593. Valid Square --M

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:

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

A:

根据4个边相等。对角线是  sqrt(2)的关系。

class Solution {
public:
    bool validSquare(vector<int>& p1, vector<int>& p2, vector<int>& p3, vector<int>& p4) {
        if(p1[0] == p2[0] and p2[0] == p3[0]) // if they are same
            return false;
        vector<int> V;
        V.push_back(getLen2(p1,p2));
        V.push_back(getLen2(p1,p3));
        V.push_back(getLen2(p1,p4));
        V.push_back(getLen2(p2,p3));
        V.push_back(getLen2(p2,p4));
        V.push_back(getLen2(p3,p4));
        sort(V.begin(), V.end());
        bool first4Equal = V[0] == V[1] and V[1] == V[2] and V[2] == V[3];
        bool last2Equal = V[4] == V[5];
        bool time2 = V[0]  * 2 == V[5];
        return first4Equal && last2Equal && time2;
    }
private:
    int getLen2(vector<int> & p1, vector<int> & p2)
    {
        int a = p1[0] - p2[0];
        int b = p1[1] - p2[1];
        return a*a + b * b;
    }
};