# 593.Valid-Square

## 593. Valid Square

## 题目地址

<https://leetcode.com/problems/valid-square/>

## 题目描述

```
Given the coordinates of four points in 2D space, return whether the four points could construct a square.

The coordinate (x,y) of a point is represented by an integer array with two integers.

Example:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
Output: True

Note:
All the input integers are in the range [-10000, 10000].
A valid square has four equal sides with positive length and four equal angles (90-degree angles).
Input points have no order.
```

## 代码

### Approach #1 Brute Force

Time: O(1) && Space: O(1)

```java
class Solution {
  public boolean validSquare(int[] p1, int[] p2, int[] p3, int[] p4) {
        int[][] p = {p1, p2, p3, p4};
    return checkAllPermutations(p, 0);
  }

  boolean checkAllPermutations(int[][] p, int l) {
    if (l == 4) {
      return check(p[0], p[1], p[2], p[3]);
    } else {
      boolean res = false;
      for (int i = l; i < 4; i++) {
        swap(p, l, i);
        res |= checkAllPermutations(p, l + 1);
        swap(p, l, i);
      }
      return res;
    }
  }

  private double dist(int[] p1, int[] p2) {
    return (p2[1] - p1[1]) * (p2[1] - p1[1]) + (p2[0] - p1[0]) * (p2[0] - p1[0]);
  }

  private boolean check(int[] p1, int[] p2, int[] p3, int[] p4) {
    return dist(p1, p2) > 0 
      && dist(p1, p2) == dist(p2, p3) 
      && dist(p2, p3) == dist(p3, p4)
      && dist(p3, p4) == dist(p4, p1)
      && dist(p1, p3) == dist(p2, p4);
  }

  private void swap(int[][] p, int x, int y) {
    int[] temp = p[x];
    p[x] = p[y];
    p[y] = temp;
  }
}
```

### Approach #2 Using Sorting

```java
public class Solution {
  public double dist(int[] p1, int[] p2) {
    return (p2[1] - p1[1]) * (p2[1] - p1[1]) + (p2[0] - p1[0]) * (p2[0] - p1[0]);
  }
  public boolean validSquare(int[] p1, int[] p2, int[] p3, int[] p4) {
    int[][] p = {p1,p2,p3,p4};
    Arrays.sort(p, (l1, l2) -> l1[0] == l2[0] ? l1[1] - l2[1] : l1[0] - l2[0]);

    return dist(p[0], p[1]) != 0 
      && dist(p[0], p[1]) == dist(p[1], p[3]) 
      && dist(p[1], p[3]) == dist(p[3], p[2]) 
      && dist(p[3], p[2]) == dist(p[2], p[0])   
      && dist(p[0], p[3]) == dist(p[1],p[2]);
  }
}
```


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