---
tags: leetcode
---

# [593. Valid Square](https://leetcode.com/problems/valid-square/)
---
# My Solution
## The Key Idea for Solving This Coding Question
## C++ Code

class Solution {
public:
    bool validSquare(vector<int> &p1, vector<int> &p2, vector<int> &p3, vector<int> &p4) {
        vector<vector<int>> points = {p1, p2, p3, p4};

        return permutation(points, 0);
    }

private:
    bool permutation(vector<vector<int>> &points, int head) {
        if (head == 4) {
            return isSquare(points);
        }

        for (int i = head; i < 4; ++i) {
            swap(points[head], points[i]);
            if (permutation(points, i + 1)) {
                return true;
            }
            swap(points[head], points[i]);
        }
        return false;
    }

    bool isSquare(vector<vector<int>> &points) {
        int len1 = getLen(points[0][0], points[0][1], points[1][0], points[1][1]);
        if (len1 == 0) {
            return false;
        }

        int len2 = getLen(points[1][0], points[1][1], points[2][0], points[2][1]);
        if (len2 == 0) {
            return false;
        }

        int len3 = getLen(points[2][0], points[2][1], points[3][0], points[3][1]);
        if (len3 == 0) {
            return false;
        }

        int len4 = getLen(points[3][0], points[3][1], points[0][0], points[0][1]);
        if (len4 == 0) {
            return false;
        }

        int diagLen1 = getLen(points[0][0], points[0][1], points[2][0], points[2][1]);
        if (diagLen1 == 0) {
            return false;
        }

        int diagLen2 = getLen(points[1][0], points[1][1], points[3][0], points[3][1]);
        if (diagLen1 == 0) {
            return false;
        }

        return len1 == len2 && len2 == len3 && len3 == len4 && diagLen1 == diagLen2;
    }

    int getLen(int x1, int y1, int x2, int y2) {
        return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
    }
};

## Time Complexity
## Space Complexity
# Miscellane
<!--
# Test Cases

[0,0]
[1,1]
[1,0]
[0,1]

[0,0]
[1,1]
[1,0]
[0,12]

[1,0]
[-1,0]
[0,1]
[0,-1]

[0,0]
[0,0]
[0,0]
[0,0]

[6987,-473]
[6985,-473]
[6986,-472]
[6986,-474]

-->