593. Valid Square

2026, Sep 03 2 mins read

1. Description

Given the coordinates of four points in 2D space p1, p2, p3 and p4, return true if the four points construct a square.
The coordinate of a point pi is represented as [x$_i$, y$_i$]. The input is not given in any order.
A valid square has four equal sides with positive length and four equal angles (90-degree angles).

2. Example

Example 1

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

Example 2

Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,12]
Output: false

Example 3

Input: p1 = [1,0], p2 = [-1,0], p3 = [0,1], p4 = [0,-1]
Output: true

3. Constraints

p1.length == p2.length == p3.length == p4.length == 2
-10$^4$ <= xi, yi <= 10$^4$

4. Solutions

Math

Time complexity: O(1)
Space complexity: O(1)

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class Solution {
public:
    bool validSquare(
        const vector<int> &p1,
        const vector<int> &p2,
        const vector<int> &p3,
        const vector<int> &p4) {
        vector<int> distances{
            distance(p1, p2),
            distance(p1, p3),
            distance(p1, p4),
            distance(p2, p3),
            distance(p2, p4),
            distance(p3, p4)};
        sort(distances.begin(), distances.end());
        return distances[0] != 0 && distances[0] == distances[1] && distances[0] == distances[2] &&
            distances[0] == distances[3] && distances[4] == distances[5] &&
            distances[4] > distances[0];
    }

private:
    int distance(const vector<int> &p1, const vector<int> &p2) {
        int dx = p1[0] - p2[0];
        int dy = p1[1] - p2[1];
        return dx * dx + dy * dy;
    }
};

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