输入N个互不相同的二维整数坐标, 求这N个坐标可以构成的正方形数量。(内积为零的两个向量垂直)
第一行输入为 N，N 代表坐标数量，N为正整数。N <= 100
之后的 K 行输入为坐标 x y以空格分隔，x, y 为整数, -10 <= x, y <= 10
输出可以构成的正方形数量
3
1 3
2 4
3 1
0
3 个点不足以构成正方形
4
0 0
1 2
3 1
2 -1
1
此4点可构成正方形
import java.util.*;
/**
* Created with IntelliJ IDEA.
* Author: Amos
* E-mail: amos@amoscloud.com
* Date: 2022/6/2
* Time: 14:57
* Description:
*/
public class Main0096 {
public static void main(String[] args) {
try (Scanner scanner = new Scanner(System.in)) {
int n = scanner.nextInt();
List<int[]> list = new ArrayList<>();
for (int i = 0; i < n; i++) {
int[] ints = new int[2];
ints[0] = scanner.nextInt();
ints[1] = scanner.nextInt();
list.add(ints);
}
int count = 0;
int len = list.size();
if (len > 3) {
for (int i = 0; i < len - 3; i++) {
for (int j = i + 1; j < len - 2; j++) {
for (int k = j + 1; k < len - 1; k++) {
for (int l = k + 1; l < len; l++) {
if (isSquare(list.get(i), list.get(j), list.get(k), list.get(l))) {
count++;
}
}
}
}
}
}
System.out.print(count);
}
}
public static boolean isSquare(int[] a, int[] b, int[] c, int[] d) {
List<int[]> list = Arrays.asList(a, b, c, d);
Map<Integer, Integer> map = new HashMap<>();
int temp = 0;
for (int i = 0; i < 3; i++) {
for (int j = i + 1; j < 4; j++) {
int x = list.get(i)[0] - list.get(j)[0];
int y = list.get(i)[1] - list.get(j)[1];
int len = x * x + y * y; //求四个坐标六个向量的长度
temp = len;
map.put(len, map.getOrDefault(len, 0) + 1);
}
}
//六条向量有四条相等且另外两条也相等则构成正方形
return map.size() == 2 && (map.get(temp) == 2 || map.get(temp) == 4);
}
}