.nextInt(); y3 = cin.nextInt(); x4 = cin.nextInt(); y4 = cin.nextInt(); Point p = new Point(x1, y1); d1 = p.dist(new Point(x2, y2)); p = new Point(x2, y2); d2 = p.dist(new Point(x3, y3)); p = new Point(x3, y3); d3 = p.dist(new Point(x4, y4)); p = new Point(x1, y1); d4 = p.dist(new Point(x4, y4)); double d = p.dist(new Point(x3, y3)); //System.out.println(d1+" "+d2+" "+d3+" "+d4+" "+d); if(d1==d2 && d2==d3 && d3==d4 &&d4 == d1 &&d1+d2==d) { System.out.println("YES"); } else { System.out.println("NO"); } } cin.close(); } }