2013
11-10

# Squares

A square is a 4-sided polygon whose sides have equal length and adjacent sides form 90-degree angles. It is also a polygon such that rotating about its centre by 90 degrees gives the same polygon. It is not the only polygon with the latter property, however, as a regular octagon also has this property.

So we all know what a square looks like, but can we find all possible squares that can be formed from a set of stars in a night sky? To make the problem easier, we will assume that the night sky is a 2-dimensional plane, and each star is specified by its x and y coordinates.

The input consists of a number of test cases. Each test case starts with the integer n (1 <= n <= 1000) indicating the number of points to follow. Each of the next n lines specify the x and y coordinates (two integers) of each point. You may assume that the points are distinct and the magnitudes of the coordinates are less than 20000. The input is terminated when n = 0.

For each test case, print on a line the number of squares one can form from the given stars.

4
1 0
0 1
1 1
0 0
9
0 0
1 0
2 0
0 2
1 2
2 2
0 1
1 1
2 1
4
-2 5
3 7
0 0
5 2
0


1
6
1


//* @author:
import java.util.Scanner;
import java.util.HashSet;

public class Main{
private int n;
private Point p[];
private HashSet< Point> pset=new HashSet< Point>();
private int sum;
public Main(int n,Point p[]){
this.n=n;
this.p=p;
for(int i=0;i< p.length;i++)
}

public int getSum(){
return sum;
}

public void doIt(){

int bound;
int a1, a2, b1, b2, ab1, ab2, x1, y1, x2, y2, x3, y3, x4, y4;
for (int i = 0; i < n; i++){
for (int j = i + 1; j < n; j++) {
a1 = p[i].getX();
a2 = p[i].getY();
b1 = p[j].getX();
b2 = p[j].getY();
ab1 = a1 - b1;
ab2 = a2 - b2;
x1 = a1 + ab2;
y1 = a2 - ab1;
x2 = b1 + ab2;
y2 = b2 - ab1;

if (pset.contains(new Point(x1, y1)) && pset.contains(new Point(x2, y2))) sum++;
x3 = a1 - ab2;
y3 = a2 + ab1;
x4 = b1 - ab2;
y4 = b2 + ab1;

if (pset.contains(new Point(x3, y3)) && pset.contains(new Point(x4, y4))) sum++;
}
}

}

public static void main(String args[]){
Scanner in=new Scanner(System.in);
int x=0;
int y=0;

while(true){
int  n=in.nextInt();
if(n==0) break;
Point p[]=new Point[n];
for(int i=0;i< n;i++){
x=in.nextInt();

y=in.nextInt();

p[i]=new Point(x,y);
//System.out.println(p[i]);

}

Main m=new Main(n,p);
m.doIt();
System.out.println(m.getSum()/4);

}
}

}

class Point
{
private int x;
private int y;

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

public void setX(int x){
this.x=x;
}

public void setY(int y){
this.y=y;
}
public int getX(){
return this.x;
}

public int getY(){
return this.y;
}

public boolean equals(Object o)
{
if (this == o)
{
return true;
}

if (o.getClass() == Point.class)
{
Point p = (Point)o;
return (p.x==x) && (p.y==y);
}
return false;
}

public int hashCode() {
long bits = getX();
bits ^= getY() * 31;
return (((int) bits) ^ ((int) (bits >> 32)));
}

public String toString()
{
return "Point[" +x+"," +y+ "]";
}
}